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STRESSES EXPERIENCED BY NOVICE TEACHERS
ATTEMPTING TO TEACH IN THE SPIRIT
OF THE NCTM STANDARDS

presented by

GARY M. LEWIS

has been accepted towards fulfillment
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6/07 p1/CIRC/DaIeDueindd-p.1

 

STRESSES EXPERIENCED BY NOVICE TEACHERS
ATTEMPTING TO TEACH IN THE SPIRIT OF THE NCTM STANDARDS

By

Gary M. Lewis

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Teacher Education

2007

ABSTRACT

STRESSES EXPERIENCED BY NOVICE TEACHERS
ATTEMPTING TO TEACH IN THE SPIRIT OF THE NCTM STANDARDS

By
Gary M. Lewis

In this study, I examine the experiences of six novice secondary mathematics
teachers who I observed attempting to implement aspects of the NCTM (1991)
Professional Standards for Teaching Mathematics. The study found that attempting such
teaching added only modestly and in complex ways to these novices’ teaching stresses,
except when they were attempting to manage classroom discourse that focused on
utilizing student thinking, conjectures, and mathematical verification in central ways with
the teacher acting in a facilitative role. Novices found orchestrating such discourse
demanding. Given the many directions such conversations could take, novices found that,
at times, those discussions pushed on their mathematical and pedagogical content
knowledge to evaluate student ideas, respond to their questions, and choose between the
many directions that such student-centered conversations ofien suggested. I also found
several new types of stresses not previously reported in the teacher education research
literature, some of which were related to novices’ attempts to enact elements of the
NCTM (1991) Standards in their teaching.

These novices identified socially-oriented coping resources (i.e. social
relationships in the presence of or without a teacher learning community) as the most
effective in alleviating their teaching stresses, while looking to their own experiences and
resources was also important, particularly those without formally organized social

resources (such as teacher learning communities). These results suggested that novices

attempting ambitious teaching do so because they have commitments that lead them to
persevere in such teaching and are able to find resources to support them in those
attempts. Novices with access to teacher learning communities reported experiencing less

stress than those who built their own social networks.

ACKNOWLEDGEMENTS

I would like to thank my advisers, John P. (Jack) Smith III and Sandra Crespo for
their tireless efforts to help me find participants, collect and analyze this data, and to
write this dissertation. I thank Sandra, in particular, for her keen insights about how to
limit the amount of time spent in unproductive directions. I thank Jack for the many years
of advice and wisdom that he has shared with me in helping to bring this document into
existence.

I also thank the members of the Mathematics Learning and Research Group
(MLRG) at Michigan State University (MSU) for their ongoing help and support while I
was working on this dissertation and the pilot study that led up to it.

Many of the faculty of the Department of Teacher Education deserves my thanks,
as well, for their help in preparing the framework for this study and locating prospective
participants, including (but not limited to) Mary Kennedy, BetsAnn Smith, Peter Youngs,
and Kelly Hodges.

Perhaps most importantly, I thank my family who has made this effort meaningful
and worthwhile. I thank my wife, Renee, for her help and support during the many years
of graduate school that it took to prepare for and to complete this dissertation. I am
gratefiil for her hours of listening to me read meaningless text to her as she acted as a
sounding board, so that we could make sense of it all. I am grateful for her unseen
influence in raising our children and supporting me in my work. Without her help and

support, I would never have been able to finish this dissertation or complete my degree. I

iv

also thank my two children, Alexis and Joshua, for their sacrifices of my time and their
patience and understanding while I have been completing this dissertation and degree.
Finally, I thank the six teachers who participated in this study and the other
prospective participants who allowed me to observe in their classrooms and were open to
the idea of participation. Without the help of the six novices who participated in
particular, I would never have learned what I did about the first few years of teaching and
the challenges that novices face. I admire them for their commitment to implementing
interesting and ambitious teaching. And I wish them all the best in their continued efforts

in and commitment to high quality secondary mathematics teaching.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................... ix
LIST OF FIGURES .................................................................................. xi
Chapter 1:

Introduction ............................................................................................ 1
Personal Experiences ........................................................................ 1
Concerns in the Field ...................................................................... 13
Issues and Questions ....................................................................... 18

Chapter 2:

Review of the Related Literature .................................................................. 21
General and Teacher Stress Literature ................................................... 22
Teacher Burnout ............................................................................ 24
Teacher Stress, More Specifically ....................................................... 24
The Stresses of Learning to Teach ....................................................... 25
Teaching Consonant with the NCTM Standards and Related Stresses ............. 26

Chazan (2000): Teaching lower-track high school students ................. 28
Romagnano (1994): Disengaged middle school students .................... 31
Heaton (2000): Figuring out what a pattern is ................................. 33
Stresses of Learning to Teach While Attempting to Implement the NCTM
Standards .................................................................................... 35
Alice in Van Zoest & Bohl (2000; 2002): Talking past her mentor
teacher ........................................................................................................ 35
Ms. Curry in Romagnano (1994): Innovative teaching outside one’s
subj ect-matter expertise .......................................................... 37
Ms. Daniels in Borko et al. (1992): Missing deep conceptual
understanding ...................................................................... 38
Allison in Wilcox et al. (1991): Learning community interrupted ......... 41
Schweitzer (1996): Frustrations of implementing a new pedagogy ........ 42
Coping Resources .......................................................................... 44

Chapter 3:

Methods ............................................................................................... 49
Review of Pilot Study ..................................................................... 49
Limits of Existing Literature .............................................................. 51
Definition of Teacher Stress .............................................................. 52
Definition of Coping Resources ............................................................ 53
Research Questions ........................................................................ 55
Overview of Method: Main Steps ........................................................ 56
Locating and Soliciting Participants ..................................................... 57
Screening of Prospective Participants ................................................... 58

vi

Actual Sample—Description ............................................................... 62

Data Collection ............................................................................. 63
Screening observations ........................................................... 63
Pre-observation interview ........................................................ 63
Classroom observations .......................................................... 64
Teaching log ........................................................................... 66
Art1facts66
Selecting video clips .............................................................. 67
Post-observation 1nterv1ew71

Data Analysis ............................................................................... 73
Coding analysis: Research question 1 .......................................... 73
Coding analysis: Research question 2a ......................................... 86
Coding analysis: Research question 2b ......................................... 87
Coding analysis: Research question 3 .......................................... 90
Coding analysis: Research question 4 .......................................... 91

Chapter 4:
Introduction to Participants and Their Attempts at NCTM Standards-Based Teaching.105

Introduction to Participants .............................................................. 106
Ms. Boone ........................................................................ 106
Ms. Grant ......................................................................... 107
Mr. Jones .......................................................................... 109
Ms. Price .......................................................................... l 10
Ms. Riley .......................................................................... 1 1 1
Ms. Wells ......................................................................... 113

Preamble: The Search for Standards-Based Teaching ............................... 114

Examples of Standards-Based Teaching from Participant Observations ......... 115
Ms. Boone: Taking a student’s conjecture seriously ....................... 115
Ms. Grant: Exploring effects of changing parameters on graphs of
quadratic functions ............................................................... 1 16
Mr. Jones: Exploring prospective congruence conditions for triangles...117
Ms. Price: Motivating the formula for the area of a circle .................. 118
Ms. Riley: Using difficult problems to help understand the quadratic
formula ............................................................................ 120
Ms. Wells: Formulating conjectures about the properties of midsegments
of a triangle ....................................................................... 121

Summary ................................................................................... 122

Chapter 5:
Stress Analysis .......................................................................................... 123

Overview of Stresses for Each Teacher ................................................ 124
Ms. Boone: Reported stresses .................................................. 125
Ms. Grant: Reported stresses ................................................... 128
Mr. Jones: Reported stresses ................................................... 131
Ms. Price: Reported stresses ................................................... 135
Ms. Riley: Reported stresses ................................................... 136

vii

Ms. Wells: Reported stresses ................................................... 140

Salient Stresses Overall .................................................................. 143
Stresses Named in the Literature and New ............................................ 148
Stresses Related to SBT and Otherwise ................................................ 152
F acilitative vs. Debilitative Stresses ................................................... 160
Summary ................................................................................... 164

Chapter 6:

Coping Resources ...................................................................................... 165
Coping Resource Framework: Categories of Resources and Examples ........... 165
Results: Group Analysis ................................................................. 167

Most frequently reported coping resources ................................... 168
Most effective, or “t0p,” coping resources ................................... 168
Coping resources overall ....................................................... 170
Coping Resources: Results by Participant ............................................. 178
Ms. Boone ........................................................................ 179
Ms. Grant ......................................................................... 184
Mr. Jones .......................................................................... l 88
Ms. Price .......................................................................... 193
Ms. Riley .......................................................................... 195
Ms. Wells ......................................................................... 198
Discussion ................................................................................. 201

Chapter 7:

Discussion and Conclusron3205
Top-Level Summary of Major Findings ............................................... 205
Contribution to the Research Literature ................................................ 212

Teacher stress literature ......................................................... 212
NCTM Standards-Based Teaching Literature ............................... 215
Coping Resources Literature ................................................... 218
Future Research Steps ........................................................... 221

Appendices .......................................................................................... 224
Appendix A ................................................................................ 225
Appendix B ................................................................................ 227
Appendix C ................................................................................ 238

References .......................................................................................... 239

viii

LIST OF TABLES

Table 1: Participant Demographic Data ........................................................... 62
Table 2: Three Potentially Stressful Events Novices Viewed during the Final

Interview ............................................................................................. 70
Table 3: Teacher Stress Coding Category Titles and Definitions ............................. 80
Table 4: Identifying Source of Stress-Coping Links .......................................... 100
Table 5: Ms. Boone’s Top, Main, and Mentioned Sources of Stress ....................... 126
Table 6: Ms. Grant’s Top, Main, and Mentioned Sources of Stress ........................ 129
Table 7: Mr. Jones’ Top, Main, and Mentioned Sources of Stress .......................... 132
Table 8: Ms. Price’s T0p, Main, and Mentioned Sources of Stress ......................... 135
Table 9: Ms. Riley’s Top, Main, and Mentioned Sources of Stress ........................ 137
Table 10: Ms. Wells’ Top, Main, and Mentioned Sources of Stress ........................ 141
Table 11: Stress Categories Sorted by Frequency as Main Stresses ........................ 145
Table 12: Teacher Stress Categories Reported in or New to the Literature ............... 149
Table 13: Top, Main, and Mentioned Stresses with SBT Links ............................. 153
Table 14: Teacher Stress Categories Listed by Proportion Related to SBT ............... 155
Table 15: Novices’ Facilitative and Debilitative Stresses .................................... 161
Table 16: Frequency of Report of Coping Resource Categories ............................ 168
Table 17: Coping Resource Category Frequency Listed by Connection to Teacher Stress
Category ............................................................................................. 170
Table 18: Main Stress Categories and Coping Resource Effectiveness Listed by
Participant Initial ................................................................................... 174
Table 19: Coping Resource Effectiveness for Ms. Boone’s Main Stresses ................ 180
Table 20: Coping Resource Effectiveness for Ms. Grant’s Main Stresses ................. 185

ix

Table 21: Coping Resource Effectiveness for Mr. Jones’ Main Stresses .................. 189

Table 22: Coping Resource Effectiveness for Ms. Price’s Main Stresses .................. 193
Table 23: Coping Resource Effectiveness for Ms. Riley’s Main Stresses ................. 196
Table 24: Coping Resource Effectiveness for Ms. Wells’ Main Stresses .................. 199

LIST OF FIGURES

Figure 1: List of the characteristics of NCTM Standards—based teaching .................. 27
Figure 2: Number of prospective participants who were chosen for or how they were

eliminated from the sample ........................................................................ 61
Figure 3: Timeline for including challenges novices experienced in the analysis ......... 76

Figure 4: Diagram showing how Ms. Price’s students rearranged cut sectors of a circle
(with arrows denoting movement) to create a “parallelogram” to determine the area... 1 19

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Chapter 1: Introduction

I begin by explaining how I became interested in the topic of my dissertation.
Broadly, the topic that I address in this study is how attempting adventurous and
innovative teaching of the type portrayed in the NCTM (1991) Professional Standards
for Teaching Mathematics adds to or changes the challenges that novice teachers already
experience and what types of supports might best help novices meet those new or
modified challenges.

I begin this section by discussing how my interns’ and my own experiences of
learning to teach while attempting to enact elements of the NCTM (1991) Standards have
motivated this study. I also look at how the mathematics education literature and current
educational policy issues led me to consider this topic for my dissertation. The literature
and issues to which I refer include novice teachers’ stresses in general and while enacting
elements of the NCTM Standards, the challenges involved in hiring a sufficient number
of teachers to meet employers’ demands during the current decade, and the difficulties
teacher educators encounter as they try to prepare, employ, and retain novices in the field

with dispositions and capabilities aligned with such adventurous teaching.

Personal Experiences

While considering a topic for my practicum and dissertation studies, I served as a
secondary mathematics field instructor. My interns talked with me about their challenges
and stresses during their internships, which at times related to their attempts at NCTM

(1991) Standards-based teaching and the contexts in which those attempts were made.

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For example, one intern, Ms. Apple (pseudonym), crafted, with the help of her
mentor teacher, many interesting lessons involving whole-class discussions and
mathematical argumentation and justification that used student data explorations and
observations as a springboard for those discussions. Near the end of her internship, she
complained that she couldn’t handle the stress of the “chaotic” environment in her mentor
teacher’s classroom. She had a very different classroom management style than her
mentor teacher did. And she said that she had consistently felt unable to change the
environment that he had set up, where students talked most of the time, even at times
while the teacher was talking without addressing the issue and without consequences.
While the environment made students comfortable and communicative during whole-
class discussions, it also made her feel very conflicted. It was hard to decide when
students were working, when they were momentarily off task, and when they had been
off task for too long and needed to get back to work. She said that she preferred a quieter
classroom, but that she enjoyed engaging in NCTM Standards-based teaching and, in my
opinion, did so quite successfully for an intern. After completing her internship, she
chose to work as a computer programmer, rather than to continue her teaching career. I
wondered if placing her with a teacher with a less flexible management style who still
enacted elements of the NCTM Standards would have kept her in the field.

I admit that this example may relate more strongly to Ms. Apple’s differences in
classroom management philosophy with her mentor than to her desire to implement
NCTM (1991) Standards-based teaching. But her belief that the environment was chaotic
and that it contributed to having an engaged, communicative group of students while

pursuing the discourse goals described by the NCTM Standards leads me to believe that

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she may have been somewhat conflicted as to how to implement NCTM Standards-based
teaching in the more structured teaching environment that she preferred in her classroom.

On the other hand, Mr. Banks (pseudonym) rarely attempted any teaching that
could reasonably be called NCTM (1991) Standards-based. During my last observation of
his internship teaching (after I had admittedly pressed him to attempt Standards-based
teaching to broaden his pedagogical repertoire), Mr. Banks’ questions elicited a great
number of student ideas and responses, but he struggled to interpret those student
responses or use them in meaningful ways in the discussion. At one point, when a student
idea was not in the exact format that he had expected, he said, “Well, I don’t know what
you’re talking about, but here’s how you do it.” He went on to show the students how to
work the problem. Mr. Banks looked surprised when I explained to him afier the
discussion that the student’s idea was correct, although not mathematically formalized.
Mr. Banks’ quick and immediate dismissal of a student idea seemed to suggest that he
may have been uncomfortable exploring an unclear (to him, at least) and potentially
fi'uitless student idea. In this case, Mr. Banks stress, if he experienced any, appeared more
due to the mismatch between his teaching beliefs and my own (as well as the teacher
education program I represented in my role as field instructor). It appears unlikely that he
would have attempted such a discussion-intensive lesson without my pointed promptings
to do so.

At times while supervising my interns, experiences like these led me to wonder
whether I expected too much as I encouraged them to acquire teaching skills aligned with
the NCTM (1991) Standards. The question seemed in some ways naive, because the

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of their teaching philosophy. While I pondered the stresses that attempting adventurous
teaching imposed and how those new stresses interacted with existing stresses, I also
knew that my interns expressed feeling a great deal of satisfaction and enjoyment from
implementing such teaching.

For example, one of Ms. Crafi’s most memorable lessons was when she set up a
4-hole miniature golf course in the school auditorium. She had her geometry students
predict, then experiment with, how hitting a golf ball at varying angles would correlate
with the angle at which it rebounded from the sidewall of the course. Then they applied
their theories to playing on the miniature golf course that she had built. The students
loved the activity, which included collecting their own data and making sense of the
results, formulating hypotheses and testing them against other groups’ data and
hypotheses, and applying their established theories in a realistic setting. Ms. Craft felt
that it was one of her best activities all year, both because of how engaged the students
were in the activity itself, as well as how engaged they were in the mathematical
discussions before, during, and after the activity. She said that her students had worked
harder and learned more on that unit than on any other all year. But it was also clear that
she had put a great deal of time and effort into that activity, which suggested to me that
that might have added to both her stress and her satisfaction in teaching.

While I was supervising teacher interns, I also worked as a graduate research
assistant on John P. (Jack) Smith’s Mathematical Transitions Project (e. g. Smith et al.,
2000). We researched the challenges that students experienced as they moved between
middle school, secondary, and college mathematics curricula that differed greatly in

terms of their underlying pedagogical models; in other words, we studied how students

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fared when moving back and forth between curricula more aligned with the NCTM
(1989; 1991; 2000) Standards and those that were more traditional in their implicit
pedagogy. The study mirrored my own questions in some ways, although I was also
interested in how teachers experienced such challenges, as well their students. I realized
that my own experiences as a student teacher and as a novice teacher involved several
examples of such transitions of my own but in the role of a teacher. So I digress to
describe those experiences and how they have played into my concerns for novice
secondary teachers who are attempting to enact a mathematical pedagogy very different
from the one they experienced as K-12 students.

During my mathematics teaching experiences as a graduate student in
mathematics and mathematics education during my three years at The Ohio State
University, I taught fairly traditionally, using a very traditional curriculum. My pedagogy
consisted mainly of lecturing and practice with a set of homework problems similar to the
few model problems presented during the class lecture.

While seeking a Master’s degree in Mathematics Education during my last year at
Ohio State, I was exposed to a variety of literature in mathematics education, including
constructivist models of mathematics education. In particular, the NCTM (1989; 1991)
Standards proposed a model that was at once radical but intriguing. My course instructors
ofien modeled the pedagogy that we might attempt in brief activities that gave me brief
glimpses of what such teaching might look like. Although I was always open to student
ideas and suggestions on how to make our classes more meaningful or useful, I had never
before considered a pedagogy that gave such an active role to students in creating the

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understood mathematics and the low grades that they consistently achieved, I felt like it
was a promising way to engage the many students that I had known who were so
disenchanted with mathematics, even if I myself did not fit into that group. So I began
attempting to use an innovative pedagogy in university mathematics courses such as
groupwork and student problem presentations, but there was little time in the curriculum
for many meaningful deviations from the prescribed course content. So my hands were
tied to some degree, even while I was learning about interesting pedagogical alternatives
that I longed to attempt to implement more fully and faithfully with the students in my
university mathematics courses.

For my internship, I was placed in a “regular” classroom in the same urban school
outside the technology-rich program, with a mentor teacher and a field instructor who
practiced the “sink or swim” approach to learning to teach. With few material,
technological, or human resources on which to rely, innovative teaching was incredibly
challenging. Although I experienced what I perceived to be a reasonable degree of
success and planned some lessons that turned out to be very enjoyable and engaging for
the students, I was impatient with the slow pace at which I was able to change the
school’s traditional curriculum materials and constantly put pressure on myself to create
more dynamic lesson plans, because my teaching was not up to my personal standards, as
I had acquired them from my university instructors and courses.

The materials were not even remotely engaging to the students in my lower
sections in particular, because they had all failed algebra one to three times and were now
retaking the course. They had seen this same textbook during each attempt, which made

their familiarity with it problematic. Often they believed that they already knew the

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content, because they had seen it before, even if they had not mastered it. And the lessons
were very boring, because there was nothing new in them unless I personally brought that
material into the lesson. I had them hand in their textbooks, because it was very
discouraging for the students to work with them. I created as many activities as I had time
for, borrowed worksheets from other teachers, and found activities and worksheets in
books or on the Internet that were not familiar to my students to dispel their boredom as
best I could.

The few activities that I was able to formulate were very engaging to the students
and, in my mind, appeared successful in helping them learn the mathematics that I
wanted. For example, I had my students make their own clinometers, measure distances
and angles of variation on objects outside the school, and then explore how the
measurements taken with the clinometers involved ratio-and-proportion. That activity
was very popular with the students and engaged them in mathematics discussions to a
degree that I had previously hoped, but not necessarily believed, possible. Since these
were non-college intending students who had failed algebra at least once (and in some
cases as many as three times), getting them to engage in mathematics again and to believe
that there was something interesting to learn seemed like a great feat, indeed. It also made
it more likely that they would pass the class, as relatively many of them did that semester.

In my first teaching position, I worked for two years with mathematically talented
secondary students in a small Midwestern city. We used the NSF -funded Core-Plus
Mathematics Project (CPMP) materials with these students, marketed under the title,
Contemporary mathematics in context (Coxford, Fey, Hirsch, & Schoen, 1996). I found

the mathematics in the curriculum to be interesting and often new to me, the implicit,

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Unfortunately, there were also distractions that lessened my enjoyment.

Because I was hired two days before the start of the academic year, I did not
receive training in the curriculum until after my first year teaching. I struggled to learn
the mathematics, the implicit pedagogical model, and the technology applications
embedded in the lessons. My mentor in the science department was of little help with
such matters. My relationship with my team teaching partner, Mr. Hochstedter
(pseudonym), was surprisingly competitive (and not by my choice). The principal
mandated using Mr. Hochstedter’s tests. Since Mr. Hochstedter was a much more
traditional teacher than I was, this created conflicts between us. For example, Mr.
Hochstedter often turned the lessons into lectures, emphasizing and drilling students in
the concepts that he believed were most important in the curriculum. But he was evasive
when I asked him to share his notes or ideas with me of what to emphasize in the
curriculum. He generally presented me with the test a day or two before we gave it, so I
had to supplement my instruction as I reviewed with my students the day before the test.
My students strongly complained about the academic disadvantages incurred by that
lesson structure. Eventually, I began curving my students’ test scores, to Mr.
Hochstedter’s chagrin, but that appeared to appease my students, at least to some degree.

While these more personal events were discouraging, I was also troubled by my
students’ and their parents’ reactions to the curriculum. The students often questioned the
validity of the content and pedagogy. They wondered whether the curriculum covered

content that appeared on standardized tests, like the Academic College Test (ACT) and

 

’ Note: Since C. Hirsch was an author of the CPMP materials and of the NCTM (1989) Curriculum and
evaluation standards for school mathematics a few years prior, there is a strong correlation between the
pedagogies suggested by those documents.

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the Scholastic Aptitude Test (SAT), and whether it was preparing them for the
mathematics and science courses that they would take in college. At times, their parents
voiced similar concerns.

The math teachers in our department also battled to create consensus about our
department’s pedagogical philosophy. While all of the teachers appreciated some merits
of the curriculum, there were more conservative and more liberal implementations of
CPMP. At one extreme, some teachers valued the pedagogical model and followed the
curriculum verbatim almost always, while at the other extreme, some teachers said that
they mainly valued the new content and lectured from the curriculum most of the time.
Often lively discussions about the faithfulness or extremity of individual teachers’
pedagogy erupted at faculty meetings. The dogrnatism of the teachers in both camps
reminded me of D. C. Phillips (1995) descriptions of “the good, the bad, and the ugly”
sides of constructivism.

At least some of us were attempting to use student ideas meaningfully in our
mathematical discussions in the classroom. Because those teachers were openly and
actively discussing pedagogical and epistemological issues with their peers (even though
those conversations turned to pointed needling, at times), we appeared to qualify to some
extent for the “good” in Phillips’ description of constructivism.

The “bad” (Phillips, 1995) was embodied by the less rational, more radical
implementations of constructivism that a few teachers exhibited. For example, during my
first few months teaching, I asked one teacher whether she felt like we were preparing
our students for their college math courses with our very literal implementation of CPMP

with our gifted students. She said that she would send them off to college and let their

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math professors figure out what to do with them. Having come from a math department, I
knew that if any student, even one labeled as gifted in high school, did not meet the
expectations of the department, he or she would end up either being placed in low-level
math courses or doing poorly in or failing more advanced math courses. So I did not find
her suggestion particularly helpful in wrestling with how to tailor the curriculum to my
students’ needs, nor did I believe her to be rationally drinking about how to implement a
constructivist pedagogy, like the one portrayed in CPMP.

I think that we qualified for the “ugly” side of Phillips (1995) description of
constructivism, because several teachers followed constructivist principles and the
curriculum blindly. In one faculty meeting, a staff member said heatedly, “You just don’t
believe in CPMP.” The other teacher retorted, “CPMP is a curriculum, not a religion.”
Clearly, the former teacher was a very literal irnplementer of the curriculum, while the
latter was one of those who generally lectured from it. In this example, the “ugly” part of
the curriculum was found in the teacher’s idea that you need to believe in a curriculum,
rather than use it as a, possibly very valuable, pedagogical tool. So all three of Phillips’
descriptions of aspects of constructivist ideology and debate appeared to be represented
in our own staff meetings and implementations of the curriculum.

My pedagogy was, at least in my opinion, on the fence between both of these
groups. At times, I abbreviated lessons when the central concept was obvious to the
students, either allowing them to explain the central idea of the activity to the class using
the models provided in the text and probing to see if they understood subtleties that the
lesson uncovered. At other times, I supplemented with activities or even worksheets, if I

felt that their academic trajectories dictated that I do so. But for the most part, I remained

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faithful to the pedagogical model and to the deep mathematical content of the curriculum,
even during these modifications.

In refusing to voice my own opinions about the curriculum, I became the object of
both traditional and the progressive teachers’ indoctrination efforts. Their increasing
urgency to get me to join one camp or the other only added to my stress as a novice
teacher with so much to learn from these more veteran teachers who clearly wanted my
loyalty in their own private “math war.” I did learn a great deal from the summer
workshops following my first and second year of teaching CPMP. But I took the first
CPMP course workshop after my last year of teaching, which explained how to set up
groupwork (finallyl). And while the administration was dedicated to the CPMP
curriculum and provided forums for our ongoing discussions of the curriculum and how
to make sure that the content aligned well with the science departments needs, they did
little to assuage these frictions between the two groups of teachers. The principal was a
scientist who moved to education. He did little to support me with management issues or
other concerns, so I was left to deal with any student or parent issues myself.

My inexperience and the lack of support for my professional growth during this
formative period made the political battles that I was embroiled in with parents, students,
and fellow teachers all the more difficult. All of these events added to my internal
struggles to define myself professionally. This setting was on the whole a highly
frustrating environment in which to learn to teach, particularly with a new and unfamiliar
pedagogy to which I was cautiously, but increasingly openly, devoted.

Finally, I taught for a year at a rural, Midwestern high school bordering a small,

Midwestern city. The math department was progressive in its attitudes, but was only

11

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preparing to change from a more traditional textbook to the CPMP curriculum the
following year. They asked me to do as much as possible to prepare students for the
CPMP curriculum the following year. While the environment was friendly, there were
few, if any, supports or resources for my continued professional growth. I fought bravely
to continue exploratory activities which I did with some success, but too often for my
taste, I found myself in the comfortable but less personally satisfying activity of lecturing
from the traditional text that they still used. Happily, my students openly voiced their
appreciation for my (modest) changes to the advanced algebra and geometry texts that
created a more social, engaging, and exploratory environment during that year.

In summary, I went through a few different pedagogical transitions in my own
teaching career, moving between settings that were less conducive to NCTM (1991)
Standards-based teaching and those that were more conducive to such teaching. I have
taught in many different contexts which allow me to see the challenges that my interns
faced through many different contextual lenses, in terms of support for such teaching, as
well as in terms of demographic factors like diversity, SES, and school size and location.
I heard about and viewed some of my interns’ struggles to enact aspects of the NCTM
(1991) Standards during their internships. Those experiences led me to wonder what
types of challenges attempting NCTM Standards-based teaching imposes on interns and
novices and how teacher educators can better support them in the face of such challenges.
All of these experiences together, both personal and viewed through my interns’ eyes,
provided me with the beginnings of a framework for studying these issues.

It is likely obvious to the reader at this point in the discussion that my empathy for

my interns was born from personal experiences, from observations and discussions of my

12

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interns’ experiences learning to teach, from my research experiences, and from readings
of the literature. I turn now to discuss how researchers, teacher educators, and current

employment trends underscore the importance of the issues examined by this study.

Concerns in the Field

I have become increasingly aware of research emphasizing the importance of this
study. There is widespread, though unsystematic, evidence in the literature that novices
experience challenges while attempting NCTM (1991) Standards-based teaching. There
is also an ongoing teacher shortage which would make losing more teachers due to
increasing their challenges during the stressful novice years problematic. Finally, there is
a high novice teacher turnover rate that makes it difficult to meet schools’ demands for
mathematics teachers and for teacher educators to change the current mathematics
teaching practices in the field through novice teachers. The latter two issues make
retention 3 high priority in the field. I will address each of these issues in turn, describing
how each adds to the significance of the current study.

The literature examining individual interns’ and novices’ attempts to enact NCTM
(1991) Standards-based teaching is peppered with accounts of challenges experienced
while attempting such teaching. For example, VanZoest and Bohl (2000) tell of an intern
who wanted to talk with her mentor about classroom management issues, while he was
more focused on helping her understand the new mathematical topics and pedagogy that
he wanted her to employ during her student teaching. Although classroom management is
traditionally an issue for interns, the lack of discussion of those issues was due, at least in

part, to the mentor teacher’s focus on helping the intern learn about NCTM Standards-

13

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based teaching. So the intem’s challenges or stresses here relate to her attempts at
Standards-based teaching because planning for those attempts interfered with other
concerns that were initially more pressing to her.

Similarly, Wilcox, Schram, Lappan, and Lanier (1991) found, after a progressive
teacher education internship experience that was arguably aligned with the NCTM (1991)
Standardsz, that some novices were very fi'ustrated when moving to more traditional
teaching contexts that did not support such teaching. For example, Allison struggled to
create a classroom learning community in her first teaching job because of the context.
She complained that the class periods were too short to use the discovery mode of
teaching. She also felt overwhelmed by more general concerns, including how much
preparation she had to do each day and the wide variety of ability levels of her students.
Allison met with challenges that stifled her opportunities to teach in more discovery-
oriented, or NCTM (1991) Standards-based, ways. Because this example shows how a
beginning teacher can experience stress as a result of her desires to enact the pedagogy
suggested by the NCTM Standards that are frustrated by her teaching context, it is
arguable related to her attempts, or at least to her desires to attempt, teaching consonant
with that document.

But I had seen examples in the literature of novices struggling to engage with a
pedagogy that they did not entirely understand. For example, Ms. Daniels (Borko et al.,
1992) struggled to explain why the algorithm for the division of fractions algorithm,
rather than just having them memorize it. When her explanation didn’t work out, she

promised to talk with the students about it the next day. She never did return to address

 

2 G. Lappan who was involved in this study was also an author of both the NCTM (1989) Curriculum and
evaluation standards for school mathematics and the NCTM (1991) Professional standards for teaching
mathematics. The course descriptions aligned with several of the new standards found in these documents.

14

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the topic, at least as far as the researchers noticed. While such incidents are common in
the literature, there is generally no follow-up on the effect on the intern or novice teacher,
particularly when the teacher is committed to ongoing attempts at such teaching. In my
dissertation, I am concerned with the struggles of novice mathematics teachers who are
committed to ongoing attempts at teaching consonant with the NCTM (1991) Standards
and which coping resources novices employ to be able to make such attempts. I also wish
to understand the intensity of those challenges, whether they are modestly or intensely
demanding, in relation to novices’ other generally predicted stresses.

I will describe more examples of such events in Chapter 2: Review of the Related
Literature, but I have illustrated here that there is at least some evidence that interns and
novices experience fi'ustration when attempting to enact elements of the NCTM (1991)
Standards in their classrooms beyond the challenges expected while engaging in a more
conservative or traditional pedagogy.

While the concerns that interns and novices face as they attempt to implement
aspects of the NCTM (1991) Standards may seem fairly common in the literature, I felt
like the research represented mainly isolated instances of such challenges, much like the
one that Mr. Banks experienced. These experiences have often been labeled as dilemmas
(e. g. Lampert, 1985) or obstacles. But the construct of such experiences as dilemmas or
obstacles does not consider the impact on the teacher in comparison to the other
challenges that teacher faced, only how effectively they implement innovative teaching
and what choices they make in the moment. Stress or challenge, rather than dilemma or

obstacle, also firrther helps to consider whether the teacher continued to engage in such

15

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activities, how common such experiences were, and how the teachers dealt with the stress
those incidents caused.

Additionally, there is a highly charged political environment that may work
against novice mathematics teachers who wish to implement any type of school reform
(e.g. Kohn, 1998). This may take the form of criticism from parents, students, colleagues,
or administrators; or it may also take the form of a well organized and heavily financed
parent group, such as the “Mathematically Correct” organization (Becker & Jacob, 2000).

There is also a very high turnover rate for new teachers of approximately 50% in
the first five years. By the 2008-2009 academic school year, we will be nearing the end of
a period when a relatively large proportion of the current teaching force will have retired
according to the US. Department of Education's National Center for Education Statistics
(Hussar, 1999). They estimate that somewhere between 1.7 and 2.7 million teachers will
have retired and been replaced by novices. As a result, many new mathematics teachers
have and will enter the profession, but probably not as many as the US. public
educational system will need, given the chronic shortfall of mathematics teachers that
appears endemic to our K-12 educational system. In consequence, we, as mathematics
teacher educators, need to hire and retain a disproportionately large number of teachers in
comparison to our past efforts.

Since we are also attempting to foment a movement in mathematics teacher
education towards, what I and many teacher educators deem, the “high quality
mathematics teaching” aligned with the NCTM (1989; 1991; 2000) Standards, this is a
critical time to ensure that we are retaining as many teachers as possible, particularly our

most promising and qualified novices. Teacher educators make a huge investment in

16

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novices to instill in them a vision of what such high quality mathematics teaching looks
like and to develop in them the skills, dispositions, and capabilities to enact such
teaching. We need to attract and retain novices who are most likely to attempt such
teaching, including those who could potentially choose to leave the profession most
easily. These novices are the most knowledgeable about mathematics and/or possess
social skills that enable them to be the most adept at teaching the mathematical subject
matter in ways consonant with the NCTM (1991) Teaching Standards.

As a result, our challenge is great. We need to find a way to retain our most
talented teachers who, in the opinion of at least some teacher educators (e. g. Farber,
1991), are the most likely to leave the field of mathematics education. And we need to do
this while working against the current high retirement and low retention trends, while
attempting to hold on to our ideals of instilling an understanding of what high quality
mathematics teaching is and developing capacities to implement such teaching in our
mathematics teacher candidates. By doing so, we attempt to retain those novices who we
are training to teach in ways consonant with the NCTM (1991) Standards. And while
many of those novice may not choose to teach in such ways, some will certainly gain an
appreciation for the value of what we deem to be high quality mathematics teaching and
invest in making such skills, aptitudes, and dispositions a greater part of their pedagogical
repertoire and professional development trajectories. Such retention increases the chance
that practicing teachers will be able to more effectively understand and attempt to engage
in the types of mathematically rich tasks and classroom discourse that they may learn
about in their continued professional development, particularly those involving university

collaborations, teacher learning communities, and continuing university coursework.

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Issues and Questions

In summary, in considering the topic of this study, I was concerned about my
personal experiences with attempting to enact elements of the NCTM (1991) Standards in
my own secondary mathematics classroom. The challenges that I and my interns faced
surprised me and led me to wonder whether we, as teacher educators, expect too much of
our novice teachers by adding the expectation of attempting this high quality mathematics
teaching early in their careers. But this concern worked directly against the great
satisfaction that many of my interns and I derived from engaging in such teaching. For
me, at least, it matched my own belief system and ideals well and engaged the students
effectively while deepening their understanding of key mathematical concepts.

I also realized that these demands were being placed on novice teachers in a
highly charged political environment that may spill over into the workplace at times, as in
the case of the Mathematically Correct (Becker & Jacob, 2000) movement, but likely in
more subtle ways, through the actions of teaching colleagues, administrators, parents, or
students. These demands, by adding more stress to the difficult novice years of teaching,
may unwittingly push talented teachers out of the field, which would add to the attrition
problem following from the current trends due to high veteran mathematics teacher
retirement, low teacher candidate enrollment, and low novice teacher retention in the high
demand field of mathematics education.

I began to formulate my research questions very broadly at first. I wondered how
attempting to enact elements of the NCTM (1991) Standards plays into or modifies the

stresses that novices already experience. I was also curious about how teacher educators,

l8

colleagues, and school administrators could help to support novices as they attempt to
enact these elements in their teaching, to make such attempts a more reasonable and
practicable pursuit. In this study, I attempt to address these two broad issues, which I will
spell out more specifically and in finer detail in the Methods chapter.

The issues that I am studying have the potential to capture the attention of many
groups. They will interest teacher educators, as they consider how best to prepare and to
offer ongoing support to novices who continue their attempts to enact the NCTM (1991)
Standards. They also inform teacher educators how to advise those who interact with
such novices about how best to support and nurture their blossoming pedagogical skills.

Some colleagues, department chairs, curriculum coordinators, and administrators
of novice teachers are invested in implementing teaching consonant with the NCTM
(1991) Standards. Such individuals will be interested in understanding the challenges
novices may be experiencing as they attempt to enact such teaching, so that they can help
to support them in the process of becoming a teacher and in obtaining some of the new
and unique pedagogical strategies and dispositions aligned with the NCTM (1991)
Standards. As a result, such colleagues and administrators can help retain progressive-
thinking novices and build a young cadre of teachers who will, in time, take the places of
their veteran mentors and administrators who retire and leave the field. It is a great
opportunity for more veteran teachers and administrators to leave behind a legacy that
will help ensure that there is what they may also deem to be high quality mathematics
teaching in the future of America’s youth in the K-12 educational system.

On a more theoretical level, teacher education researchers, psychologists, and

anthropologists may also be interested in these issues. Because this study touches on

19

issues of teacher stress and coping broadly, it may be of interest to psychologists and
anthropologists who have interest in how stress affects specific actors in the human
services occupations, in this case, secondary mathematics teachers. Teacher education
researchers who want to understand how novices experience attempting to enact a
pedagogy very different than the one they generally have experienced in their K-12 and,
at least to some degree, university educations may also be interested in this study. Even
though my study is focused on high school teachers, it is not difficult to imagine that
middle school and, to some degree, elementary teachers, will share similar challenges as
they attempt to enact elements of the NCTM (1991) Standards in their classrooms.
Finally, this study is likely interest policy makers who wish to understand how to
structure educational careers and professional development opportunities in the first few
years. Such attention to detail could help novices maximize their professional learning
and encourage the Optimal use of their limited resources in dealing with the challenges of
attempting to enact elements of the NCTM (1991) Standards. It could also help policy
makers suggest better ways to provide novices with the most effective resources or make

them more available and more easily accessible.

At this point, I move to present a review of the related literature in the chapter that
follows, giving greater attention to many of the issues that I have touched on here briefly,
including in particular, a more thorough review of the stresses and challenges that
novices face, both as they attempt to learn to teach and as they attempt to enact a
pedagogy very different from the one that they experienced as K-12 students that is

aligned with the NCTM (1991) Standards.

20

Chapter 2: Review of the Related Literature

In Chapter 1, I described how my personal experiences attempting to teach in the
spirit of the NCTM (1991) Standards were filled with challenges that included conflicts
with students, parents, administrators, and colleagues. I was at times conflicted myself
about the strength of my understanding of and commitment to such teaching, at least as it
was portrayed by the various camps of teachers where I taught. I saw some of my interns
struggle to understand, interpret, and put such teaching into practice at my own
admonition. The literature indicates that much of the teaching workforce, including
mathematics teachers, will retire during the next few years. This turnover implies a need
to heighten new teacher support and retention above and beyond our past efforts. But it is
also a great opportunity for mathematics teacher educators to have a strong and possibly
lasting impact on teaching practice.

In the current chapter, I turn my attention to the literature that discusses teacher
stress in greater detail; in particular, I first reviewed the literature that examines and
describes stress in general, then the stresses of teachers, and then more specifically
teachers’ stresses while attempting to implement aspects of the NCTM (1991) Standards
in their mathematics teaching. The latter challenges have generally been framed as
dilemmas of teaching or as challenges related to implementing a new pedagogy (rather
than looking at teacher stress as a whole and the place of pedagogical challenges in that
fi‘amework). But those studies were helpfirl in developing an understanding of the types
of challenges that interns, novices and experienced teachers reported or that observations

suggested to both motivate and to begin to build a framework for the current study.

21

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General and Teacher Stress Literature

A recent review of the teacher stress literature (Kyriacou, 1998) identified
teaching as one of the most stressful of the human service occupations, particularly when
self-report measures were used. Kyriacou further asserted that somewhere between a fifth
and a quarter of all teachers experience a great deal of stress fairly frequently, while
Travers and Cooper (1996) extended the possible range to as high as one-third.

On the other hand, some researchers suggested that such widespread claims about
teaching as a high stress profession were exaggerated. Pithers and F ogarty (1995) found
that teachers exhibited higher stress on only one of several scales as compared to a group
of non-teachers, while Bentz, Holliseter, and Edgerton (1971, in Travers and Cooper,
1996) found that teachers’ mental health was slightly better than that of the general
public, and only one in three teachers reported even moderate or mild emotional
symptoms. Clearly, the findings about the magnitude of stresses that teachers experience
have been mixed, but the majority of studies indicate that teachers are more highly
stressed than their counterparts in similar professions. But few researchers, if any, that I
could find, suggested that the first few years of teaching are not highly stressful.

The stresses of teaching have been studied from two different perspectives. The
first perspective is that of teacher stress, which focuses on the immediacy of events and
situations in teaching that cause teachers stress. The second perspective is that of teacher
burnout, which is the result of continued failed efforts to deal with the stresses that a

teacher experiences. I begin with the more severe of these two, teacher burnout, then

22

return to discuss the more fleeting foundational components of teacher burnout, namely
teacher stresses.

The foundational literature on stress firrther complicates our understanding of
teacher stress. Although stress is often portrayed as an inhibitor in models of human
behavior, it can also act as an activator or energizer of learned responses (e. g. Yerkes &
Dodson, 1908). Adding stress can have positive effects on human performance up to a
point where any further stress erodes performance, but the difficulty in determining how
much stress is too much depends as much on the individual’s talents, resources, and
personality as on the amount of stress (Abouserie, 1994; Pithers, 1995). Dunharn (1980)
suggests that stress can also demonstrate positive effects, such as developing better
coping skills, an increased sense of self-concept, more effective teaching styles and
behavior, more positive relationships with students, and improved interpersonal
relationships with other teachers. Another variable adding to the complexity of ways that
individuals experience stress is task complexity (or the number of steps involved in
completing a set task) or task difficulty (Standish & Champion, 1960).

In summary, the general research literature tells us that the context in which
practitioners teach and their individual talents, resources, and personalities also play into
the stresses that they experience. Stress is good up to an optimal point, after which
performance erodes. But individual differences in how individuals experience events
makes it difficult to judge what the optimal level of stress for any given teacher may be,
because each teacher’s ability to deal with various stresses effectively depends on so

many different variables.

23

Teacher Burnout

Many researchers have found it useful to characterize the stresses of teaching by
studying the related phenomenon of teacher burnout (Blase, 1982, 1986; Byme, 1994;
Cunningham, 1983). These researchers generally define teacher burnout as the end result
of sustained stress over a long period, often described as decreasing teacher productivity
over time (DeMoulin, 1991). F arber (1984) further refines this definition of burnout as
“the final step in a progression of unsuccessful attempts to cope with negative stress
conditions” (p. 324). He questions whether teachers burn out, due to overwork resulting
from a passion for their teaching, or whether they are “worn out,” becoming less invested
in their teaching and in their students over time. Because I am studying novice teachers, I
feel that they have generally not been teaching long enough to experience burnout. As a

result, I choose to operationalize the challenges novice teachers face as teacher stress.

Teacher Stress, More Specifically

Cox (1975; 1978) and Kyriacou and Sutcliffe (1978) identified two different
characterizations of stress in the research literature. The first characterizes stress as
“pressure exerted by the environment on an individual.” The second describes stress as “a
state or response pattern.” Kyriacou and Sutcliff and Cox argued that these two
conceptualizations of teacher stress are not mutually exclusive.

As a result, Kyriacou and Sutcliffe (1978) characterize teacher stress as a
response syndrome of negative affect (such as anger or depression) by a teacher usually
accompanied by potentially pathogenic physiological and biochemical changes resulting

from aspects of the teacher’s job and mediated by the perception that the demands made

24

constitute a threat to the teacher’s self-esteem or well-being and by coping mechanisms
activated to reduce the perceived threat. In other words, teacher stress involves the
teacher perceiving a teaching situation or event in the teaching context as challenging and
feeling a negative emotion about it; such emotions are in some ways alleviated to some
degree by coping resources (such as getting advice from teaching peers) that the teacher
employs.

Six major categories of environmental factors involved in teacher stress are
repeatedly cited in the literature (Phillips, 1993; Kyriacou, 1989), as follows: poor
motivation of students, poor student discipline, poor working conditions, time pressure
and work overload, low status and opportunities—including pay, promotion, and career
development, and poor school ethos—including conflict with colleagues and
administrators. A recent preliminary study (Lewis, 2004) on the stresses of learning to
teach by the NCTM Standards adds new subcategories to several of the aforementioned
categories such as challenges related to the textbook, technology, and preparing students

for standardized tests, as well as introducing the new category of pedagogical concerns.

The Stresses of Learning to Teach
Before discussing the stresses novices experience during their first few years, I
want to clarify that I define a novice teacher as a teacher with less than three full years of
teaching experience, as is generally accepted by many researchers (e.g. Berliner, 1988).
Novice teachers struggle with survival skills during the first few years of
teaching. It is widely known that learning classroom management is a primary concern to

most incoming teachers. Nearly all novices believe the well-worn maxim “if you can’t

25

control your class, you can’t teach.” An example of a novice teacher struggling to learn
such skills in a difficult context is found in Sedlak, Wheeler, Pullin, and Cusick’s (1986)
study of bargaining in teaching. The observer was surprised by the complete lack of
student engagement that one novice teacher faced in a particularly difficult class, with
students ignoring her, refusing to work, and generally making jokes throughout the class
period. After the class was over, she complained that she did not know what to do, cried,
and pleaded with the researcher for help. Prospective teachers appear to lack many of the
tools needed in their careers, including management skills and the well-practiced routines
that help free cognitive resources for the more intellectual tasks involved in teaching
(Berliner, 1988).

Lortie (1975) explains that due to the overwhelming workload imposed on
beginning teachers, they have been shown to be highly stressed during their first few
years of teaching. He argues that in great part this is due to the “sink or swim” model of
teacher induction in the United States, in which novice teachers are expected to carry the
same workload as their more experienced colleagues with little or no external support.

Borko and Putnam (1996) hypothesized that new teachers may be too stressed to
learn efficiently from their experiences. Given the continued prevalence of Lortie’s “sink
or swim” model of teacher induction in the United States, researchers’ and teacher
educators’ concerns that novice teachers may be too stressed to learn effectively from

their experiences appear warranted.

Teaching Consonant with the NC T M Standards and Related Stresses

26

When I talk about NCTM (1991) Standards-based teaching, I refer to teaching
that attempts to meaningfully implement aspects of those Standards. I define Standards-
based teaching (SBT) using the six principles listed in Professional Standardsfor

Teaching Mathematics (NCTM, 1991) (see Figure l).

 

Worthwhile Mathematical Tasks
The Teacher’s Role in Discourse
Students’ Role in Discourse

Tools for Enhancing Discourse
Learning Environment

Analysis of Teaching and Learning

 

 

 

Figure 1. List of the characteristics of NC T M Standards-based teaching.

First, Worthwhile Mathematical Tasks involves creating challenging mathematical
activities that explore worthwhile and meaningful mathematics and encourage students to
gain and communicate connected, deep mathematical knowledge. Second, The Teacher’s
Role in Discourse describes the teacher’s role as facilitator of student mathematical
discussions by posing meaningful questions, determining issues to pursue, encouraging
students to justify their ideas. and deciding when to formalize mathematical language and
notation. Third, Students’ Role in Discourse describes how students contribute to
meaningful class discussions as mathematically authoritative participants, relying on
evidence and argument.

Fourth, Toolsfor Enhancing Discourse involves amplifying discussions using
technology, concrete materials, and multiple representations of mathematical concepts,
including oral, visual, written, and conventional representations. F ifth, Learning

Environment describes creating suitable time, space, materials, and ambience to allow

27

students to grapple collaboratively with significant mathematical ideas and to take
mathematical risks. Sixth, Analysis of Teaching and Learning describes gathering
information to assess students based on these principles and to evaluate the impact of the
environment and tasks that the teacher employed.

While some researchers have studied teachers’ attempts to implement a pedagogy
consonant with the NCTM (1991) Standards, very few, if any, have looked at their data
through the lens of teacher stress. Those that have studied such phenomena have more
often looked at these issues as dilemmas in teaching or as challenges of acquiring new
knowledge, skills, and capacities. I look through such studies here with the lens of
teacher stress, focusing in this first section on the efforts of experienced teachers, in an
effort to show that the literature suggests that that attempting teaching consonant with the
NCTM Standards generates challenges for more experienced teachers. As a result, it
stands to reason that less experienced teachers would experience at least as much, if not
more challenges than their more experienced counterparts.

I review these studies in order of relevance to the current study, citing those
related to secondary teachers first, then to middle school, and finally to elementary
teachers. While my focus in this dissertation is on novice secondary teachers, I feel that
there is something to learn from looking across these bodies of literature, particularly

given that the research in each area is thin, but taken together there is a good deal of data.

C hazan (2000): Teaching lower-track high school students.

Chazan (2000) talked about his attempts to teach non-college intending secondary

students using a teacher-written curriculum that involved rich mathematical tasks,

28

mathematical discussion and justification, and student mathematical conjectures about
concepts that was arguably based on the NCTM (1991) Standards. In Chazan’s teaching
experiment with Ms. Bethell, they noticed that the non-college intending students they
taught were often disengaged in math class. He said, “My first year was a rude
awakening” (Chazan, 2000, p. 27). Their students often resisted their attempts to bring
them into mathematical conversations, but at other times, the students participated

actively. Generally, they could not predict the level of student participation beforehand.

As a teacher of a lower-track math class in a high school, I found issues of
“student motivation” an important part of my subjective experience of
teaching. Students’ engagement in class varied dramatically, and it was
hard to predict. Sometimes, students were quite engaged. When students
were disengaged, on some occasions, they made their views known loudly
and forcefully, and at other times, disengagement was expressed in quiet
and sullen ways. However, on a regular basis, the students that Sandy
[Bethell] and I taught were not motivated; they did not come to class ready
to work on the academic tasks we had so carefully designed or chosen.
Sometimes we were able to overcome initial disengagement. At other
times, there were serious issues that occupied students’ minds and made
doing mathematics relatively unimportant: Someone had stolen property
from their locker, or a classmate was pregnant and planning to get married
and drop out of school When then had to decide how to respond. And,
sometimes, we did not find out what was on their minds or why they did
not want to invest their all in our studies (Chazan, 2000, p. 38).

Chazan offered specific examples of students who were disengaged with school
and, in particular, with mathematics class. Joe and Bob two were examples of the 35% to
40% of students who dropped or failed Algebra 1 each semester who exhibited
“classroom behaviors that I found perplexing” (Chazan, p. 29). Joe was very bright and

articulate. Chazan expected him to be an excellent student, but found that Joe would only

engage in class activities when Chazan was physically nearby. Some days, Joe would

29

happily disengage when Chazan was not nearby, while on other days, he would explode
if he was not receiving what he felt was adequate attention from C hazan. Bob, too, was
inconsistently engaged. One day, he drew two faces on his knees and had them talk to
each other loudly and then proceeded to teach the rest of the class how to clap loudly
with only one hand, disrupting the class numerous times throughout the hour. But the
following day, Bob was the driving force behind his group’s perseverance in exploring an
extension to the mathematical task that Chazan posed. So the inconsistency of students’
engagement in mathematics was another challenge that Chazan dealt with, including that
the disengaged students were a moving target, depending on the day that the lesson was
held. Chazan elaborated further in the following quote.

Chazan (2000) also noticed that some students didn’t engage in his mathematics
lessons because they thought that they knew the material already; they had seen these
topics so many times over the years that they looked familiar, even though they may not
have mastered them. For example. Danielle felt that she knew the material during one
lesson, because she had memorized a number of faulty algebraic rules. What added to the
challenge of teaching Danielle was that she had no means of evaluating her solutions to
determine whether they were correct. So students felt like they knew the material, in spite
of having memorized many faulty rules: because they had no means of evaluating their
answers, they did not even realize that their work was very often incorrect.

In other words, while Chazan’s lens was not that of stress, he used words and
talked in ways that suggested that he experienced students’ disengagement and
undesirable behaviors that detracted from his attempts at NCTM (1991) Standards—based

teaching as stressful.

30

Romagnano (1994): Disengaged middle school students.

In an experiment attempting teaching arguably in the spirit of the NCTM (1991)
Standards, Romagnano (1994) found that at times he didn’t like how directive his
teaching was, in spite of his best efforts to incite discussions involving his students in
roles like those advocated in the NCTM (1991) Standards. While Romagnano often
talked about his and his team teaching partner’s challenges in terms of dilemmas, he also
talked about frustrations and difficulties that they experienced along the way. While a
dilemma suggests a sort of psychological tension that could be considered a stress, I will
focus on those passages that most clearly appear to describe events that appeared to be
the most obviously stressful for Romagnano3.

Like Chazan (2000), Romagnano (1994) felt frustrated when his students did not
choose to engage in class activities and discussions by taking the more central role that he
and his team teaching partner, Ms. Curry, wanted. He, like Chazan, was particularly
frustrated when the most capable students chose not to participate. For example, he said
two students, Paul and Neil, were “giving me crap all the time” and “are not putting in
any effort. . .even though they do know, and they’ve show me that they know more than a
lot of other [students]” (Romagnano, p. 73).

Another aspect of Romagnano’s (1994) and Curry’s difficulties with students’

disengagement is that they had chosen each mathematical problem carefully and with

several mathematical goals in mind for that problem. But those problems could not

 

3 Romagnano had 14 years teaching experience at the beginning of this study, while Ms. Curry was in her
first year of formal teaching after substitute teaching the year prior. I will focus on Mr. Romagnano’s
stresses here and discuss Ms. Curry’s stresses in the next section when I talk about novices’ stresses.

31

always be geared specifically towards students’ interests due to mathematical content

demands.

We were faced with a dilemma. We wanted to do problems that were real
so that students would not ask why we were doing them. These problems
would require our students to use a significant amount of cognitive
energy... But it was precisely this lack of clarity, level of commitment,
and the fi'ustration it caused that led our students to disengage. The
“genuine problems” I chose were of little interest to them, or grew
tiresome for them quickly... On the other hand, the problems the students
found most interesting were only of marginal interest to me as I tried to
teach about functions. Ms. Curry had done several “consumer math”
topics, such as developing a budget and buying stocks, during the year
prior to the study. These applications of basic skills were the topics that
had the most relevance for our students... If we chose only problems such
as these, for which we had to stretch to include the mathematics I wanted
to stress, we risked sending the message that functions is not a particularly
important concept. We also would seem to be saying that what our
students were then interested in is all that is truly important about
mathematics (Romagnano, 1994, pp. 80-81).

While the problems often did expose the mathematical concepts that Romagnano
and Curry wanted, some students complained at times that, while the problems were
better than working in the textbook, they were still boring. For example, Sandy told Ms.
Curry, “1 don’t like it very much. It’s better than bookwork, but kind boring.” Dr.
Romagnano wondered, “Is it a good problem if students don’t like it?” (Romagnano,
1994,p.79)

So, like Chazan, Dr. Romagnano and Ms. Curry faced issues of student
disengagement in mathematics class. And it also appeared that there was a tension
between the type of problems that the students found most relevant to their personal lives

and the type of authentic problems that would allow Dr. Romagnano and Ms. Curry to

teach the mathematical content of functions that they wanted to share with their students.

32

And they encountered these challenges as they attempted to teach in the spirit of the

NCTM (1991) Standards.

Heaton (2000): Figuring out what a pattern is.

In describing the dilemmas of student disengagement in class activities,
discussions, and with the curriculum as frustrating and difficult, Romagnano (1994)
suggests that he did experience some degree of stress as he attempted to implement a
pedagogy and curriculum based on the NCTM (1989; 1991) Standards.

In studying her attempts to implement teaching consonant with the NCTM (1989;
1991) Standards, Heaton (2000) relied on the Comprehensive School Mathematics
Program (McREL, 1986) curriculum. She had taught elementary school for nine years
and chose to return to try NCTM Standards-based teaching as an experiment. She said
that the first few weeks of attempting this type of teaching were “wrought with
difficulties and frustration” (Heaton, 2000, p.19).

Heaton describes what appeared to be her first lesson on finding patterns in a table
of data (where the output was 12 more than the input). The students noticed many
patterns, but most of them were not relevant to the mathematical concept that she wanted
to explore and that the teacher’s guide suggested. For example, one student noticed that
for an input of 8000 and an output of 8012, both numbers started with “80.” The student
called that a pattern. Heaton was unsure of what to do with such observations and went
home “distraught and troubled by the day’s events” (Heaton, 2000, p.28).

Heaton said that not only did she not know what she herself meant by a pattern,

but she also didn’t know how to move the conversation forward. She was frustrated with

33

the teacher’s guide, because it provided her ideas of what types of student ideas to expect
that were constructive and helpful, but failed to help her understand what to do with the
other ideas she was getting from her students. Heaton also felt discouraged by her failed
attempts to get her students to engage in mathematical discussions. Even though some
students were offering their ideas, many of those ideas seemed irrelevant. She felt that
there had to be more to her role as a facilitator of discussions than just asking questions.

While Heaton’s (2000) difficulties were resolved over the course of her teaching
experiment, it was clear that she did undergo many stresses in attempting to teach in ways
consonant with the NCTM (1991) Standards that would not have been problematic if she
had chosen to teach in the ways to which she had grown accustomed during her previous
nine years of teaching.

There is evidence that all of the seasoned teachers that I have mentioned in this
section experienced stresses while attempting teaching consonant with the NCTM (1991)
Standards. These teachers talked about their fi'ustrations with getting students to engage
in mathematical explorations and discussions, with getting students to appreciate
meaningful mathematical problems that they posed, and with their own inability to
orchestrate the type of meaningful mathematical conversations that they wanted to have
with their students. At least logically, such stresses may be even more severe for novices
who are attempting such teaching but do not yet have access to many of the basic skills,
knowledge, and capacities that their more veteran colleagues have developed. So I now
tum to consider the literature that has reported the challenges faced by beginning teachers

who are attempting to enact important aspects of the NCTM Standards.

34

Stresses of Learning to Teach While Attempting to Implement the NC T M Standards
Learning to teach while attempting to implement the NCTM (1991) Standards
appears, at least theoretically, to be a daunting task. While few studies have directly
addressed this issue, the literature is peppered with reports of events that appear
challenging to student teachers and novices who are attempting to teach in ways
consonant with the NCTM Standards. As in the previous section, I will look across all
levels of K-12 education, but mention secondary teachers and interns first, then middle
school teachers and interns, and finally elementary teachers’ and interns’ purported

stresses.

Alice in Van Zoest & Bohl (2000; 2002): Talking past her mentor teacher.

Van Zoest and Bohl (2000; 2002) studied a secondary student teacher, Alice, and
her cooperating teacher, Gregory, who both shared reform-based ideals and were working
with the Core-Plus Mathematics Project (CPMP) (Coxford, Fey, Hirsch, & Schoen, 1996)
materials. Their conversations focused on Alice’s understanding of the content, much of
which was new to her, as well as considering questions to focus on during classroom
discussions in order to direct students’ conversations towards the type of mathematical
understandings that they were trying to foster. Alice was a bit fi'ustrated at first by
Gregory’s focus on mathematical content, when she felt that she needed more help with
management issues. The following is a quote from Alice’s journal and then an analysis of

the situation by Van Zoest and Bohl.

35

“He was more concerned with, ‘well does this power model fit it [better]
with 1/x"2, or is the 1/x"3 [better]?’ To me, I wasn’t concerned about
which one was actually better, I just wanted [the students] to be doing it.
So it’s hard because I get impatient because I really want to know how to

teach it. . .”

[Alice’s] journals indicated that her biggest concern throughout the
experience was classroom management, and that her pedagogical concerns
centered mostly around wanting to know procedures for running activities
and orchestrating productive student groups. Although she desired to help
students understand mathematics better by engaging them with it, she was
apparently at a point in her own development where she was not quite
ready to engage with it herself (Van Zoest & Bohl, 2000, p. 16).

The interviewers also reported that Alice felt “frustrated by her need to rethink

her plans every day” (Van Zoest & Bohl, 2000, p. 13). She explained as follows:

It is the night before. . .that I sit down and formally write out the lesson
plan. I do this because I can never seem to predict where we will end

up. . .I find it so awfully hard do navigate the timing of this stuff, because
most of the time I just don’t know how the kids are going to react and how
things will go. I cannot [overstate] the amount of frustrated energy I have
spent on this. This material many times seems to depend so much on the
students themselves and whether or not I can hit upon the appropriate
strategy of questioning and explanation (Van Zoest & Bohl, 2000, p. 13).

Although Alice also balanced such quotes with others that expressed her positive
feelings for and experiences with the curriculum, it is clear from these quotes that she
experienced challenges while learning to implement CPMP and its implicit pedagogy that
is strongly aligned with the NCTM (1991) Standards. While Alice also came to a greater

appreciation of the conversations that she and Gregory had about the mathematical

36

content of the curriculum and eventually felt more confident in dealing with management
issues, it is important to note her reported frustration in a placement that many would
consider ideal for learning about NCTM Standards-based teaching (e. g. Vacc & Bright,
1999). In other words, Alice did experience stress related to her attempts at NCTM

Standards-based teaching that, according to the researchers, dissipated over time.

Ms. Curry in Romagnano (I 994): Innovative teaching outside one ’s subject-
matter expertise.

In Romagnano’s (1994) study, Ms. Curry was beginning her formal teaching
middle school after gaining certification and after a year substitute teaching. She was
certified to teach science, but was asked to teach both science and math that year. She and
Dr. Romagnano collaboratively taught their general math sections. It was also clear that
she was undergoing what appeared to be stress, at times, during the dilemmas that
Romagnano described.

While discussing the dilemma they faced in deciding how much to tell the
students, Ms. Curry and Mr. Romagnano explained that they wanted to let students work
things out for themselves and come up with their own ideas as much as possible. While
scaffolding a graphing activity, one of Ms. Curry’s students, Charles, complained that he
didn’t know how to graph. Ms. Curry angrily voiced her fi'ustration. “We’re doing it!
Right now! I’m getting a little upset here. We’re going through the steps, and I don’t see
anybody starting it” (Romagnano, 1994, p. 106). She was frustrated that Charles did not
realize that she was talking about just that and that other students were not paying

attention, as well.

37

Ms. Curry also described how she herself at times struggled with mathematical
content during class discussions. She also shared Romagnano’s previously described
difficulties in getting students to engage in working on the carefully chosen set of
mathematical problems, which could not always be geared towards the students’
interests. For the students, these problems were boring at times, creating difficulties for
the teachers related to students’ lack of engagement in the assignments.

In summary, Ms. Curry reported a few challenges during this year-long teaching
experiment. She appeared frustrated by her students’ inability to understand her
scaffolding at times in developing student autonomy on these activities. And she was also
concerned that her students did not always wish to engage in the carefully chosen
problem sets that she had helped Dr. Romagnano craft. So there was evidence that she
too experienced stresses related to her attempts at NCTM (1991) Standards-based

teaching.

Ms. Daniels in Borko et al. (1992): Missing deep conceptual understanding.

In the Learning to Teach Mathematics project (Borko et al.; Eisenhart et al.,
1993), one participant, Ms. Daniels, struggled in her middle school student teaching
because she possessed a very limited number of representations for mathematical
concepts. The researchers found evidence that her conceptual understanding of how a
factor tree gives the prime factorization of a number and why zero is not a counting
number (Eisenhart et al.). They also found a great deal of evidence that she did not

understand why the division of fractions algorithm worked (Borko et al.).

38

It appeared that Ms. Daniels difficulties, at least with explaining multiplication
and division of fractions, had at least some roots in her mathematics methods course
(Borko et al., 1992). The instructor attempted to use paper-folding activities to illustrate
two algorithms, multiplication of fractions and division of fractions. First, to demonstrate
how to find 1/4 of 1/2 using paper folding, the instructor had the teacher candidates take a

piece of paper and start by creating 1/2 by folding the paper in half.

A student asked, “How do you explain that you always do the second
number first?” the response was, “If I want one fourth of one half, that
says I have to have the half first” The students wondered aloud, “Do you
think they [my students] will understand?” the instructor repeated his
verbal description, but the student’s difficulties persisted... They faltered
when trying to explain. . .what the conceptual link was between paper
folding and the algorithm... At one point a student said, “I’d be terrified if
something like this came up in my class.” The students’ problems seemed
to increase with the move to division of fractions. The instructor believed
that the ground work for division of fractions had been laid

during. . .multiplication. .. For division of fractions. . .he continued by
saying that 1 divided by 2/3 is the same as asking, “How many 2/3’s are
there in 1?” He demonstrated the problem by folding a strip of paper into
thirds, tearing of two of the thirds, and showing that half of a two-thirds
segment is left. Therefore, 1 divided by 2/3 is 1 1/2... The student
teachers’ responses suggested that they did not recognize the conceptual
distinction... Their confusion was exemplified in their repeated requests
for an “explanation” of the invert-and-multiply rule and their
disorientation when the response took the form of verification (Borko et
al., 1992, pp. 213-214).

So, although these student teachers, and in particular, Ms. Daniels, had been given
some tools for verifying that the algorithms worked, they still did not understand that
they had been given verifications for the algorithms and not justifications for how the

algorithms for multiplication and division of fractions could be conceptually developed

39

by their students. It was clear that the entire class was uncomfortable with this lesson and
that at least one student teacher was “terrified.”

To illustrate how this caused difficulties in her teaching, the researchers shared a
teaching episode where a student asked why the division of fiactions algorithm worked
(Borko et al., 1992). Ms. Daniels was reviewing multiplication of fractions during her
student teaching when a student, Elise, asked why you flip the numbers and multiply if
you’re dividing. Ms. Daniels struggled at the board to reproduce the paper folding
activity that would have verified the answer, rather than helping Elise see why you use
the specific algorithm for division of fractions. But she could not recall how to do it and

began to actually produce the representation for multiplication of fractions.

Ms. Daniels realized that she had made an error. She paused for about 2
minutes, studying the board. She then decided to abandon the attempt to
provide a concrete example, saying, “Well, I am just trying to who you so
you can visualize what happens when you divide fractions, but it is kind of
hard to see. We’ll just use the rule for right now and let me see if I can
think of a different way of explaining it to you. OK? But for right now,
just invert the second number and then multiply.” Ms. Daniels stood at the
board, working on the division problem... After a few minutes ...she said
to the researcher. . ., “I just did multiplication.” She did not indicate to the
students that the example illustrated multiplication. Further, she did not
attempt a correct representation on the following day (Borko et al., 1992,
p.198)

She promised the children to look into it, but never returned to address the subject
to the researchers’ knowledge. While Ms. Daniels said that her explanation wasn’t very
good, she was pleased with the lesson overall. What leads me to believe that she may

have experienced stress in this teaching episode is that she paused for several minutes,

she explained herself to the researcher but not to the children, and she did not return to

40

discuss the topic again as she told the children that she would. It was also clear that many
of the teacher candidates expected to be stressed if this topic ever came up in their
textbook because of the instruction that they had received in their methods course. So
while this episode is less clearly stressful than others, there is at least an indication that
such a situation is potentially stressful for a student teacher or a novice teacher,
particularly one committed to returning to teach topics in the spirit of the NCTM (1991)

Standards.

Allison in Wilcox et al. (1991): Learning community interrupted.

The Teacher Education and Learning to Teach at Michigan State University
researchers prepared a sequence of mathematical content courses, a methods course, and
a seminar designed to expose interns to a teacher learning community (Wilcox et al.). The
classroom community was especially helpful as a site for “posing problem situations,
offering conjectures and arguments about problems and their solutions, and reflecting
upon understandings and the connections and relationships among various mathematical
ideas” (Wilcox et al., p. 34), emphases that the NCTM (1991) Professional Standards for
Teaching Mathematics also suggest.

One student, Allison, struggled to create a classroom learning community at her
field placement and continued to struggle with similar challenges to her efforts to teach
for conceptual understanding at her first teaching job. In spite of having access to rich
curricular materials, Allison felt constrained by the school’s 45-minute class periods.

Allison said, “I get so fi'ustrated. These classes are so short. I don’t have time for the

41

discovery mode. I feel like sometimes I have to tell them. . .the formulas. It’s so
fi'ustrating (Wilcox et al., 1991 , emphasis in original)”

Allison also felt overwhelmed by the amount of preparation required and
the wide range of ability levels among her students. For these reasons, she gave
up all attempts at group work, developing a sense of community, and conceptual
understanding and replaced them with a self-paced, self-study course of

instruction in mathematics.

Schweitzer (1996): Frustrations of implementing a new pedagogy.

Ms. Schweitzer had a year of teaching experience when she began her attempts to
implement an innovative elementary mathematics curriculum. In the accounts of teaching
experiments from the SummerMath for Teachers inservice program (Schweitzer), she
recounts her struggles with implementing NCTM (1991) Standards-based mathematics
teaching. At first, Ms. Schweitzer had difficulty posing meaningful questions. Then she
noticed that, although the students were answering her questions more often, they were
still not listening to each other’s comments during whole class discussions nor were they
talking to each other while they were working on problems. Ms. Schweitzer described
feeling frustrated, discouraged, and disappointed by these early attempts at innovative
mathematics teaching. She also tells us that when she talked with the teachers at
SummerMath, she was relieved to find that the other teachers were feeling similarly

frustrated. The following quote from her journal illustrates Ms. Schweitzer’s frustration:

I feel so discouraged. I’ve been looking and looking for signs of a child
who has learned something that I wanted her or him to learn, but I haven’t

42

seen any. I am so fi'ustrated that lately I’ve just wanted math to go away!

.. .I’ve tried to create math lessons that were engaging and meaningful, but

the children seem inattentive during discussions and my questions often

are answered with silence. I’ve tried to use resource books to set up

activities that are “proven” in order to stimulate thinking and talking, but

nothing happens except that I get even more frustrated. So I try to listen to

the kids for a direction to go in, but I guess I don’t know what I’m hearing

yet because that doesn’t help either (Schweitzer, 1996, p. 55).

Ms. Schweitzer also felt fi'ustrated, as she insinuates in her journal entry above
that the resource books and problem sets felt like disjoint sets of problems. She did not
feel like she knew what direction her mathematics curriculum would take that year. So
there was a great deal of fi'ustration for Ms. Schweitzer in her first attempts to create
discussions with her students, the activities that she was posing, and the curriculum that
she was trying to piece together. Eventually, however, she did find greater success in
implementing this curriculum, after an idea from Deborah Schifter, her SummerMath

instructor, helped her see how to scaffold students’ thinking and activities more

successfully.

All of these examples from novices’ and interns’ experiences appear to
demonstrate the stress that attempting to enact elements of the NCTM (1991) Standards
can impose on beginning teachers. These teachers and interns expressed their difficulties
with their mentor’s emphasis on deep mathematical content and questioning techniques at
the expense of management issues. They described frustrations related to implementing a
pedagogy that required students to meaningfully and actively participate in exploratory
activities and classroom discussions. Observations suggested that they experienced

frustrations at their lack of conceptual of mathematics. Some of these issues resolved

43

themselves and some went unresolved, but all appeared to cause these novices and interns
stress.

While I did not directly address my resources for coping with teaching stresses in
Chapter 1, I did have a variety of resources in each of my teaching contexts, such as my
colleagues, myself, curricular materials, and physical resources. I do think it was clear
that the effectiveness of those resources in relieving my teaching stresses definitely
varied between contexts. I now turn to a discussion of the coping resources that the
literature argues that people in general employ in dealing with their stresses, relying
primarily on the seminal work of Lazarus (1966; 1976). I then more specifically identify
coping resources suggested in and described by various studies in the teacher education

literature.

Coping Resources

Coping resources have mainly been described in the general stress literature, but
have not been addressed often in the teacher stress literature. In the general stress
literature, Lazarus (1976) described behavioral and cognitive strategies for coping with
stress. For behavioral strategies, he described direct action, or actual behaviors that
change a person’s relationship to their environment. The behavioral strategies he
described as direct action included preparation against harm, aggression, and escape.

Preparation against harm describes actions that reduce or eliminate the perceived
stress, as when a student studies intensely prior to taking a test, or when a teacher
prepares an entertaining lesson carefully constructed to the students’ needs. Both of these

events reduce the likelihood of experiencing stress. In the former, the student’s intense

studying makes the probability of receiving a good grade more likely. In the latter, the
teacher’s preparations make it more likely that the students will enjoy the lesson and will
learn from it, rather than feeling bored and frustrated. Aggression is the targeting of the
source of stress and destroying it or inducing injury. Such action is generally not
effective, because it is often not appropriate in the particular setting. Escape is the third
form of direct action, involving leaving the situation in which the stress takes place.

Palliation describes the process of moderating stress to reduce its psychological
and physiological impact, using symptom-directed or intrapsychic strategies (Lazarus,
1976). Symptom-directed strategies include the use of alcohol or illegal or prescription
drugs, as well as exercise, muscle relaxation, and other body-centered techniques.

Intrapsychic strategies of palliation are cognitive defense mechanisms against
stress (Lazarus, 1976). These strategies include identification, displacement, repression,
denial, reaction formation, projection, and intellectualization.

Identification is the process of recognizing and internalizing characteristics of
others. The most significant identification process is how children develop their
personalities and socialization processes from their parents. The identification process is
also used to describe why victims, like Jews in Nazi concentration camps, began to think
and act like their captors. Identification helps the victims to show themselves as worthy
of friendship and camaraderie rather than anger, as they adopt the culture of the
oppressor. Displacement is the process of expressing aggression towards a target other
than the source of stress, particularly if that source of stress is more powerful than the
victim. This action helps the victim express anger towards a target in a safer environment,

although clearly that anger is misplaced. Repression is an unconscious defense

45

mechanism by which a thought, idea, or wish, in other words an internal stress, remains
unacknowledged and unexpressed. It is crucial that it be unconscious, otherwise it is
suppression. Repression helps the victim avoid pain due to breaking an internal
prescription or punishment from an external source.

Denial is the act of denying that an external source of stress exists, which may
involve elaborate processing of information to find the stressful information false to
avoid feeling or dealing with that particular stress. This may occur when a patient is
diagnosed with cancer and finds reason to discredit the doctor’s credentials or motives,
the laboratory’s results or procedures, etc. Reaction formation is when a person expresses
the opposite of what they are feeling to avoid expressing their true feelings. Because the
magnitude of that expression must be the same, the expression often comes across as
exaggerated or insincere. Projection is the act of finding evidence of a trait, attitude, or
behavior in one’s self and, rather than acknowledging it, projecting it onto another
person. Intellectualization is the process of detaching one’s self emotionally from a
threatening situation by treating it analytically, as a subject for study or curiosity. For
example, a physician treating a patient with cancer may wish to think of it as an ordinary
case of chronic illness, rather than acknowledging it as a human situation involving death
and loss.

Many of the aforementioned strategies might not be revealed while interviewing
or observing a novice teacher. For example, some actions are highly personal and/or
embarrassing (such as aggression or using palliative techniques like drugs or alcohol),
while others may be difficult to verbalize because they are abstract (like

intellectualization). But of those previously-listed strategies, I could hear about examples

46

of preparation for harm, modest forms of denial, and possibly mild forms of displaced
social aggression. As an example of preparation for harm, the teacher might prepare a
very engaging lesson for his or her students. An example of denial would be if a teacher
said that sometimes the students’ behaviors really get under her skin until she thinks
about how she was at that age and reminds herself that she is the mature adult, while they
are still children. Finally, a teacher might report she vents to her husband when she is
feeling really frustrated, which is a mild form of aggression that gives her a release from
her stress.

While there is little in the teacher stress literature that explicitly and directly
discussed coping resources, the teacher education literature on learning to teach suggest
several coping resources that were used with varying degrees of effectiveness. For
example, many teachers talk about the significance of the role of a teacher learning
community in their professional growth (e. g. F ennema, 1996). Some talk about how a
teacher educator helped them understand a concept that they attempted to teach to their
students (Borko et al., 1992; Eisenhart et al., 1993). Others talk about how curricular
materials (e. g. Van Zoest & Bohl, 2002) or a curricular framework (e.g. F ennema) helps
make their teaching more effective and enjoyable. Some teachers or interns talk about
how situations that were originally stressful become less so over time (Van Zoest &
Bohl) as the intern developed strategies on her own for dealing with management issues;
so the intern herself was actually her own coping resource. These examples from the
literature are also somewhat representative of the coping resources that I found during

this study, as I will shortly explain.

47

Lazarus’ (1976) seminal work, in particular, gave me an idea of which resources
to look for during observations and what to ask about during interviews with these
novices. But the data arising from my study actually inspired the categories of teacher
resources that I chose and refined using a grounded analysis of the data (Glaser &
Strauss, 1967). I will discuss this process in greater detail in Chapter 3. As a result, I
define coping resources as means of avoiding, alleviating, or eliminating teaching stress;
such resources take the form of physical assets, social relationships, or resources arising

from one’s own knowledge, skills, or capacities.

48

Chapter 3: Methods

In this chapter, I discuss the pilot study that prepared me to perform this
dissertation research. I then describe the methodology of the current study. I define the
key terms that I use, such as teacher stress and coping resources for dealing with that
stress. I also review my methods during participant recruitment. I discuss the steps in the
data collection process. Finally, I describe the data analysis that I performed on the data

once it was collected.

Review of Pilot Study

My pilot study researched the sources of stress that both novice teachers and
interns experienced as a (heterogeneous) group. I sought to find out which sources of
stress novices and interns reported, which were related to their attempts at SBT and
which were new to the literature, and how surveys and interviews complemented each
other as means of gathering information on sources of teacher stress.

The pilot study consisted of a survey and a follow-up semi-structured interview.
The survey asked about the sources of teachers’ stress while teaching, their pedagogical
style and beliefs, their teaching goals, etc. Out of approximately 100 surveys sent out to
teachers, 19 were returned. I conducted follow-up interviews with 9 novice teachers and
interns that probed their sources of teaching stress and indirectly and subtly examined
how their pedagogical style influenced those sources, analyzing the 5 participants’
interviews who had attempted Standards-based teaching and had completed their

internship by the end of the study.

49

While the survey worked relatively well at uncovering sources of teaching stress,
it showed no indications of when participants were attempting SBT. The interviews, on
the other hand, were filled with descriptions of teacher attempts at SBT, even though
those attempts were not directly solicited until the last few minutes of each interview; in
other words, teachers were only asked to describe their teaching, but not how it
intersected with the NCTM Standards until the very end of the interview. Another
surprising result was that the sources of each teacher’s stress varied markedly between
their survey and interview responses. Results suggested that the teachers may have
reported sources of stress that they had experienced within a few days prior to taking the
survey, while they spoke about the firll scope of sources of their stress that they
experienced across all of their teaching experiences during the semi-structured
interviews.

I was also surprised at how many of the novices I spoke with reported attempting
SBT at various times during their internship and first few years of teaching. I wondered
whether such events were observable, or whether their perceived attempts at SBT were
not visibly in the spirit of the NCTM Standards to any meaningful degree (e.g., Cohen,
1990)

The pilot study identified several new categories of sources of teacher and intern

stress, including firming to teach in new waLs, Challenges associated with professional

 

development, Learning and teaching unfamiliar content, Preparing students for
standardized tests, Working with technology, and Managing classroom discussions, as
well as demonstrating the validity of many categories already present in the teacher stress

literature.

50

My pilot study also demonstrated the difficulty with which teachers talked about
the construct of NCTM (1991) Standards-based teaching. Teachers failed to engage with
the concept on the survey and struggled to understand and speak in terms of such
teaching, even with extensive explanations during the interview. They often confused the
NCTM Standards with state and district standards, and, although such documents do

overlap to some degree, they are generally written for very different purposes.

Limits of Existing Literature

Some survey researchers have emphasized that few researchers, if any, have gone
into classrooms in an effort to more deeply understand the challenges that novice teachers
face in any systematic way (e.g., Manthei, Gilmore, Tuck, & Adair, 1996). Most of the
literature in this area has been conducted using surveys.

Given the findings of my pilot study (Lewis, 2004) about the immediacy of events
reported on the survey, concerns about how observable teacher attempts at SBT were,
and the difficulties teachers experienced at engaging with the construct of SBT, it
appeared crucial to situate further studies on the intersection of novices’ attempts at SBT
and their challenges in the context of their classrooms accompanied by semi-structured
interviews, allowing opportunities for researcher observation of teaching, explanation of
challenging constructs, and probing for the time, duration, and impact of reported sources
of teaching stress.

Conducting semi-structured interviews with participants gives me, as a researcher,
the advantage of probing to determine when the participant is talking about the sources of

their immediate stresses and how those sources relate to the usual sources of their stress,

51

as well as allowing me to broaden the discussion to the bigger picture of participants’
teaching stresses throughout the course of the year. As a result, using observations as a
springboard for discussion together with semi-structured interviews may help me, as the
researcher, understand the bigger picture of sources of teaching stress, including which
sources are consistently the most challenging for teachers or have been in the past, how
those sources have changed over time, and which resources teachers employed to mediate
the resulting stresses.

I have used the existing stress and teacher stress literature to develop definitions

of the constructs of teacher stress and coping resources for dealing with teaching stress.

Definition of Teacher Stress

I define teacher stress as the psychological state resulting fiom teachers’
perceptions of teaching related events as demanding, challenging, and/or frustrating. This
definition meets my ability to identify and analyze the perceived stresses that teachers
report.

My definition of teacher stress is a modified version of Kyriacou and Sutcliffe’s
(1978) to meet my purposes and the tools here in this study for two reasons. Because I am
not researching physiological or biological factors related to this study, I omit any
reference to such elements of teacher stress. I also view the expectation that stress is a
“response syndrome” or “creates a demand that constitutes a threat to a teacher’s self-
esteem or well being” as too great of a bar to reach in the modest interview and
observation format that was reasonable to perform with the six teachers I invited to

participate in this study. So I omitted such references in the definition used in this study.

52

This definition also does not include a reference to coping resources, because I

have not yet defined them. I do so below and talk about how they relate to teacher stress.

Definition of Coping Resources

I define coping resources as physical, psychological, or social means of dealing
with, avoiding, or alleviating stress, whether targeted at the symptoms or sources of that
stress or at changing the classroom context to alleviate or eliminate that stress. For
example, a teacher might engage in yoga, meditation, vent to her spouse or colleagues, or
justify such stresses, like saying “Oh, they’re just kids and that’s how kids are.” Such
mechanisms are aimed primarily at dealing with the aftermath of stressful events. On the
other hand, discussing new classroom management techniques with a colleague or
creating more interesting lessons to engage the students are aimed at dealing with the
sources of stress, which in these two examples are problematic student behaviors and lack
of student interest/motivation, respectively. Such strategies may be intentionally sought
or unintentionally found and employed. Finally, as previously mentioned, creating more
engaging lessons would aim to draw students into the discourse of the classroom and to
engage them by changing the classroom context to one where learning is a more
attractive choice for at least some of the students.

My definition relates to Lazarus’ (1966) and Kyriacou’s (1981), but I have chosen
to be more specific in my discussion of “targeting sources of stress,” (i.e. employing
proactive strategies to alleviate or avoid stress altogether), rather than including that idea
under “preparing for harm,” as Lazarus includes such actions. In my study, examples of

the types of proactive strategies that Lazarus describes abound and include planning

53

lessons that will better engage students in classroom activities, creating contracts with
students about how they will improve their behaviors, etc. Such constructive activities
also assert teachers’ and students’ shared responsibility in promoting a classroom
environment conducive to learning, as well as emphasizing the personal power that
teachers have in dealing with the challenges that they encounter.

I also acknowledge that many stresses that teachers perceive are also seen after
being subject to the mediating forces of the teacher’s coping resources, which vary with
each individual teacher and teaching context. As a result, my definition of teaching stress
remains intact, with the understanding that many times, I view those stresses after coping
resources have been employed on them to alleviate them partially or completely.

As a reminder, my purpose in working on this study is to help teacher educators
and school administrators to understand the stresses that novices experience and to allow
them to judge for themselves which of those experiences are the most constructive,
because stress impairs the reasoning and reflective thinking which are the hallmarks of
learning from one's experience. If teacher educators and school administrators hope that
novice teachers will continue to learn from their experiences, they need to find ways to
help them limit those stresses, whether by shielding them from some of the initial
stresses, offering them scaffolding by providing access to appropriate coping resources,
and teaching them how to employ such resources in more effectively dealing with their
teaching stresses.

In response to these issues, I have constructed my dissertation study around the
following research questions. The numbered questions unpack the general research

questions that are mentioned first.

54

Research Questions

Which stresses do novice teachers attempting NCTM (1991)

Standards-based teaching experience and how do they respond to them? In

what ways are those stresses related to their attempts at Standards-based

teaching?

1.

What sources of teacher stress do novice secondary
mathematics teachers who have exhibited some elements of
NCTM (1991) Standards-based teaching experience in their
teaching?

a. Which of those sources of teaching stress are predicted
by the existing literature and which are new to the
literature?

b. Which sources of teaching stress are related to their
attempts at Standards-based teaching and how are they
related?

What sort of impact do the sources of teaching stress that

novice teachers experience have on them, i.e. do they judge

them to be facilitative, neutral, or debilitative?

What coping resources do novice teachers utilize to mediate

the teaching stresses deriving from the different sources of

teaching stress that they experience?

55

Overview of Method: Main Steps

As a result of my research of the literature, I have chosen to use teaching
observation as a central tool in this study. As mentioned previously, I hope to be able to
understand the challenges that teacher’s face in the context of their daily teaching
environment and to use my observations and the teacher’s comments on those
observations as a springboard for inquiry. I intend that this process, as previously
described, will open up opportunities for situating a discussion of the sources of each
teacher’s stresses in the classroom, while allowing me to expand the conversation to gain
a broader understanding of the sources of stress that each teacher regularly experiences
and how those sources have changed over time.

I chose to look at a three- to five-day “subunit” in each teacher’s classroom, or a
series of lessons that were somewhat related and cohesive. I asked each teacher for three
to five days when they would be covering related topics that would be a good time to
observe. I avoided “project days” when they did not appear to be an integral part of the
teacher’s pedagogical strategies. In this way, I hoped to see a slice of the teacher’s
teaching experiences and to be able to follow a topic through its development, if possible.

I also chose to hold an interview beforehand, to get demographic data and an idea
of what the teacher’s overall impression of his or her challenges were before beginning
the observations. Afterwards, I planned a second interview to review the observation
data, to discuss the teachers’ perceptions of their challenges in more depth, and to Ieam
about the coping resources that they use to meet those challenges.

To attempt to answer my research questions, during the interviews I asked the

teachers to elaborate on the sources of their teaching stresses. By looking at the

56

observations and reading the interview transcripts, I hoped to learn about the sources of
their teaching stresses and to be able to identify at least some instances in which those
sources were related to their attempts at SBT. In the data analysis, I will compare the
sources of teaching stress mentioned during the interviews to the ones predicted by the
existing literature including those predicted by my pilot study. Finally, during the
interviews primarily, I hoped to find out which coping resources the teachers employed to
meet the demands imposed on them by their teaching contexts and by their expectations

of themselves and of the individuals and resources in those contexts.

Locating and Soliciting Participants

To begin locating and soliciting participants, I talked with a fifth-year secondary
mathematics content/methods instructor of a progressive, highly ranked teacher education
program of a Midwestern university (hereafter, MU) who helped create a list of recent
graduates teaching at the middle and high school levels who were most likely attempting
SBT based on their classroom participation, field placements, and observations of their
student teaching. I found out where many of those graduates were employed by talking
with the fifth-year instructor, their MU field instructors, and members of their student
teaching cohort.

I ranked the graduates based on the fifth-year instructor’s comments and the
practical issues involved in data collection (i.e. distance from MU) in the order in which I
hoped to solicit their participation, omitting graduates who had already participated in my

practicum study. But in the course of data collection, I found that each teacher’s

57

availability and suitability as a participant were the actual limitations in finding, locating,
and recruiting participants.

I contacted all prospective participants at their schools within a reasonable driving
radius of MU to see if they would let me sit in on one of their classes, explaining that I
was looking for prospective participants for a study on the challenges of teachers who
were relatively new to the profession. I omitted any mention of Standards-based teaching
until the end of the data collection process for several reasons. First, I was concerned that
participants might feel that they were being evaluated. Since they had had that experience
as interns, I felt certain that they would know what I was looking for and might alter their
teaching accordingly, yielding inauthentic data. Second, I didn’t want to elicit feelings
that the Math Wars tend to bring out in teachers, either for or against educational reform.
I wanted to avoid teachers changing their teaching and conversations to reflect their
personal biases in regard to such issues that would also yield less authentic data than I
might otherwise find. i

As I sought to recruit a cadre of participants, the most salient feature of recruiting
participants was the difficulty of the process. It was difficult to determine where all of the
prospective participants currently taught. As mentioned previously, I spoke extensively
with their prior university content and field instructors, as well as to members of their
cohort to eventually locate a satisfactory number of participants. Because novice teachers
are often very busy, or even overwhelmed, during their first few years of teaching, it
proved difficult to persuade them to participate in additional extracurricular activities

outside of their already assigned duties.

58

Screening of Prospective Participants

I returned to those teachers’ classes who were willing to participate. I conducted a
screening observation in a class that the teacher described as talkative and where much of
that talk focused on mathematics. I took field notes during the observation, paying close
attention for and recording any evidence of SBT in each class that I observed.

After each screening observation, I analyzed the events in the field notes for
evidence of SBT using an instrument that I created for that purpose (see Appendix A),
based on the NCTM (1991) Professional standards for teaching mathematics. Using that
instrument, I categorized each event that represented a non-trivial attempt at SBT into
one of the six categories listed in the NCTM Teaching Standards, as previously
mentioned.

To digress, an example of a trivial attempt would be if a teacher asked a question
involving more than a right or wrong answer and then said “Never mind,” and moved
forward immediately with the lesson as if deciding on a different pedagogical move. If
the teacher asked the question, waited a few seconds, asked a few students to respond or
attempt the question, but no one engaged with the idea, so she decided to ask simpler
short-answer questions instead, that would constitute a non-trivial attempt at SBT in this
analysis.

As another example of a trivial attempt at SBT, a teacher could give out a project
that called for student exploration and then lead the class through the entire project by
lecturing and asking students simple short-answer questions requiring right or wrong

answers. On the other hand, if the teacher did try to get the participant’s to generate some

59

of the mathematical ideas or conjectures themselves, even though she was lecturing, that
would be an example of a non-trivial attempt at SBT.

So by “non-trivial,” I mean that the teacher did not entirely subvert her own
attempt at SBT. On the other hand, if the students subverted those attempts or failed to
engage with them, I considered that to be a non-trivial attempt, because the teacher had
made a good faith effort to enact teaching consonant with the NCTM Standards.

After classifying all of the participant’s non-trivial attempts at SBT, I looked
across these events, using the screening instrument, for each prospective participant and
judged each teacher as having attempted SBT if I found non-trivial, observable attempts
at SBT in at least two of those six categories.

In one screening observation, the participant did not meet my criteria, but there
was good reason to believe that she might attempt SBT due to an overwhelmingly
positive content/methods instructor recommendation, so I returned for a second screening
observation. That participant qualified for participation at the end of the second screening
observation.

Of the 30 teachers recommended by the fifth-year content/methods instructor as
most likely to be attempting SBT (see Figure 2), 4 had already participated in my pilot
study, so I removed them from the list of prospective participants. 4 of the others that I
located were too far from MU for me to practically recruit them as participants. I could
not locate 4 of the remaining prospective participants. This left me with a list of 18
prospective participants. I contacted the remaining teachers in the order of their proximity
and availability to participate in a screening observation. Of the remaining 18 prospective

participants, I contacted the 13 for participation who taught closest to the MU campus

60

(i.e. less than one and a half hours from MU). 2 of those teachers elected not to
participate. Of the l 1 teachers who I screened for participation, 7 met my criterion for

having attempted SBT during their screening observation(s). The remaining 5 prospective
participants, located between one and a half and three hours from MU. were not

contacted. because my sample was already complete.

 

 

 

 

30 Prospective Participants
Could not locate , , ,
Frnal partrcrpants
4
6
Too far
from MU 4 Screened
1 but not
.................................................. . ‘3‘: - - - T ‘ ‘ ' ' ' ‘ ‘ r - - - - - - - analyzed
_ “ 4
4 .‘ .\
Pilot study Didn’t pass
participants . 5 2 screening
interview
Chose not to
Not invited . . .
, pa rtrcrpate rn
(1.5-3 hr drive) screening
interview

 

 

Figure 2. Number of prospective participants who were chosenfor or how they were
eliminated from the sample.

Those 7 participants who met my criteria for SBT during the screening

observation were invited to participate: others were sent a letter thanking them for their

61

willingness to participate and explaining that only a limited number of participants could

be chosen. But of those 7 qualifying participants, only 6 made visible, non-trivial

attempts at SBT during their classroom observations as research participants. The 6

participants who attempted SBT during my classroom observations after being invited to

participate in this study are the focus of my analyses. The l participant that made no

visible attempts at SBT after the screening interview was dropped from the analysis.

Actual Sample—Description

Table 1

Participant Demographic Data

 

 

 

 

 

 

 

 

Participant Years Class Contrast Other
Name Teaching School Context Observed Class Classes
Mr. Jones 1.25 Maple Rural Integrated 2 Integrated None
(Algl/Geom) 13
Ms. Boone 2.50 Maple Rural Integrated 3 Integrated AP
(Alg2) 2 Calculus
Ms. Grant 2.00 Elm Urban Algebra 1 Algebra Algebra
1C 2C
Ms. Riley 1.25 Holly Semi- Advanced Geometry None
rural Algebra
Ms. Wells 1.50 Redwood Urban Geometry Algebra 1 None
Ms. Price 2.75 Linden Semi- Geometry Algebra Algebra
rural 1B 2

 

 

 

 

 

 

 

My sample consisted of 6 teachers, each with less than three years of teaching

experience. 1 of the participants was male and 5 were female. The participants taught in a

variety of settings, including, roughly categorized, 2 rural (Mr. Jones and Ms. Boone), 2

semi-rural (Ms. Riley and Ms. Price), and 2 urban (Ms. Wells and Ms. Grant) schools

62

 

(see Table 1). Also notice that participants had a variety of experience levels, although
none of them were first-year teachers.

Only 2 of the 4 first-year teachers who I screened, Ms. Riley and Ms. Wells, met
my criteria for attempting SBT. Unfortunately, both of those teachers asked me to wait
until the following year for data collection. They both told me that they had way too
much on their plates to participate at that time, but that they would be willing to
participate the following year. I also attempted to contact Mr. Jones during his first year

of teaching, but was unable to locate him until the following academic year.

Data Collection

Screening observations.

The aforementioned screening observation(s) were used to select participants who
were making a reasonable number of non-trivial attempts at SBT. For the screening
observation(s), I asked each prospective participant to select a class in which they felt
most comfortable being observed and where the students were talkative and where much
of that talk focused on mathematics. I took extensive field notes of each prospective
participant’s class, particularly focusing on events where the teacher appeared to attempt
SBT. After the class, I judged whether the teacher had met my criterion for attempting
SBT during the observation, as mentioned previously, by seeing whether the participant
demonstrated non-trivial attempts in at least two of the six categories mentioned in the

NCTM (1991) Professional standards for teaching mathematics.

Pre-observation interview.

63

I met with each participant for an approximately one-hour audiotaped interview to
ask about their field experiences, first experiences teaching, curriculum used, perceptions
of that curriculum, resources for teaching, other demographic information, and generally
about the challenges they had encountered to date during their teaching experiences. I
also asked each participant either during or around the time of this interview to think of a
series of three to five lessons on related topics that would be convenient for me to
observe and videotape. I asked the teacher what challenging issues they expected to
encounter during this series of lessons.

Because I wanted to get a general picture of the challenges that each teacher faced
on a daily basis before observing them or focusing on specific classroom events, I chose
to ask questions about their challenges more generally, as well, in their teaching context.
I also asked them what resources they had for meeting the challenges that they faced on a
daily basis inside the classroom. At times, I referred back to these ideas during the final
interview, if the teacher mentioned them again or mentioned a related challenge or

incident.

Classroom observations.

I videotaped a series of at least three lessons about related mathematical topics in
a class in which each participant felt comfortable being observed (hereafter ‘focus class’)
and where the class was talkative and much of that talk focused on mathematics in hopes
of finding an environment where each participant would feel most comfortable
attempting SBT. For most participants, this was the class in which I held the screening

interview, except for two, Ms. Price and Ms. Riley.

Ms. Price participated the year following her screening observation, teaching a
section of the same Geometry course in which I observed her for the screening
observation. Ms. Riley also participated the year following her screening observation.
Because she was teaching at a new school and I was observing a different class and
textbook series, I counted her first observation as a screening interview, which she
passed, while I observed her the following year. I discuss these events in more detail in
the Results chapter.

I focused on a class where students were constructively talkative with the
intention of getting an idea of what their teaching looked like under the best
circumstances in their teaching context, as well as getting an idea of the challenges that
they might experience over a series of days in their classroom. I videotaped one to two
additional days in some participants’ classes when doing so allowed me to see the end of
an activity, project, or conversation in which the class was engaged, or when I needed a
substitute for a videotaped day that appeared to be less than half a period of typical,
related, constructive work. Observations were either postponed or extended several times
during the study. One observation was postponed by a cancelled class hour (Ms. Price’s
class). Another set of observations was extended by a pop quiz (Ms. Wells’ class) and an
atypical day in the computer lab that did not necessarily link to other classroom events
(Ms. Wells’ class). Finally, a set of observations was extended by a continuing whole-
class activity and discussion that lasted two additional observation days (Mr. Jones).

For the sake of contrast, I also videotaped one class period (hereafter ‘contrast
class’) in the class where each participant reported that their challenges were most

different from those experienced in the focus class. The challenges in these classes

65

usually, but not always, related to classroom management. In this way, I hoped to get an
idea of the range of challenges that the teachers experienced across their classes and to
facilitate a conversation about as many of the challenges that they experienced as
possible for the modest investment of time that I was able to practically solicit from the

participants.

Teaching log.

Each participant kept a daily teaching log during observations, discussing events
that were surprising, challenging, or unexpected to them during videotaping. In this way,
I hoped to bring to mind all events that were potentially stressful for the teacher. During
conversations with teacher researchers prior to the current research, I heard that many
teachers experience surprising or unexpected events as stressful, even though they may
not readily identify or immediately register them as such. As a result, I used those

adjectives to elicit as many potentially stressful events in the teaching log as possible.

Artifacts.

I asked each participant for copies of their lesson plans and the assignments that
were handed out, worked on, or discussed in the focus class during my observations. I
also requested their lesson plans, but no participant actually used formal lesson plans.
Most participants said that they made mental rather than written plans, at times writing
their ideas on a worksheet or a piece of scratch paper, so there were few formal lesson

plans for these observations.

66

Selecting video clips.

I selected three video clips to discuss with each participant that lasted altogether
approximately ten minutes.

First, I reviewed the videotapes to find all events that appeared to be stressful to
the teacher; in other words, I looked for and noted in detail when I identified physical or
verbal cues that the participant may have been experiencing stress in the video clips.
Examples of physical cues included a teacher rolling her eyes or staring fixedly at the
class while occasionally glancing at a clock or wristwatch. Examples of verbal cues
included raising her voice or a verbal reprimand (like saying, ‘That’s not appropriate
language’ or ‘I’ll be holding the whole class for 15 seconds after the bell rings today’). I
made sure that the detail in these notes was sufficient to identify SBT-related events and
situations. For each event, I listed the starting and ending times of those events on the
videotape and wrote a summary, paying particular attention to give enough detail to be
able to identify the sources of stress and whether there were SBT-related components for
each potentially stressful event.

I then carefully selected the events that also appeared to be related to attempts at
SBT; in other words, I identified apparently challenging events that non-trivially satisfied
at least one aspect of any of the six NCTM (1991) Professional standards for teaching
mathematics. I made a list of three to five events that appeared to represent the sources of
each participant’s SBT-related teaching stresses and then, if there were less than five
events, added in events that represented classes of events in the data that were not

necessarily related to SBT.

67

After reviewing the videotapes of the observations, I read through the unexpected,
surprising, and challenging events that the participant had noted in the teaching log. I
looked for related groups of events, particularly those that also coincided with
participants’ attempts at SBT by the participant’s explanation or by my observation of
those events. I identified three to five events from the teaching log that appeared to be
representative of patterns in that data, giving preference to those related to SBT. After
that, I gave preference to isolated events that appeared related to attempts at SBT, then to
a those events that represented patterns of challenges in the data not related to SBT.
Isolated events not related to SBT generally were not part of this list.

From these two sets of events, the list generated from my review of the
observation videotapes and from my review of the teacher’s teaching log, I looked for
overlap in the two lists of events, focusing on those most strongly related to attempts at
SBT. If there was more than one event related to a single source of stress, I chose one to
represent that source of stress. In this process, I also tried to choose the events that
represented the overlaps in the two lists that were most readily observed and understood
in the observation tapes, selecting the participant-identified events from the teaching log,
wherever possible. Where the teacher described an abstract idea, like “general chattiness
of the class was out of hand,” I chose a video clip from the list I had created as I reviewed
the observations that appeared to represent that concern in a clear, observable way to
facilitate meaningful discussion during the Post-Observation Interview.

After I had found episodes most strongly related to SBT representative of the
overlap I saw in the teaching log and the videotaped observations, I chose other events

that related to attempts at SBT. Finally, if I still needed another event, I chose events that

68

were reported as or appeared to be the most challenging or frequent for each participant.
As a result of this process, I selected and refined a final list of 3 events. I then created
video clips of those events, each lasting from about 15 seconds to four minutes that I
could share with the teacher during the Post-Observation Interview. I edited the video
clips to be generally about a chunk of the lesson, perhaps focusing on solving one
problem, discussing one or a series of questions, or looking at one or a series of
interchanges with a student, depending on the event and source of stress that the clip was
intended to represent. As mentioned previously, I tried to limit the total viewing time to
ten minutes or less for each participant’s three video clips.

For a few teachers, I selected a fourth video clip when one of the clips appeared
that it might be too poignant to present, when it was difficult to find one clip that exactly
fit comments in the teaching log, or where the judgment of and event as stressful
appeared to be difficult to judge because it was subtle, if it was a stress at all for the
teacher. An example of the latter occurred in Ms. Wells’ class, when I couldn’t find an
event where student talking was clearly causing her stress. So I chose two clips that I
considered borderline cases to show her, in case the event in the first clip was not actually
stressful for her.

Generally, these clips contained only one of the sources of teaching stress that I
had identified, although at times there appeared to be several sources present, but one of
those sources was the primary focus for my research purposes. This was often due to the
distribution of challenges in the course of classroom events. For example, while Ms.
Price presented a problem involving the area of a regular polygon, I was primarily

interested in the challenges that related to the misbehavior of the student who had asked

69

the question, but Ms. Price also made several mistakes due to a copy error during the

same clip. Since the participant mentioned both of these challenges during the

presentation of the clip, we talked about both, even though I had chosen the misbehavior

as the primary reason for viewing the clip.

This process was intentionally designed to bring stressfirl events related to

participants’ attempts at SBT into the conversation during the Post-Observation Interview

and to situate those events in the classroom context. Table 2 lists the three events for

which I created video clips for each of the 6 participants whose data I analyzed for this

study, omitting alternate clips that were selected but not viewed during the Post-

Observation Interview.

Table 2

Three Potentially Stressful Events Novices Viewed During the Final Interview

 

 

 

 

 

 

 

 

Participant Event 1 Event 2 Event 3

Ms. Boone A student swore in Teacher felt the Teacher was
class. “general chattiness of surprised by an

the class” was interesting student
excessive. idea in familiar
lesson.

Mr. Jones Students didn’t see Teacher struggled to Teacher struggled
how drawing get students to with getting students
triangles helped explain intuitively to understand the
determine validity of why ASA proves “path” to take to
prospective congruence. prove a geometric
congruence theorems conjecture and to
(i.e. SSA, ASA, SSS, properly justify
SAS, AAS, etc.). assertions.

Ms. Grant Students didn’t see Teacher struggled to Students struggled to
how changing “c” use results of class use the calculator to
altered the graph of discussions to predict find an x-intercept
the equation y=x2+c. the shape of the graph using left and right

of the equation bounds.
y=ax2+bx+c.

 

70

 

Table 2 (continued)

 

 

 

 

Ms. Riley Teacher tries to Students struggle to Students solve a
review absolute solve by completing completing the square
value, but realizes the square. problem, but teacher
that students don’t later realizes that they
remember it. made a mistake.

Ms. Price Student confuses two Student says they Students attempt to
formulas, then starts divided the regular rearrange 8 pieces of
talking with fiiends hexagon into 6 a circle into a
even after the teacher equilateral triangles, ‘parallelogram,’ but
looks at him several but class can’t prove aren’t sure what the
times, so she triangles are shape they found
confronts him. equilateral. really is.

Ms. Wells Students struggle to A student conjecture Teacher has to
find lengths of sides that the four triangles repeatedly shush the
using the angle created by the class during a quiz
bisector and the midsegments of a and threatens to take
Pythagorean triangle are congruent points off one
theorem. surprised the teacher. student’s quiz.

 

 

 

 

Post-observation interview.

During the Post-Observation Interview, I met with each participant for one to two

hours to discuss the three video clips of specific events that were challenging to them

during my observations of the focus class during formal participation in the study. By

design, the selection process favored events that coincided with attempts at SBT.

To put these events in the bigger picture of classroom events, I also asked about

all of the other related events from the teaching log, as well as about the most salient

 

challenges from the notes I took while reviewing the observation video tapes, particularly
patterns of events that were not represented in the video clips. For example, if the teacher
had an entry in her teaching log about Responding to problematic student behaviors and I
had several others in my notes, but none of the events were represented in the video clips,

then after our discussions of the video clips, I would talk about what the teacher had

71

written in the teaching log and, during that discussion and bring up a few of my
observations in the video clips to see whether the teacher viewed those events as stressful
and how they may have related to her planned pedagogy.

After that, I showed participants a list of the top 8 categories of challenges that
teachers mentioned during my pilot study (Lewis, 2004) and asked them to discuss their
challenges in each of those categories of events, as well. At this point, many participants
pointed out which was their top challenge, as well as mentioning other salient challenges,
and pointing out which events or situations were not really challenging for them. In this
way, I got an idea of all of the challenges in the classroom that were meaningful and
salient for the teacher and whether the challenges that they had discussed from the video
clips (which generally favored incidents related to SBT) were actually meaningful,
salient, and/or regularly occurring for the teachers in their teaching contexts. I then asked
how representative those challenges were of the ones that the participating teachers
experienced each day in their teaching and whether there were others that had not arisen
during our discussions.

I also asked each participant about the resources they had for dealing with the
challenges they encountered and whether those resources were meeting their needs. I also
asked how well they felt that the graduate program had prepared them for teaching.
Throughout this conversation, I referred back to the challenges and resources that
teachers mentioned during the first interview, if the teacher mentioned them again or
mentioned a related challenge or resource to facilitate making connections among the

various challenges and resources that each teacher mentioned. These questions were

72

designed to determine which resources teachers found most helpful in meeting their

challenges and where they judged such resources were lacking.

Data Analysis

Before beginning the analysis, as mentioned above, I transcribed verbatim each
participant’s interview audiotapes, summarizing events not directly related to the
interviews, like small talk at the beginning of the interview, an announcement over the
loudspeaker, interruptions by students, parents, colleagues, or administrators, etc. If the
conversation following such events related to our discussions of the sources of teacher
stress, I transcribed those events; otherwise, I summarized those portions of our

conversations, as well.

Coding analysis: Research question I.

As a reminder, my first research question asks “What sources of teacher stress do
novice secondary and middle school mathematics teachers who have exhibited some
elements of Standards-based teaching experience in their teaching?”

To answer my first research question (and to later help answer my second and
third research questions), I reviewed the interviews for any mention of sources of
teaching stress by each participant, as previously described. I broke out challenges
reported by each participant from the interview transcripts as “chunks” of information.
These data chunks were from one sentence to several pages long and could include one or

several interviewer and participant “turns” talking, as long as the participant stayed on the

73

topic of the same challenge. I summarized each of those data chunks in a short sentence
at the top of each data chunk in the file to facilitate analyzing the data.

As a reminder, my definition of teacher stress is “the psychological state resulting
from teachers’ perceptions of teaching related events as demanding, challenging, and/or
frustrating,” which are also mediated by the personality of and the coping resources
utilized by each teacher.

I operationalized my definition of teacher stress using teachers’ statements that
they found something challenging for them or that it was accompanied by negative affect.

In my analysis, some of the words in a data chunk that indicated that a situation or
event was challenging for the teacher included the following: hard, difficult, stress,
challenge, etc. Other words were not strong enough to meet this condition. For example,
words like “issue” did not clearly indicate stress to me.

Some of the words that indicated that a situation or event was accompanied by
negative affect included the following: hate, frustrate, disappoint, bother, peeve, irritate,
annoy, etc. Words like “concerned” were not strong enough to indicate negative emotion
in this analysis.

Also, I judged that a negative description of an event indicated negative affect as
well, such as “a bad thing” or my sixth hour class is “out of control.” Words like “an
unusual situation” were not strong enough to be considered a negative description.

During the first pass at the data analysis, however, I collected a broader array of
data chunks to look at before giving my definition of teacher stress such precision. As a
result, I looked for any words that might be considered as indications of stress, qualify as

negative emotion and/or negative descriptions of an event or situation, or express a

74

In

participant’s unmet teaching goal(s). In this first rough pass at the data, I gathered all of
the examples and non-examples listed above, including those using wording to weak to
be considered as stress under my operationalized definition. For example, an unmet
teaching goal that I captured in the first pass at the data was subsequently removed from
the analysis, because I judged that it was not strong enough to be categorized as a
teaching stress. Ms. Grant’s assertion that “good lessons are a combination of a lot of
things, and I feel like I don’t have that opportunity at this school” (Ms. Grant, Pre, 5.25-
5.41) is a non-example of teacher stress, because Ms. Grant used words like “issue” and
“concern.” So this passage was included in my first pass at the data, but was removed
during my second pass.

In sharpening my operationalized definition of teacher stress to the one previously
described, I eliminated nearly all non-examples from the list; however, for those
statements that used wording that I considered borderline in describing a stress or
difficulty, such as “concern” or “issue,” I looked to see if there were other data chunks
that identified that event or situation as a source of stress. If so, I felt that there was
justification to say that those more modest wordings in the data chunks identified and
elaborated on a teacher’s sources of stress, so I kept those data chunks into the file with
the sources of stress, rather than removing them.

I also removed all data chunks that talked about unmet teaching goals from the list
of sources of teaching stress that did not explicitly use words that identified them as
stressful events or situations (or did not include borderline words and have other stresses
in that category in the final analysis) and placed them into a separate list. In other words,

the two lists, teaching stresses and unmet teaching goals, are mutually exclusive. If a data

75

chunk qualified for both lists, it remained in the list of data chunks describing sources of
teacher stress only; otherwise, it was placed in a file for data chunks relating to unmet
teaching goals that were not clearly sources of stress for that teacher.

I created the list of data chunks on unmet teaching goals, because previous studies
(e.g., Lewis 2004) have suggested that one of teachers’ most important priorities is to be
able to teach in ways congruent with their teaching beliefs. Teachers often experience
unmet teaching goals as stressful. Although these teachers did not always talk about their
unmet goals as being stressful to them, I wanted the opportunity to later think about this

data and what it might reveal about the existing data set and the participants’ teaching

 

 

 

 

 

contexts.
Timeline for Experiencing Challenges
P . C‘r'rrrentd
revrous
Program Internship (1 to 2) years (2” 0" 3r )
experiences year teaching year
\ J teachrng
V

Challenges not counted if resolved
before current (2" or 3"!) year teaching

 

 

 

Figure 3. Timelinefor including challenges novices experienced in the analysis.

I alsojudged when each teaching stress occurred. Ifit occurred prior to the

teaching year in which the teacher participated in the study. I placed it in a “past stress”

76

file. If it happened in the current teaching year, I left it in the teaching stress file. If it was
an issue which the teacher reported as a continuing challenge during the first few years of
teaching, I labeled it as a “now and past” stress and placed the data chunk in both the past
and current stress files. The focus of my analyses hereafter will be primarily the current
teacher stress data, but I saved the past stress data as a context in which to view the
current teacher stress data (see Figure 3).

In some cases, it was not possible to completely separate two sources of teaching
stress; yet, if it was clear that there was at least one sentence in the data chunk where the
participant was talking about each source separately, I coded the chunk under both
categories. If there was a single source of stress related to two or more different
categories of sources of stress and I could not find separate passages discussing the
distinct sources or the stress appeared to be more strongly related to one source category
than another, I revised the category definitions, so that that data chunk would fit into a
single category. For example, in the following passage, notice that the teacher talks about
a source of stress that might qualify in two categories, Challenges associated with

mofessional development and After hours work/long hours.

Ms. B: The first year, we had two days required at the beginning of the
year, kind of inservice type days that... the novice teachers were required
to go to. We got to go to [a teambuilding experience]. It was so fun... It
was a really great way to build some camaraderie between the new
teachers. We did problem solving. It was a great experience in team
building and all that stuff. It was great. The next year we came back. And
we weren’t doing [the teambuilding experience], even though every one of
us said, “This is great! We want to do this again next year.” But they
didn’t listen. So right off the bat we were kind of like. .. All of a sudden
we were looking at the calendar of events. And not only are we [not]
doing those two days [of teambuilding], all of a sudden twelve hours got
built in through the year... We still had to do the two days at the

77

beginning of the year doing something else. And then there was this

additional 12 hours tacked on. And I’m like, “That’s huge.” That’s like an

extra day and a half of work, so we went from two to three and a half

days... And it was just, everything that was going on, we got really

frustrated (Post, 9.1-9.15).

Since the professional development was a relatively short-lived event, the source
of stress appeared more aligned with professional development than the amount of time
involved in that activity. I decided to word the categories so that this data chunk landed in
Challenges associated with professional development. I revised the category descriptions
accordingly.

I also ignored interview text, at times, if the participant was momentarily
distracted or taken off topic while continuously discussing the same challenging situation
or event. For example, if we were talking about lack of student engagement in class and
then a student interrupted to ask a question and the teacher talked about that for a few
turns before returning to the original challenge, lack of student engagement, then I
ignored the interruption and the few turns resulting from it. Such events, or at least
portions of those events, were generally paraphrased in the transcripts, so this was
relatively simple to do.

Also, if the teacher talked for several turns about details that did not relate to why
the event or situation was challenging and then continued elaborating on the same topic, I
omitted the irrelevant turns from the text being analyzed, but kept the chunk as a single
chunk still, because the participant had continued to talk about the same challenge during
our conversation. Usually this data was also paraphrased either during transcription or for

the analysis, since oftentimes, such data gave identifying information that would not

ensure the confidentiality of a participant’s and their students’ identities.

78

I separated the challenges participants reported experiencing in the current school
year into coding categories. I initially developed these coding categories during a pilot
study that researched the challenges that a group of interns and novice teachers reported
facing. At first, I began with the categories of (sources of) teaching stress cited in the
teacher and student teacher stress literature based primarily on survey research. Recall
that the most commonly cited (sources of) teaching stress in that literature include the
following: Poor motivation of students, Poor student discipline, Poor working conditimrs,
Time pressure and work overload, Low status and opportunities—includingpay,
flmotion, and career development, Poor school ethos—including conflict with
colleagges and administrators, Beiggobserved and evaluated by universig faculty and
staff, Being observed and evaluated by mentor teacher, and University coursework
concerns (Phillips, 1993; Kyriacou, 1989; Miller & Fraser, 2000; Murray-Harvey et al.,
2000; Hart, 1987).

I then spoke informally with teachers and teacher educators to refine those
categories to also include new sources of teaching stress, including sources related to or
coinciding with attempts at SBT. While analyzing the pilot study data, I further refined
those categories as I reviewed and coded the data I added several new categories of
sources of teacher stress (Lewis, 2004), including the following: Learning to teach in new
vLays, Challenges associated with professional development, Learning and teaching
unfamiliar content, Preparing students for stan_d_ardized tests, Working with technology,
and Managing classroom discussions.

For this study, I eliminated sources of teaching stress related exclusively to the

student teaching/internship experience, namely Beingobserved and evaluated by

79

university faculty and staff, Beigg observed and evaluated by mentor teacher, and

University courseworlgoncems (Miller & Fraser, 2000; Murray-Harvey et al., 2000;

Hart, 1987). I then added to and refined the existing categories in the literature, including

from my own pilot study (Lewis, 2004) similar to the open coding method described by

Glaser and Strauss (1967). In other words, the coding for this study employs an educated

“top-down” method, based on the existing codes in the literature and adding to and

refining those codes as the analysis continued during my pilot and, currently, my

dissertation study. My analysis yielded the 22 categories of sources of teacher stress that

are named and defined in Table 3 that follows. Appendix B names and defines the list of

categories of the sources of teacher stress, but also illustrates each category with a teacher

example.

Table 3

Teacher Stress Coding Category Titles and Definitions

 

 

 

 

 

 

Code title Code definition

Managing Stresses deriving from teachers’ attempts to involve students

classroom actively in classroom discussions and contribute ideas that the

discussions teacher anticipates or hopes to solicit to that discussion, while the
teacher primarily acts as a facilitator for the discussion. (If the
teacher has difficulty getting students to participate in conversation
and calls it a shared problem or it is unclear why they do not
participate, it belongs in this category. If the teacher characterizes
them as resisting participation or lacking interest, put it in Lack of
student interest/motivation.)

Responding to Stresses deriving from teachers’ attempts to engage with and pursue

unexpected unexpected student ideas offered during classroom discussions.

student ideas

Creating, Stresses deriving from teachers’ attempts to organize, create,

aligning, modify, and implement the school’s chosen curriculum, or to align it

modifying, or with the NCTM Standards or Michigan’s State Standards. These

implementing stresses include how well the chosen textbook or curriculum fits the

curricula teacher’s pedagogical goals.

 

80

 

Table 3 (continued)

 

Directing
students’
explorations of
mathematics

Stresses deriving from engaging students in activities where they
explored, alone or in pairs or small groups, a problem or situation.
(If the teacher characterizes students as not participating and
describes it as a shared problem or does not explain why they do not
participate, place it here; otherwise, if the teacher characterizes it as
student lack of interest or resistance to participation, place it under
Lack of student interest/motivation.)

 

Working with
technology

Stresses deriving from teachers’ attempts to integrate technology
into the curriculum. These stresses could be related to the pedagogy
they wished to employ, the time that teaching students how to use
technology took, the lack of availability of resources to perform
such teaching, or the teacher’s lack of knowledge about the
technology that they wished to employ.

 

Relationships
and
communications
with colleagues

Stresses deriving from teachers’ interactions with their peers. Such
stresses often related to differences in beliefs about classroom
management or “teaching style,” including pedagogical, teacher
collaboration, and classroom management issues.

 

Lack of student
interest /
motivation

Stresses deriving from teachers’ attempts to engage students in their
lessons and/or students’ resistance to engaging in those lessons,
whether their resistance took the form of avoiding any participation
or whether they avoided meaningful, rather than superficial,
engagement. (If it is clear that chattiness is slowing students’ or the
class’ progress, it was coded here; otherwise, it was coded as
Respondiggto problematic student behaviors.)

 

Learning and
teaching
unfamiliar
content

Stresses deriving from teachers’ attempts to teach content that they
had either never seen before (e.g., graph theory or statistics), had not
seen recently (e.g., geometry), or had had limited opportunities to
learn (e.g., calculus).

 

Planning lessons

Stresses deriving from teachers’ attempts to prepare individual
lessons. Sometimes this involved creating or adapting existing
lessons to their curricular objectives. (If the stress related to tailoring
lessons for students of varying ability levels, it was placed in the
Teaching students of varyigg ability levels category. If teachers
related planning interesting lessons to lack of student motivation, it
went in Lack of student interest/motivation; otherwise, it goes here)

 

 

Responding to
problematic
student behaviors

 

Stresses deriving from teachers’ attempts to deal with student
behaviors that were inappropriate for the classroom or irritating to
the teacher, such as loud or excessive talking, disrespectful remarks
to the teacher or other students, whining about an assignment or
lesson, etc. (If the teacher says that the talking or chattiness is
delaying progress or occurs while the teacher or other students
talking to the class, it was coded as Lack of student interest /
motivation. If the issue is talked about generally or the timing is
unclear, this is the default code.)

 

81

 

Table 3 (continued)

 

Finding and
utilizing
resources

Stresses deriving fi'om teachers’ attempts to find physical,
curricular, or human resources to meet their pedagogical goals.
Often these involved Internet and library searches that met with
limited or low rates of success, or unsuccessfirlly trying to get the
students to be resources for each other.

 

After hours work

Stresses deriving from teachers’ attempts to manage extracurricular

 

 

 

 

 

/ long hours work hours so that they could complete their preparation and
grading for their classes and think about management issues, while
also attempting to have a personal life outside of school. (If
professional development took a lot of time, it was still coded as
Challenges associated with grofessional development.)

Challenges Stresses deriving from teachers’ feeling about the adequacy of their

associated with professional development experiences. At times, this frustration

professional related to the number of hours required by the state in which they

development taught. At other times, it related to the school- or district-provided
professional development experiences which they viewed as
maladapted or inadequate to their needs. (If professional
development took a lot of time, it was still coded as Challenges
associated with grofessional development.)

Student diversity Stresses deriving from teachers’ attempts to relate to and involve all

issues students, including students’ whose racial, linguistic, or ethnic
background was different from the teacher’s or some of their peers.

Dealing with Stresses deriving from teachers’ attempts to deal with the challenges

class length, related to the length of class periods, the pace at which they felt

pace, or schedule

obliged to teach due to an agreed upon teaching curriculum or
schedule, or the demands of their particular schedule, including the
number of preps, types of classes, room changes, or unexpected
events like fire drills, team practices or competitions, assemblies.
(Pace issues related to Teaching students of varying ability levels
were placed in that category instead of here. Pace issues related to a
test given in all sections of a course in the school were placed in
PreparigLfor, administering. and evaluating standardized tests
instead of here.)

 

Assessing
student
understanding

Stresses deriving from trying to assess whether students understand
the mathematics that they are learning, whether formally or
informally. This category does not included standardized tests, as
defined in Preparing for, administering, and evaluating standardized
t_e_s_t_s category.

 

 

Preparing for,
administering,
and evaluating
standardized
tests

 

Stresses deriving from teachers’ attempts to prepare students for
standardized tests, including modifying lesson plans and curriculum,
administering those tests, evaluating the tests where applicable, and
determining how to utilize feedback from those tests to inform one’s
teaching. Such tests included F ederal- and State-mandated tests, as
well as school- or district-created and/or -mandated tests.

 

82

 

Table 3 (continued)

 

 

Teaching Stresses deriving from teachers’ attempts to effectively teach
students of students with a variety of perceived or measured ability levels
varying ability within a single class.

levels

Relationships Stresses deriving from teachers’ interactions with parents. Often,
and these stressful events involved parental disapproval of the teacher’s
communications responses to student misbehaviors or the parent’s reaction to their
with parents child’s low grades.

 

Teacher boredom Stresses deriving from trying to deal with one’s own boredom while
teaching when the content, lesson format, or students were not
particularly engaging for the teacher. These stresses could be short—
lived or persistent.

 

 

 

 

 

Relationships Stresses deriving from administrators’ decisions that made the

and working environment less comfortable for the teacher or from
communications teachers’ attempts to enlist administrators help with classroom
with management, professional development, and pedagogical concerns.
administrators

Relationships Stresses deriving from maintaining or lacking relationships with
and students.

communications

with students

 

While there is overlap between these categories, I attempted to define the
categories in ways that would allow for as little overlap as possible. I did this by
identifying and listing chunks of data that were difficult to code. One file listed chunks of
data where the code was “unclear.” Another file listed chunks where there appeared to be
two or more “intertwined” codes that could not be easily separated into distinct “chunks”
of data. I looked at each data chunk for which the coding was unclear. If there was no
existing category for the particular “chunk” of data, it was placed into a newly invented
“Other” category, like Other: Controlling emotions which talks about the challenges of a
teacher who couldn’t return to her classroom after an intense encounter with a parent. I
eventually turned each “Other” category into its own category or melded that data in with

the existing categories, possibly revising their definitions to include the new data

83

chunk(s). For example, the Other: Controlling emotions category involved a single
participant and described the aftermath of a parent confrontation, so I placed that data
chunk under Relationshfis and communications with parents and eliminated the Q_th_q;
Controllirg emotions category.

In order to determine the sources of teaching stress that were more salient or
meaningful to participants, I judged the categories of challenges that appeared to be
“main” (i.e. having a meaningful and significant impact) or simply “mention ” (i.e. not
having a particularly meaningful or significant impact, but still mentioned by the
participant) by looking at several different variables, each of which on its own suggested
that the participant may have perceived the situation or event as a meaningful or salient
challenge.

First, I looked for “repetition within” a single interview for each category, i.e.
whether the source of stress was mentioned in more than one chunk within a single
interview for each category. In other words, I looked at whether the participant returned
to discuss the topic again after we discussed another topic. Such repetition suggested that
the teacher may have been emphasizing such events as meaningful.

I looked for “repetition between” the two interviews, or whether the source of
stress was mentioned in both interviews. This type of repetition seemed to show a
consistent concern for such events across our interviews, so this also seemed to be a
reason to identify such events as potentially meaningful for the teacher.

I looked for how much “detail” the participant used in describing the event as an
indicator of that challenge. Because detail in describing an event or situation can often

identify when one is troubled by or has thought a great deal about the event, detail may

84

reflect an event’s importance to the teacher. If the participant used at least three phrases
detailing—not merely naming—a particular challenge, I considered that to meet my
criterion for using detail in that particular instance.

I also looked for the use of “magnitude words” in each interview, namely, I
looked for words that indicated the magnitude of the challenges the teacher was facing or
that related to strong feelings the participant was having about those challenges, like that
is a “huge problem,” or “that was {guy frustrating.” The use of such words appears to
denote the salience of difficulties or negative emotions on the part of the teacher related
to those challenges. I also noted when the teachers used dismissive words when referring
to their teaching challenges. If the participant used dismissive wording, like “but that
really isn’t that big of a deal for me” or “it used to be really frustrating to me, but not
anymore,” I coded that as canceling one use of magnitude words about that specific data
chunk if magnitude words were used, or to cancel the entire statement that the event or
situation was challenging if magnitude words were not used.

I looked for the participant’s own choice of a “top stress,” if that surfaced in the
interview. I generally asked each participant to name her top challenge or stress. I
considered it significant if a participant used wording to identify one source of stress in
particular. Clearly, if a participant meets this criterion, they also meet the criterion for
using magnitude words simultaneously. This gives more weight to this criterion, which
appears to help in accurately reflecting participants’ perceptions of their most salient and
important challenges.

Finally, I judged each participant in the five aforementioned criteria for each

category of sources of stress. If a category for a particular participant met the criteria in at

85

least three of the above categories (i.e. repetition within, repetition between, detail,
magnitude words, and top stress), I considered that category to be a “main” source of
teaching stress, or one that was particularly salient and meaningful for the participant. If
the category met two or fewer of those criteria, I considered it to be a “mentioned” source
of teaching stress, or one that was less salient or less meaningful to the participant.
While the choice of the number of criteria that distinguished a “main” from a
“mentioned” source of stress was difficult, I wanted a way to judge which categories of
sources of stress appeared the most meaningful and salient for the participants. I could
picture a participant meeting two of the criteria for a “main” source of stress without it
being particularly meaningful for them. For example, using “repetition between” and
“repetition within” for one coding category may signify events that occur relatively
frequently but are merely a minor irritation. But I had a more difficult time picturing a
challenge as a minor irritation or a relatively insignificant concern if it met three or more
of those criteria. On the other hand, requiring that participants meet four of the criteria
seemed too high, because, for example, if the participant did not name a source of stress
as their top challenge, that challenge would have to meet every other criteria to be
considered a main source of stress. That seemed like an exceptionally high standard. So
meeting three criteria seemed like a reasonable bar for judging whether each source of

stress was “main” or simply “mentioned.”

Coding analysis: Research question 2a.

Research question 2a asks “Which of those sources of teaching stress are

predicted by the existing literature and which are new to the literature?”

86

I returned to the research literature on teacher stress to determine whether the
sources of stress that I had found related to those categories. Several clearly related to
that list, such as Responding to student misbehaviors and Lack of student
interest/motivation, while others did not, such as Working with technology and Preparing
for, administering, and evaluating standardized tests. I elaborate more on the results of

this analysis in the Results chapter of this study.

Coding analysis: Research question 2b.

Research question 2b asks “Which sources of teaching stress are related to their
attempts at Standards-based teaching and how are they related?

To answer the second half of my second research question, I returned to the raw
data, searching for any evidence of non-trivial attempts at SBT in all of the categories of
sources of teacher stress. I read participant reports in the interview transcripts, read the
participants’ journals, and watched the participants’ videotapes, where the videotapes
gave me information about a classroom event to which the teacher was referring. For
each chunk from the interview data for which there was sufficient evidence, I listed the
NCTM (1991) Teaching Standard(s) that the teacher, students, activity, or situation met
that related to challenge(s) reported and/or observed in that chunk of data. Of course, in
some cases no Standard applied explicitly enough, so that the data chunk needed to be
dismissed, while in other situations, one or more Standard(s) applied to the teacher’s
actions, students’ actions, chosen classroom activity, or teaching situation. Because the
Teaching Standards are not a mutually exclusive list of categories, but overlap and

interrelate, the focus of this analysis was primarily to find out whether an event met a

87

particular Teaching Standard. I do not pretend that the list of the Standards met is in any
way exact or exhaustive, simply that the specific Standard(s) listed were met in each
event. They could easily be interpreted as meeting a different Standard(s) by another
researcher, but I believe that the judgment as to whether or not they relate to attempts at
SBT would be very similar.

While some of the categories of sources of stress referenced the Teaching
Standards, there were three in particular that appeared directly related to teaching actions
referenced by the Standards and were often, if not always, related to those actions,
namely Managing classroom discussions, Responding to unexpected student ideas, and
Directing student-led explorations of mathematics.

Managing classroom discussions describes the process of trying to actively
involve students in the discourse of the classroom. While some of these processes could
be considered less central to discourse than to asking for answers, the act of trying to
have a discussion with students is a central aspect of creating discourse. For this reason,
this category is included as one of the three that I describe as being centrally related to
SBT.

Responding to unexpected student ideas is clearly a special case of the above
category that was separated out in the course of defining specific categories. Because
teachers found it challenging to engage with the unexpected student ideas that surfaced
during discussions, but only reported those experiences as stressful when they attempted
to engage with the unexpected comments, this category of teacher stress appears directly

related to the Teaching Standards, as well.

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Finally, Directingstudent-led explorations of mathematics is another category
directly related to the Teaching Standards. Because such explorations involve students
actively pursuing mathematical knowledge independently, it appeared that the students
would most often be constructing mathematical ideas and formulating conjectures
independently during such activities. There were very few exceptions to this premise in
the data, as well.

There were also other categories for which one might imagine a connection to the
Teaching Standards, but in the data, no such connection was found. These categories
include the following: Relationships and communications with students, Teachimg
students of ng ability levels, Relationships and communications with parents,
Preparinfir, administering, and evaluat'mg standardized tests, Teacher boredom,
Challe_nges associated with professional development, and Relationships and
communications with administrators.

Finally, the remaining 12 of the 22 categories were inconsistently related to
Standards-based teaching. They were not necessarily directly linked to the NCTM (1991)
Professional standards for teaching mathematics in the way that they were defined, but
they did intersect at times with teaching attempts consonant with that document. An
example of such a category includes Working with technology. While the fourth
Teaching Standard, “Using tools to enhance discourse” describes the importance of using
technology in this process, it was not always clear that teachers would be using
technology in ways other than to check answers or to make arithmetic calculations less
burdensome on assignments. For this reason, I was not comfortable classifying this

category as directly related to the Teaching Standards. On the other hand, there was data

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in my data set that indicated that Ms. Grant used calculators to facilitate classroom
discourse.

Another example is the category Finding and utilizirg resources. While at least
one teacher, Ms. Grant, did seek activities involving classroom discourse online, it is easy
to imagine a teacher who simply was looking for resources like technology, textbooks,
paper, access to a photocopier, etc. that at times are challenging for urban teachers
(Farber, 1984; Abel & Sewell, 1999), so that I felt confident listing this as possibly, but
not directly, related to SBT attempts. There were other categories that the teachers did not
explicitly connect in any way to those attempts during the interviews.

In determining whether attempts to teach according to the NCTM (1991)
Teaching Standards was a salient component of their sources of teaching stress overall, I
decided that if at least half of a teacher’s main sources of stress or at least half of all of
the teacher’s non-empty categories of sources of stress related to the NCTM Teaching
Standards, then attempts at SBT were a salient component of the sources of stress that the
teacher experienced. I later eliminated the second half of this criterion, so that at least
half of each teacher’s main sources of stress indicated that such attempts were a salient
component of their sources of teaching stress, because this simpler criterion yielded the

same results as the more complex one.

Coding analysis: Research question 3.
Research question 3 asks “What sort of impact do the sources of teaching stress
that novice teachers experiences have on them, i.e. do they judge them to be facilitative,

neutral, or debilitative?”

9O

The data that I collected for this research question was modest, because teachers
struggled to engage with the ideas of constructive, neutral, and debilitative sources of
teaching stress. I sorted this data into the categories of sources of teaching stress as
mentioned above and identified how the teacher describe each source, whether it was a

constructive, neutral, or debilitative force in their teaching environment.

Coding analysis: Research question 4.

Research question 4 asks “What coping resources do novice teachers utilize to
mediate the teaching stresses deriving from the different sources of teaching stress that
they experience?”

To answer the fourth research question, I need to digress to a discussion of the
literature before describing my definitions and conceptual definitions and proceeding.
Lazarus (1966, 1976) describes the general methods of coping with stress as two types:
direct action and palliation. Direct action involves actual behavior aimed at changing the
person’s relationship to their environment and includes preparation for harm, aggression,
and avoidance. Preparation for harm includes acting to reduce the actual danger (such as
studying intensely for a final exam) or its threat value (such as denying the importance or
fairness of the final exam, working harder at other assignments to offset the anticipated
detriment to one’s grade, etc.). Aggression involves acting aggressively towards a target
that allows a release of tension, which may simply be a target that is more vulnerable
rather than the actual cause of the stress. Avoidance involves finding a means of escape
from a stressful situation, rather than acting in ways that could alleviate or eliminate the

stress.

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Palliation, or reducing the impact of stress without acting on its root causes or
modifying the environment, encompasses moderating stress by reducing its
psychophysiological effects. This can be achieved through symptom-directed or intra-
psychic modes. Symptom-directed modes include using alcohol, prescription or non-
prescription drugs, training in muscle relaxation, and other body-centered techniques.
Intrapsychic methods describes cognitive defense mechanisms, including identification,
displacement, repression, denial, reaction formation, projection, and intellectualization.

Kyriacou (1981) gives a definition similar to Lazarus’ (1966, 1976) in describing
stress, but as it relates more specifically to teaching; however, Kyriacou also points out
that means of mediating such stresses might also be external to the teacher. My definition
expands Lazarus’ and Kyriacou’s definitions to include the proactive strategies that
teachers employ to eliminate, alleviate, or avoid stress altogether, rather than the slightly
Lazarus’ slightly narrower category or preparing for harm; such proactive strategies
include planning lessons that will better engage students in classroom activities, actively
working to strengthen relationships with their students, etc. Such constructive activities
also assert teachers’ and students’ shared responsibility in promoting a classroom
environment conducive to learning, as well as emphasizing the personal power that
teachers have as agents of change in the face of the challenges that they encounter. I
define coping resources more specifically as means of avoiding, alleviating, or
eliminating teaching stress.

During the interviews when teachers spoke about teaching resources, I mostly
heard teachers share direct actions that alleviated or avoided, stress. Only occasionally

did I hear about teachers using intrapsychic methods to reduce their teaching stresses, as

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my interviews were not structured to explore any specific category of teaching resources
directly, unless such information was volunteered by the participant. For example, no
teacher mentioned symptom-directed means for dealing with stress, like exercise,
meditation, alcohol, etc. So my definition focuses more on the direct actions, intrapsychic
methods, and physical and social resources (including external interventions) that I was
more likely to hear discussed by the teachers during our interviews.

In creating my own categories of coping resources for teacher stress, I looked at
all of the teaching resources that teachers shared with me, whether internal or external to
the teacher, in the context of the observations and interviews. For me, a teaching resource
is a physical or virtual (as in Internet) asset, social interaction or intervention, strategy,
idea, or psychological technique that had the potential to help the teacher be more
effective or comfortable in the act of teaching. It is also important to mention that here I
am defining teaching broadly, as all acts and thinking related to classroom teaching,
regardless of where or when those actions or thoughts took place, so the teacher might be
planning at home, creating curriculum with other teachers after school, or grading at the
library on the weekends, but in my definition, those are all construed as acts comprising
the act of teaching.

I used the grounded or open coding method described by Glaser and Strauss
(1966, 1976), similar to the methods that I employed in coding my teaching stress data
for these participants; however, for the teacher coping resources, the literature is much
less complete. As a result, this analysis was closer to being a truly open coding method or
more grounded in the actual coping resources data than was the teacher stress data

analysis.

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As a result of employing this grounded coding of the data, I found that the data
fell into four general coding categories, as follows: Social, Self, Collective, and Physical
coping resources. In beginning this analysis, I looked for all of the teaching resources that
participants reported, then I narrowed that list of resources to only those that teachers
directly linked as using in an attempt to alleviate their teaching stresses. If the teacher
said that s/he generally employed a teaching resource to alleviate stress without
elaborating on which specific categories of stress s/he meant, I judged that that coping
resource alleviated “GENERAL” stresses, a miscellaneous category that I introduced
only for the coping resources analysis.

Teachers’ coping mechanisms always involved the use of teaching resources, if
the teacher is considered as their own potential resource. Like Kyriacou (1981), I too
believe that people and resources external to the teaching environment can influence
teachers’ experiences of stress. These people and resources can inspire the teacher to
actions. The people can also take action themselves to reduce or eliminate stress (as when
a principal reprimands a student or permanently switches them to another teacher’s
class). Therefore, in summary, the actions that the teacher takes depend on the teacher’s
own thoughts and ideas, the thoughts, ideas, and supportive words or actions of others
(such as a spouse, professional colleagues, administrators, friends, relatives, etc.) and/or
the physical resources that they find that help them to deal with or alleviate those
challenges (such as books, the Internet, hands on materials, manipulatives, calculators,
etc.). I attend to these categories of coping resources in this analysis.

Coping resources take the form of physical assets, social relationships, or self as

means of dealing with, avoiding, or alleviating stress, whether targeted at the symptoms

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or sources of that stress, including changing the classroom context or the teacher’s
perceptions of or relationship to it.

I will give a few examples of these categories of resources. When faced with
challenging student behaviors, a teacher might vent to his/her spouse or colleagues or
shrug off stresses, like saying “Oh, they’re just kids and that’s how kids are.” Such
mechanisms are aimed primarily at dealing with the aftermath of stressful events. The
first, venting to a spouse or colleague, would be using social relationships to deal with
those events. The second, mentally shrugging off such events uses psychological means
within one’s self to cope with such stresses. On the other hand, asking a colleague for
more engaging classroom lessons or working on more engaging lessons on one’s own
would target problems with lack of student interest/motivation by attempting to change
the classroom context. The former involves the use of social relationships, while the latter
involves the use of self as a resource to alleviate stress.

I operationalize my definition of coping resources as resources for teaching that I
could link to avoiding, alleviating, or eliminating the effects of at least one specific stress
statement from the stress data analysis for that teacher or to their stresses generally.
Because of how I conducted the stress analysis, I only linked these coping resources to
stress(es) from the school year in which the interview was held. Teachers also reported
when some coping resources helped them deal with stress generally, but were not specific
enough to pinpoint an exact stress passage from the stress data analysis.

I define the coping resource of physical assets as artifacts or virtual materials that
the teacher uses to avoid, alleviate, or eliminate stress. These physical materials may take

many forms, but are all external to the teacher, such as the physical arrangement of the

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classroom, textbooks, books about pedagogy or classroom management, using the
Internet as a source of other teacher’s lessons or software, graphing calculators, hands on
materials, manipulatives that make one’s teaching more interesting to the students, etc. I
operationalize the definition of physical assets as a teacher statement of a coping resource
that primarily emphasizes finding and using physical materials in order to deal with one’s
teaching stresses. When I say “primarily emphasizes,” I refer to the subjective aspect of
this analysis that is difficult to reduce. I will say more about this later, after discussing the
remaining subcategories of coping resources.

I define the coping resource of social relationships as communications with or
actions taken by another person or persons about one’s teaching (as l have broadly
defined “teaching”) to avoid, alleviate, or eliminate stress. That communication may take
the form of venting, asking for and receiving advice about pedagogy or classroom
management, creating curriculum, inciting the other participant to intervene in your
classroom, etc. I operationalize the definition of social relationships in two separate
categories. First, I defrne social resources as a teacher statement describing
communication(s) to another teacher or teachers where the teacher emphasizes his/her
role in asking for and receiving help, whether that help allows the teacher to vent about
the stress or whether the teacher seeks advice about how to deal with the situation
causing that stress. Second, I define collective resources as a teacher statement describing
communication(s) to another teacher or teachers where the teacher emphasizes himself or
herself as an active participant in a community of at least three people that meets on a
regular or ongoing basis to work on curriculum, pedagogy, or other salient teaching

issues. So collective resources are never dyadic in the data, while social resources may or

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may not be. What distinguishes the two categories when three or more people (including
the participant) are involved is the regular, ongoing, and purposeful nature of the work
(rather than just venting, for example), as described by the participant.

I define the coping resource of self as using one’s self as a resource, including
thought patterns and creative processes to avoid, alleviate, or eliminate stress. The
resource of self includes such activities as intrapsychic methods (reassuring self,
justifying or interpreting events, etc.), creating or modifying lesson plans, coming up with
new ideas about how to deal with students’ behaviors, etc. I operationalize the definition
of the Self coping resources as a teacher resource statement that primarily emphasizes
using intrapsychic methods or one’s own creative abilities as means of dealing with one’s
teaching stresses.

Admittedly, the “self” category could be thought of as the default category, since
teachers may have initially found a coping resource through social means or as physical
assets and then integrated them into their teaching, so that now they describe them as
their own. This process of appropriation and integration is subtle. Since these teachers are
novices, this phenomenon is less likely to be a problem than for more experienced
teachers, but that possibility does need formal acknowledgement. As a result, it also
seems appropriate to include coping resources in this category where the source is
unclear, since ultimately it is the self that decides whether, how, and to what extent to
implement such ideas in the classroom (McLaughlin, 1987).

Also, when I say “primarily emphasizes” for each category, I would like to clarify
that there was overlap in the data Some passages involved more than one of the four

categories, but I looked to see if there was a salient resource in each. For example, when

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talking about physical assets, if those materials were already in existence, I coded the
teaching resource as being a physical asset. In other words, if a colleague gave the novice
a worksheet that helped alleviate stresses related to Lesson plann'mg or Lack of student

interest/motivation, I coded that coping resource as Physical, because the worksheet (not

 

the colleague) was the primary resource that acted to alleviate the stress.

If the teacher or others were acting to create the physical assets (for example, a
student exploration activity), I coded it under Self, Social, or Collective, depending on
which code applied, because the act of creation appeared to me to be the salient aspect of
the coping resource. If self intersected with social or collective, I generally judged the
resources to be social or collective resources, since self can generally be considered as a
part of those resources, as well.

In summary, to code for RQ4a, I looked at all of the interviews and coded any
teaching resources (including teaching strategies that could be considered a resource) that
the participant mentioned. In looking for teaching resources, I first reviewed the passages
in the teacher stress data analysis; then, I returned to the original interviews and further
expanded the data set, adding new teaching resource passages or modifying existing
passages to include more of the teacher’s words that made it clearer what teaching
resource was used and how effectively. At times passages contained more than one
teaching resource, so I gave each teaching resource in the passage its own line in the data
analysis table.

After finding a preliminary list of teaching resources, I looked in the teacher stress
data to see whether the teacher mentioned specific stress(es) related to each coping

resource. If the participant mentioned a stress in the stress data analysis (or mentioned

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that the teaching resource helped avoid, alleviate, or eliminate stress in general), then that
teaching resource was judged to be a coping resource. If I could not find a stress that the
teacher had mentioned that related to the specific teaching resource, then I eliminated that
teaching resource from the coping resources analysis. I also kept track of teaching
resources that related to stresses participants had experienced in the past that I had noted,
but not included, in the stress data analysis. Although I kept track of them, they were not
included, in the coping resources data analysis. The frequency with which such mentions
were made by the teacher in the coping resources passage is denoted by T in Table 4.

At times, the connections between the coping resource and teaching stress(es)
were clear, because the passage from the coping resources data overlapped or nearly
overlapped with the stress analysis data, so the connection was clear and unquestionable
(i.e. the teacher had made the connection during the interview). At other times where
there was not a clear and compelling link, as the researcher, I had to look for possible
links between the stress data and the teaching resources data based on the information in
the teaching resource passage and judge whether the teacher resource appeared to
alleviate a teacher stress in the analysis, retaining only those teaching resources as coping
resources that met that standard. The frequency with which the researcher found related
stresses in the stress data and judged them to be related to the coping resource is denoted
by R in Table 4.

For example, Ms. Riley mentioned that she talks to her mentor when she needs
help with the content in her Algebra 2 class (Ms. R, Pre, 7.35-8.39). Notice that Ms.
Riley’s comment about the teaching challenge that her mentor was helping her with in

this passage are not strongly stated (i.e. “needs help” was not considered to be a

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statement of stress for the purposes of my analysis, although the potential for causing
stress is clear). But in the stress data analysis, I noticed that she spoke more specifically
about her challenges with the Algebra 2 content at the beginning of the year, explaining
that she couldn’t remember the content well at first. She said, “At first, I was really
scared. I thought [the content of Algebra 2] was really hard” (Ms. R, Pre, 6.6). As a
result, I judged that that specific passage in Ms. Riley’s coping resource analysis should

be retained, since it dealt with a stress passage present in the stress data analysis.

Table 4

Identifying Source of Stress-C oping Links

 

 

 

 

 

 

 

 

 

Researcher
Participant Teacher Researcher Total percentage_

Ms. Boone 3 19 22 86.4%
Ms. Grant 5 l I 16 68.8%
Mr. Jones 15 l l 26 42.3%
Ms. Riley 5 7 12 58.3%
Ms. Price 10 IO 20 50.0%
Ms. Wells 15 7 22 31.8%
Total 53 65 118 55.1%

 

 

 

 

 

 

Note. This table indicates the frequency with which the teacher (T) or the researcher (R) linked each coping
resource with a specific stress or stresses that it alleviated.

In Table 4, notice that more than half of these links between statements of coping
resources overall were made by the researcher. Half or more of the links were made by
the researcher in 4 of the 6 cases, as well. While this number may seem high, the reader
may also recall that the researcher had to have at least some evidence from the coping
resource passages before looking for passages in the stress analysis data So this is clearly
an indication of researcher involvement in creating links in the analysis between these

two data sets, but does not necessarily do great damage to the validity of the results;

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however, I did want to acknowledge the frequency of this process and expose the process
to closer scrutiny.

In judging how successful these resources were at modifying the teachers’
teaching environments or situations to help alleviate teachers’ stresses, I looked at
whether the participants talked about the stress alleviation directly, or whether they talked
about the resources using strongly positive (“helpful” or “cool”), moderately positive
(“pretty good,” “okay,” or it works “sometimes”), or negative (“not really helpful” or “it
still happens,” respectively) language. If the teacher used strongly positive language to
describe the stress, I judged that the stress was successfully alleviated and rated the
participant statement as Y (for Yes). I judged that moderately positive language indicated
that stress was somewhat alleviated and rated it as S (for Somewhat). Finally, I judged
that negative language indicated that the stress was not alleviated to a meaningful degree
for the teacher and rated it as N (for No).

If such language was not present, I looked at the resource to see if I could judge
whether it even had the potential of being effective. If the teacher avoided the stress (like
“I bailed” on the problem or “I’ve decided not to teach that anymore”), I judged that the
attempt was not successful at alleviating the stress (at least not directly), because it
avoided the root cause of the stress. If it was unclear whether the stress was effectively
mediated, I judged the coping resource’s success in alleviating stress as “unclear” (or U).

I looked at the results in each category for each participant. In each case, I looked
at the collection of all effectiveness ratings (Y, S, N, or U), ignoring the U judgments. I
counted Y as H, S as 0, and N as -1. For the judgments of each category for each

individual participant, I placed the lower boundary at +0.5 for effectiveness and the upper

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boundary at -0.5 for ineffectiveness, inclusive of the endpoints when determining the
effectiveness of coping resources for each stress category; therefore, the range for
somewhat effective coping resources for individual participants’ stresses was (-0.5, +0.5).

To explain, I chose these cutoffs for the coping resources in each individual
teacher stress categories, because it generally meant that if there were two adjacent
effectiveness ratings that the students chose (i.e. Y [effective] and S [somewhat
effective]), the most frequent one would be chosen. That seemed to match what the
teachers were emphasizing in their speech patterns. While teacher ratings generally
included similar ratings for coping resources within a single stress category, I also
noticed that there were two instances where a teacher rated coping resources related to a
single stress category as Y or N (but not S). Those two teachers’ were Mr. Jones for
Respondiflto problematic student behaviors and Ms. Riley for Managing classroom
discussions. While it could be stressful for him and at times his resources were
ineffective, overall Mr. Jones said that he had sufficient resources for Responding to
problematic student behaviors and that he had it “under control.” On the other hand, Ms.
Riley said that the two situations were anomalies when she dropped a topic and didn’t
return to it (so the resources were judged to be ineffective in those two cases), but that
she generally felt comfortable and effective Managing classroom discussions. But there
was no rule that would have accommodated both of their positions. So I chose to place
both of them in the “Somewhat” category by choosing the +0.5 and -0.5 cutoffs.

I chose to calculate the effectiveness scores for participants’ coping resources
overall (or across all stress categories) somewhat differently. I found the average score

for these entries, then determined the overall score for that category of coping resources

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as follows: effective (Y) if the average is greater than 1/3, somewhat effective (S) if the
average was between -1/3 and +1/3 (including the endpoints), and ineffective (N) if the
average was less than -l/3.

I initially struggled with where to place the cutoffs for effective, somewhat
effective, and ineffective scores for participants’ coping resources. I wanted the cutoffs
symmetric, because the scale that I had created was symmetric. So I considered whether
to place the bar for effectiveness and ineffectiveness of coping resources at +1/3 and -1/3
or +1/2 and -1/2, respectively. Those seemed like two logical places to locate the cutoff,
because the former divided the interval {-1, 1] into three equal parts, while the latter was
a more conservative cutoff, providing only half of a unit for each effectiveness and
ineffectiveness scores for coping resources. The latter cutoffs also coincided with the
cutoffs for the individual categories of teacher stress by participant.

Because Ms. Riley was the only teacher initially in this range, I mainly considered
her data in making this decision. Ms. Riley felt that her new school was providing her
with many of the coping resources that she needed, particularly compared to the school
where she taught the previous year, but also in general. That told me that she needed to
be included with those who I had rated as possessing effective coping resources overall;
therefore, for my calculations to match her own evaluation of the effectiveness of her
coping resources, I needed to place the bar lower than +40 to indicate a successful
transition. As a result, I chose +1/3 and -1/3 as the cutoffs for this judgment.

Because I felt like the +1/3 and -1/3 cutoffs were already quite large for
determining effective and ineffective coping resources, I excluded the endpoints on those

intervals. In other words, the average for ineffective coping resources fell in the [-1, -1/3)

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range, somewhat effective fell in the [-1/3, 1/3] range, and effective fell in the (1/3, 1]
range. I also determined scores for each participant for major stresses and for SBT-related
major stresses. Those scores were determined using the same algorithm, with cutoffs at

+1/3 and —1/3 and the corresponding intervals of effectiveness previously described.

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Chapter 4: Introduction to Participants and Their Attempts at NCTM Standards-Based

Teaching

In this chapter, I introduce the reader to each participant, including their teaching
contexts, and the classes that I observed during this study. I then talk briefly about the
challenges I encountered while searching for novices who were attempting NCTM (1991)
Standards-based teaching (SBT). This seems important to my study, because I am
interested in this phenomenon, which is the driving force behind many of the new
curricula, teacher education programs, teacher development programs, and teacher
collaboratives across the US. Finally, I describe at least one example of an attempt to
enact elements of the NCTM (1991) Standards that I observed in each novice’s classroom
in this study to help the reader get an idea of what form these novices’ attempts at SBT
took.

The purpose of this introduction—to my six teachers, the contexts of their
teaching, and the examples of Standards-based teaching that I observed in their
classrooms—is to frame the main results chapters that follow. In Chapter 5, I analyze the
various sources of stress that the teachers reported in some detail and assess the influence
of their attempts at Standards-based teaching on the stress they felt in their teaching
work. Next, in Chapter 6, I analyze the resources that they employed to address the
sources of stress that I identified in Chapter 5. Collectively, I hope that these three
chapters provide a detailed portrait of six beginning teachers, how their attempts at SBT
contributed to the stresses they felt in their teaching, and how they responded to that

Stl'ESS.

105

Introduction to Participants

I now proceed to give a brief overview of each teacher’s experiences and teaching
context, describing the schools where they worked, the textbooks they were assigned, the
classes they taught, and the two classes that I observed (focal and contrast). I also

foreshadow the main themes in each case study that follows in the next chapter.

Ms. Boone.

Ms. Boone taught at Maple High School with about 1100 students and located in
a rural town on the outskirts of a medium-sized city. Ms. Boone was nearing the end of
the first semester of her third year teaching at Maple High School when I observed and
interviewed her. She appeared to have a strong rapport with her students and was very
positive and upbeat.

Ms. Boone taught Integrated 3, Integrated 2, and AP Calculus. Integrated 3 was
mainly an Algebra 2 course with other topics like graph theory and statistics interspersed.
Integrated 2, as mentioned above, is a mix of traditional Algebra 1 and Geometry topics.
AP Calculus covers topics traditionally seen in most advanced placement calculus
courses. For the screening and focus class observations, I observed Ms. Boone in a
section of Integrated 3, because, as the reader may recall, I asked all participants to
choose their most constructively talkative class for the screening observation and for the
focus class. For the contrast class, I observed a section of Integrated 2 that Ms. Boone
suggested because she felt that that was the only other class that she felt comfortable

being observed in. She felt uncomfortable being observed in Calculus, where her

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challenges were reportedly the most different from those in the focus class, so a section
of Integrated 2 was really the only remaining class most different from the first.

As stated previously, the Integrated courses are based loosely on ideas fiom the
McDougall Littell, Integrated Mathematics textbook series. The actual curriculum was
created by the work of the teacher collaborative that initially forged the curriculum over a
summer and has continued to modify and update the curriculum on an ongoing basis, so
she used the textbook very little for those courses. The AP calculus course was based on
the Smith and Minton, Calculus (2"d edition) textbook. Ms. Boone had to create this
course on her own. She found herself using the book more than she was accustomed to
initially, but gradually pulled in more outside resources as the semester progressed.

Ms. Boone reported many challenges and many Main challenges compared with
the other novices. Her Main challenges generally focused on issues of student behavior
(e. g., talking during tests), lack of student interest/motivation, and curriculum alignment

and workload, such as working long hours to plan or rework her lessons.

Ms. Grant.

Ms. Grant taught at Elm High School that enrolled about 1500 students and
located in the urban center of a medium-sized city. The student population is very
diverse, including ESL students who speak 24 different languages.

Ms. Grant appeared to have an excellent rapport and to connect exceptionally well
with her students. She felt like she was able to build relationships with her students by

intentionally and genuinely taking an interest in their traditions and cultures (Post, 26.1-

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26.9). My limited observations of and visits to her classroom, including her interactions
with students during passing time and after school, tended to confirm this assertion.

Ms. Grant was certified to teach both English and Mathematics, although she
currently only teaches mathematics. I observed Ms. Grant near the end of her second year
teaching at Elm. Before graduating, Ms. Grant taught as a long-term substitute at a local
professional development school, Hamilton High, which she very much enjoyed. This
detail merits mention, because it gives the reader a flame for understanding why Ms.
Grant’s current teaching placement was relatively unsatisfying for her, particularly in
terms of her interactions with colleagues.

During the semester that I observed Ms. Grant, she taught Algebra 1, Algebra 1C,
and Algebra 2C. Algebra 1C and 2C were two in a sequence of three slower-paced
standard high school Algebra 1 courses. For the screening and focus class observations, I
observed Ms. Grant in an Algebra 1 section. I observed an Algebra 1C section for the
contrast class observation that she described as completely out of control, so the
challenges were the most different in that class. All of these courses are based on the
McDougall Littell Algebra 1 textbook, but Ms. Grant reported using these books very
little for her actual lessons, using them more as a problem base for homework
assignments than for instruction.

Ms. Grant reported many different Main stresses as compared to the other novices
in this study, such as problems working with technology, modifying curriculum,
relationships with colleagues and her own boredom with teaching mathematics. Several
of her stress categories, e. g., working with technology and relationships with colleagues,

were unique to her alone, as I describe in her case study.

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Mr. Jones.

Mr. Jones, like Ms. Boone, worked at Maple High School, with about 1100
students and located in a rural town. Mr. Jones was in the middle of the first semester of
his first year as a permanent teacher at Maple High during his participation in this study.
For at least the first half of the previous year, he taught at Maple as a long-term
substitute. He also completed his fifth-year internship at Maple High.

As a secondary student, Mr. Jones attended a professional development high
school affiliated with Midwestern University with which the author has had repeated and
extended contact during Mr. Jones’ secondary years. The teachers voluntarily engaged in
a teacher learning community. They shared a teacher written curriculum that varied in
style and content across classes. But they did all incorporate many aspects of the NCTM
(1991) Standards in their classroom discussions and teaching.

Like Ms. Grant and Ms. Boone, Mr. Jones was very well liked by his students and
clearly had a strong rapport with them. During the year I observed him, Mr. Jones taught
his school’s Integrated 2 and Integrated 1B courses. The Integrated courses at Maple
High School are a sequence of courses with spiraling content strands in algebra (1 and 2),
geometry, statistics, and graph theory. The Integrated 1 course, which takes a year for
regular track and college bound students, is split into two years for lower-track students,
Integrated 1A and 1B, so they can move more slowly and look more deeply into the
content. The Integrated 2 class is a regular- and college-track, year-long course primarily
taken by sophomores and advanced freshmen. All of the Integrated courses at Maple

High School are based on the McDougall Littell, Integrated Mathematics textbook series.

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As I mentioned in Ms. Boone’s case, Mr. Jones used the materials of the teacher
collaborative that were based on the Integrated Mathematics textbooks, so he reported
rarely taking them off the shelves.

Mr. Jones an Integrated 2 section for the focus class. He chose his first hour
Integrated 1B class, because they were usually very hesitant to take part in the
mathematical conversations that he encouraged in his classes.

Mr. Jones, like Ms. Grant, also reported many stresses, many of which were
related to SBT. Mr. Jones’ Main stresses related to student-focused issues, including
Lack of student interest/motivation and Responding to problematic student behaviors, as
well as to his attempts to engage students in meaningful ways in the classroom discourse

to build and assess their understanding of mathematics.

Ms. Price.

Ms. Price taught at Linden High School with approximately 2100 students located
in a semi-rural community located about 10 miles from a very large city. Ms. Price
appeared to have a good, professional rapport with her students.

Ms. Price taught Geometry, Algebra 1B, and Algebra 2. Algebra 1B was the
second year of a slow-paced Algebra 1 course. Algebra 2 was a fairly traditional, year-
long Algebra 2 course. For the screening and focus class observations, I sat in on a
section of Ms. Price’s Geometry course. For the contrast class, I observed in a section of
her Algebra 1B class, because she described that class as providing her most different

challenges because of the classroom management issues in that class section.

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In her Geometry course, Ms. Price used Exploring Geometry published by Key
Curriculum Press. For Algebra 2, she and a colleague were piloting the Discovering
Algebra 2 text from Key Curricultun Press. Ms. Price used the Glencoe Algebra I
textbook in Algebra 1. She liked the approach of the Serra textbook in particular. She
talked about how she supplemented the textbook by including investigative and group
activities in her classroom. She also said that she was considering whether to change the
approach the textbook’s approach to teaching circles. So Ms. Price did appear to extend
or modify the curriculum at times from the written textbook.

While Ms. Price reported quite a few challenges, few were Main challenges or
related to her attempts at SBT. The two challenges that were judged as Main challenges
related to issues of student behavior and students’ lack of interest or motivation in her
classroom. While these issues of student behavior and engagement were among the most
common with the other teachers, as well, she appeared to experience fewer additional

stresses that qualified as Main.

Ms. Riley.

1 performed Ms. Riley’s first screening observation in a Geometry course at
Western High School with about 2500 students located in a medium-sized city. Ms. Riley
was very unhappy with her teaching experiences at Western. While she enjoyed her
colleagues, she said that classroom management was difficult, because the administration
gave minimal consequences for misbehavior setting the wrong tone at the school. After

the screening observation, Ms. Riley asked to postpone participation in this study until

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the following year. That summer, Ms. Riley was offered a teaching position at Holly
High, the school she attended as a K-12 student, which she accepted.

While participating in this study, Ms. Riley taught at Holly High School with
approximately 2500 students located in a small city. Holly operated on the trimester
system. Each class lasts for 75 minutes every school day and students take five courses
per trimester. During participation in this study, Ms. Riley was nearing the end of her first
trimester at Holly and was in her second year of teaching.

Though I had already screened Ms. Riley for participation, I counted the first
observation at Holly in an Algebra 2 section as a second screening observation because I
needed to acknowledge that different school contexts might show a different pedagogy
from her. Since she again qualified for participation, I completed her data collection at
Holly. I observed Ms. Riley in Geometry for the contrast class, because she said that it
was the most different from her other classes, but then qualified that statement by
explaining that none of her classes at Holly were nearly as challenging as her classes at
Western High. All of the courses that Ms. Riley taught used the University of Chicago
School Mathematics Project (U CSMP) textbooks. Ms. Riley reported that the UCSMP
textbooks did not contain many real world applications of the mathematics, so she
enjoyed supplementing the materials in that way. She reported finding other resources to
supplement the text online or through colleagues, as well. But she also reported that she
used the same tests and quizzes as her colleagues, which were the ones from the book.

Ms. Riley’s Main stresses were diversely related to issues of student engagement,
managing classroom discussions, the trimester schedule that she worked under, and her

communications with administrators, as will be discussed further in her case study. The

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first two stresses, student engagement and managing classroom discussions were

particularly common across this group.

Ms. Wells.

Like Ms. Riley, Ms. Wells asked to postpone participation until her second year
of teaching. She taught at Redwood High School with approximately 1100 students in a
diverse student body in a suburb of a very large city. Redwood is located in its own
district, even though its service area lies within the city limits. By standardized test
scores, it ranked as one of the best schools in that city.

Ms. Wells appeared to have a strong rapport with her students. She was very
tolerant of student talking and other behaviors that did not detract from other students’
work. Ms. Wells said that she arrived at school early each morning and stayed until late
each night helping her students and completing her work.

Ms. Wells did not qualify for participation in the first screening observation.
Because her 5"n year content/methods instructor described her as the most likely in her
cohort to be attempting SBT, I returned for a second observation in the same Geometry
class which she passed, so I commenced with data collection in that class. For a contrast
class, I observed a section of Algebra 1, because she said that her management issues in
that class were considerably greater than in her other classes. Those are the only two
classes that she taught that year.

Ms. Wells and her colleagues used three different textbooks that the district made
available to them, the McDougall Littell series, the Prentice Hall series, and the Cognitive

Tutor, a Carnegie-Mellon University computer-based algebra curriculum. She described

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how her department worked together to piece these curricula together and to supplement
it with materials and ideas of their own, circumventing the administration’s expectation
that they use the Cognitive Tutor curriculum exclusively.

Ms. Wells reported relatively few stresses or Main stresses. The few Main stresses
that she reported related to issues of student behavior, motivation, and to the long hours

that she worked.

Preamble: The Search for Standards-Based Teaching

Next I briefly consider how these six novices’ teaching involved attempts to
implement aspects of the NCTM (1991) Standards and foreshadow the results of the
more thorough analysis in the chapter that follows. My purpose in looking at these
novices’ attempts at Standards-based teaching (SBT) is to follow up on previous studies
assessing whether the Standards are having an impact on the quality of teaching for
novices educated about the meaning and implementation of this document. Because the
NCTM (1991) Standards describe what the authors judge to be quality teaching practices,
there is clearly a subjective quality to the importance of seeking for such practices.
Clearly, I align myself with those who deem such practices to be worthwhile and
beneficial to students and teachers alike.

One significant overall result of this study, as explained in the Methods chapter,
was that SBT was not particularly common, even when searching among the most
promising graduates of progressive Midwestern University’s secondary mathematics
education program. Of the 11 novice teachers who I screened for this study, only 7 were

observed attempting aspects of SBT during screening. And of those 7, one did not

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attempt SBT in any meaningful way during his participation in the study, so he was
dropped from the analysis. He was, in effect, a “false positive” from his initial screening.
And, as a reminder, my criterion for attempting SBT was a relatively modest bar, namely
attempts in at least two of the six standards articulated in the NCTM (1991) Principles
and Standards for Teaching Mathematics.

I struggled to find appropriate novice teachers, even though a major goal of
Midwestern University’s and many other universities’ teacher education programs across
the United States is to develop and graduate novices with such abilities and propensities.
This underscores how challenging the task of Standards-based teacher preparation is.
These results also show that attempts at such teaching are occurring more frequently, in
contrast to the absence of such teaching in some previous studies by mathematics teacher
educators studying implementation of NCTM Standards-based teaching (e. g., Wilcox et

al., 1991).

Examples of Standards-Based Teaching from Participant Observations

I would like to illustrate what I describe as meaningful attempts at SBT for the
participants in this study. I offer the following excerpts from my observations in each
teacher’s classroom to give the reader an idea of the evidence that I had that these

teachers were attempting SBT.

Ms. Boone: Taking a student’s conjecture seriously.

While observing Ms. Boone teach a lesson on graph theory, her student Danielle

hypothesized that it would take a minimum of eight roads to join nine locations on a map.

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Ms. Boone stopped for a moment and hesitated. She asked the student if she was saying
that it would always take one less road than the number of locations to join them on the
map with a minimum number of roads. Danielle affirmed that she was. Ms. Boone
paused and thought for a few tense moments, then said that it looked to her like that was
true. She made the proof of that conjecture a homework problem for the entire class.
Afterwards, she told me that she had never had a student make that conjecture in the three
previous times that she taught the class. She said that she was going to incorporate that
conjecture into that unit in the future, because she thought that it was interesting and
important for the students to learn.

I judged this segment of Ms. Boone’s teaching as a non-trivial attempt at SBT,
because she considered a student’s idea seriously and made it a part of the curricultun,
rather than dismissing it as a tangential fact. In so doing, she clearly valued the student’s
conjecture and the mathematical thinking that generated it and demonstrated her
judgment to the class by assigning a homework problem based on the conjecture. This
would meet NCTM Standard 3: Students’ role in discourse, because the student offered a
conjecture that was non-trivial and meaningful. The teacher not only considered that an
interesting find, but also made it a part of the current (and future) curriculum of her

course, meeting Standard 2: Teacher’s role in discourse.

Ms. Grant: Exploring eflects of changing parameters on graphs of quadratic

functions.
Ms. Grant had her students explore the effect of changing the a, b, and c

coefficients on the graph of the general quadratic equation, y=ax2+bx+c. She asked the

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students to create a table that described what happened when they changed the
coefficients in the equation one at a time. She had not considered how the a and c
coefficients interacted with the b coefficient, and the effect of changing the b coefficient
in the equation on the graph is more complicated to describe in a general manner than is
the case for a and c. She also had not considered that if the equation were written in the
form y=a(x-h)2+k, the effect of changing a coefficient would be much easier to describe.
So when it came time for students to predict the effect of changes in the b coefficient on
the shape of an arbitrary quadratic equation, the students’ prediction (e. g., that the graph
would move up and to the right) proved inaccurate.

Although Ms. Grant was not adequately prepared to teach this topic, because she
herself had not explored the mathematics completely, she also made moves that led me to
classify this episode as a non-trivial attempt at NCTM Standards-based teaching. First of
all, she had the students explore a significant and worthwhile mathematical task
(exploring how changing each parameter in a quadratic equation affects the shape of the
graph) and organize the resulting data, thus addressing Standard 1: Worthwhile
mathematical tasks. Second, she had the students discuss and describe their results to
help them all understand how changing the coefficients in the equation affected the
graph. This meets Standard 3: Students ’ role in discourse, because the students were
offering mathematically significant conjectures to the discussion. It also meets Standard
2: Teacher’s role in discourse, because Ms. Grant was acting as a facilitator, rather than

an authority at many points in that discussion.

Mr. Jones: Exploring prospective congruence conditions for triangles.

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Mr. Jones taught a lesson where he engaged students are engaged in an activity to
discover the congruence theorems for triangles, including such conditions as SSS, SSA,
ASA, AAA, etc. They explored all possible congruence theorems abbreviated as a list of
all three-letter combinations of the letters A (angle) and S (side) where repetitions were
permitted. The students were supposed to try to draw to different triangles to identify
those conditions that were not sufficient to prove congruence. After the students had
attempted to draw two different triangles for each possible congruence theorem, they
discussed the results as a class and whether each condition was sufficient to prove
congruence.

This episode was an example of Mr. Jones’ attempts at SBT, because he engaged
students’ in a worthwhile mathematical task (Standard 1), an open exploration of the
sufficient conditions for congruence in 2-D figures. The students made conjectures
(Standard 3) and listened to other student’s conjectures that they, at times, validated or
refuted with mathematical evidence (Standard 5). As a reminder, Standard 5 refers to
setting up an environment in the classroom that supports mathematical discussions. In
this discussion, Mr. Jones often acted as a facilitator of the students’ mathematical

reasoning, meeting Standard 2, as well.

Ms. Price: Motivating the formula for the area of a circle.

In a lesson about the properties of a circle, Ms. Price had her students cut out a
circle and then cut it into 16 congruent sectors (see Figure 4). She then asked the students
to use those pieces to create a new geometric shape for which they knew the area to see if

they could figure out the area of the circle from it. The students all worked to create

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different shapes and eventually nearly all of the students (in my range of sight and by the

teacher’s account) had created the shape shown in Figure 4.

 

 

 

 

Figure 4. Diagram showing how Ms. Price ’s students rearranged cut sectors of a circle
(with arrows denoting movement) to create a “parallelogram ” to determine the area.

Ms. Price asked them what type of shape they had made. One student said that it
was a rectangle, but a second student said that it was a parallelogram. A third student
agreed with the second and said that a rectangle has to have perpendicular sides, but that
two of the sides weren’t perpendicular to the other two. Ms. Price, agreeing with the latter
two students, reminded them that they had just learned the formula for the circumference
of a circle. She explained how to derive the formula for a circle using A=b*h
(Area=base*height). She explained that the bases had length 2ITR/2= IIR, while the

height was R. because that was the radius. She wrote A=bh= (ITR)*R= 1'le .

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This is an example of an attempt at Standards-based teaching, because Ms. Price
had the students “prove” (in an approximate sense) the area of a circle by decomposing
the circle into sectors and then rearranging the sectors into a shape whose area they
already knew. Then they offered solutions (Standard 3: Students ’ role in discourse) and
used mathematical arguments to determine which of their answers was most useful in this
situation (Standard 5: Learning environment). Admittedly, this relatively popular
intuitive “proof” of the formula for the area of a circle is flawed in that the object formed
is not a parallelogram, nor is it intuitively obvious that its area is the same as that of a
parallelogram with base HR and height R. But the process by which the teacher enacted
the task (i.e. allowing students to use mathematical arguments to determine what shape

the circle sectors took. on) was aligned with the NCTM Standards to a meaningful degree.

Ms. Riley: Using difficult problems to help understand the quadratic formula.

During a lesson on completing the square, Ms. Riley asked her students to attempt
to solve the problem 4x2+16+k during a class discussion by finding the k that would
complete the square and allow them to factor the expression. This was the first
completing the square problem that the students had encountered where the coefficient of
x2 was not 1. The students tried to work the problem. More than one student offered
suggestions as to how to solve it. Finally, the class came to a consensus, finding the
solution to be k=64. Ms. Riley continued with the lesson, but noticed a few minutes later
that their solution was incorrect. She tried to explain why their answer was incorrect but
fell short, because the students could not understand why they had to factor out the 4 in

front of the x2 term before solving finding the constant, k, that would allow them to

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complete the square. Then she asked the students to ignore that problem and told them
that it wouldn’t be on the test and moved forward with the rest of the lesson. During the
post-observation interview, she explained to me that that problem was not part of the
curriculum and that colleagues had told her not to cover it, but she wanted to help the
students understand the quadratic formula, so she had attempted it anyway. When it
didn’t work out and she could see that she wouldn’t have time to teach the topic, she
decided not to attempt teaching it again.

Even though Ms. Riley had not sufficiently prepared her students to address and
solve this problem effectively, there were elements of SBT in her efforts. Ms. Riley
allowed the students to offer suggestions about how to solve a problem and to come to a
consensus on that solution (meeting Standard 3). She acted as a facilitator during that
discussion (meeting Standard 2). Though she had not adequately prepared the students to
tackle such a problem, she did clearly attempt to engage them in offering mathematical
ideas that they defended with (albeit incorrect) mathematical arguments in attempting to

solve this problem.

Ms. Wells: Formulating conjectures about properties of a triangle ’s midsegments.

While I only observed relatively modest attempts at SBT in Ms. Wells' class, one
of those attempts resulted in evaluating a student conjecture that was interesting. Ms.
Wells held up a picture of a triangle with all three midsegments drawn connecting the
three sides. She asked students if they could see anything that was true about one side and
the midsegrnent that ran parallel to that side. One student said that they would all be

congruent. Ms. Wells probed and found out that the student meant that all four triangles

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in the diagram would be congruent. She had to think on her feet a bit. She said that that
would be true for the diagram and said she did not know if it would always be true for
any triangle. After a few tense moments, she decided and told the class that the statement
was always true.

Because Ms. Wells asked her students for conjectures about the diagram and did
not dismiss a conjecture out of hand that was not precisely what she had asked for, she
allowed students to have a role in formulating the content of the course. This meets, at

least in part, NCTM Standard 3: The students’ role in discourse.

Summary

These six beginning teachers were among the few that I observed from their
respective cohorts attempting SBT, even though they were carefully selected by their
fifth year content/methods teacher. Their attempts were, at times, mathematically limited
or misguided, although they clearly made meaningful attempts to implement the NCTM
(1991) Standards in their classrooms. But each made some honest attempts at aspects of
pedagogy proposed in the NCTM Standards, and most involved efforts to engage their
students in the search for and discussion of mathematical relationships, in their own, as
opposed to direct instruction of those relationships. In the next chapter, I explore each
participant’s observed teaching more thoroughly and carefully, looking at each
participant’s experiences, identifying teaching challenges they reported, and how those
challenges related to their attempts at SBT. This chapter also examines the

challenges/sources of stress of these teachers when aggregated as a group.

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Chapter 5: Stress Analysis

In this chapter, I present the results from the stress analysis, including which
sources of stress novice teachers reported who exhibited some elements of NCTM
Standards-based teaching (SBT). This helps answer Research Question 1, “What sources
of teacher stress do novice secondary and middle school mathematics teachers who have
exhibited some elements of Standards-based teaching experience in their teaching?” I do
this by looking at each individual teacher’s salient stresses, then by looking at some of
the patterns in the novices’ stresses as a group.

By NCTM Standards-based teaching, or SBT, I mean teaching that is consonant at
least to some degree with the NCTM (1991) Principles and Standards for Teaching
Mathematics. I analyze which sources of stress were “Main” and which were merely
“mentioned” for these participants. As a reminder, Main sources of stress met specific
criteria that indicated the novice teachers were attributing emphasis to those stresses,
namely using detail, magnitude words, repetition within an interview, repetition between
interviews, and/or reporting it as a top stress. Teachers also reported that some stresses
were their “top” stresses; I report these stresses as well that were entirely a subset of their
Main stresses for all of these novices. For more detail on the criteria by which I judged
whether a stress was “Main” or merely “mentioned,” I refer the reader back to the
Methods chapter.

As a reminder, I use the term “sources of stress” to indicate a focus on the origins
of the aggregate teacher stresses that these novices reported. For ease of expression, 1 will

refer to “stresses” when I distinguish and analyze these sources of stress.

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I first look at the salient stresses for individuals and then across the results for the
entire group in this analysis to determine which stresses were predicted by and which
were new to the literature. This answers Research Question 2a, namely “While novice
teachers attempt Standards-based teaching, which stresses are predicted by the existing
literature and which are new to the literature?”

I also analyze for the group as a whole how the reported stresses related to
participants’ attempts at Standards-based teaching (SBT) to answer Research Question
2b, specifically “Which sources of teaching stress are related to their attempts at
Standards-based teaching and how are they related?”

Finally, I analyze whether each participant judged any of their stresses to be
facilitative (or constructive), neutral, or debilitative (or nonconstructive) to answer
Research Question 3, “What sort of impact do the sources of teaching stress that novice
teachers experiences have on them, i.e. do they judge them to be facilitative, neutral, or
debilitative?”

In summary, I begin by looking at the individual participants’ cases, determining
which sources of stress (hereafter “stresses”) they reported and which of those stresses
were reported or judged as being top or Main stresses respectively. Then I discuss overall
patterns that I saw in the teacher stress data, including salient stresses reported, how
reported stresses relate to those predicted by the existing teacher stress literature, which
stresses related to novices’ SBT attempts, and whether teachers described those stresses

as facilitative, neutral, or debilitative.

Overview of Stresses for Each Teacher

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I begin this chapter by listing all of the stress categories that each novice reported
during our interviews, distinguishing between stresses they declared as “Top” for them,
stresses that were “Main” as scored by my criteria (repetition within, repetition between,
detail, magnitude, reported as top; see Chapter 3 for details), and finally those that were
merely mentioned sometime, but not with compelling emphasis, in the interviews. To
refine this description, I then give examples of the actual stresses that novices reported
that fit into those stress categories and were most important to each novice, according to
the following guidelines. When novices reported two or more top stresses, I give
examples of all those stresses". When they reported a single “Top” stress, I share an
example of that stress, followed by examples of all of their other Main stresses. Although
my criteria did not overtly require it, the top stresses were always a subset of teachers’
Main stresses. As a result, top stresses are entered twice in the teacher summary tables
below, as both “Top” and “Main” stresses. In all 6 cases, teachers generated at least one

“Top” stress and at least one additional “Main” stress.

Ms. Boone: Reported stresses.

Ms. Boone reported the second highest number of categories'of teaching stresses
overall, 13 of the 22. She also reported the highest number of Main stresses (6 of those
13) and the highest number of top stresses (3 of those 6 Main stresses. Ms. Boone’s Top

teaching stress categories were Challenges associated with professional development,

Relationships and communications with administrators, and Responding to problematic

 

student behaviors.

 

" Despite my efforts to get the novices to name their single top stress, some named more than one “top”
stress.

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Table 5

Ms. Boone’s Top, Main, and Mentioned Sources of Stress

 

Stress salience Stress categories

 

Top stress(es) Relationships and communications with administrators
Challenges associated with professional development
Responding to problematic student behaviors

 

Main stresses (M) [Relationships and communications with administrators]
[Challenges associated with professional development]
[Responding to problematic student behaviors]

Creating, aligning, modifying, or implementing curricula
Lack of student interest/motivation

After hours work/long hours

 

 

Mentioned stresses (m) Managing classroom discussions

Relationships and communications with students
Teaching students of varying ability levels
Learning and teaching unfamiliar content
Relationships and communications with parents
Teacher boredom

Dealing with class length, pace, or schedule

 

 

Note. Brackets indicate stresses that were top, but then are necessarily also Main.

While Ms. Boone reported her Relationships and communicziions with
administrators were generally good, she was very frustrated that the administration had
added on additional professional development hours and required her and her cohort of
2nd year teachers to attend what turned out to be a new teacher orientation geared towards
first-year teachers. Ms. Boone and her peers had all described what they wanted to do for
that professional development experience, work on more teambuilding as they had done
the previous year. So they were all very disappointed that their professional development
was such also an irrelevant experience, because it was also completely unrelated to their

original request.

Ms. B: And I had to go. And I was a second year teacher. We had like two
first year teachers. And the rest of us, ...we’re all in our second or third

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year. And we just felt like it was such a cop out to [require us to attend a
new teacher orientation]. And we were so frustrated... So we went to the
principal and expressed our fi'ustration with it... We were just like, “You
know what? This is not helpful to us. It is a waste of time. Let us do
something else.” So we had a meeting with the principal. And we had all
these great ideas. Why not require us to go to a conference in our subject
area? We have the [regional education headquarters] right here. Why not
require us to go to pick one or two classes? Something that could be
helpful. If we want to build a website, maybe we should go to the website
class, or something like that... We had a ton of ideas (Post, 923-102).

The previous quote also related to Ms. Boone’s Qallengg associated with
professional development, because the nature of the professional development was part of
the problem, as was the administration’s failure to listen and to act on feedback about her
professional development experiences and goals.

Ms. Boone also reported feeling frustrated by Respondinw student behaviors,

especially when the students didn’t listen to her when she was talking or when they

talked while other students were finishing up quizzes or tests.

Ms. B: ...There’s one thing that happened in class the other day that
stresses me out more than anything in the world. And that’s when kids are
done with their quizzes or tests and start talking before everybody’s done
with it. That is my number one stress. I literally will get a headache,
because I’m trying to keep them quiet, or trying to keep them working on
something. And I get, I just get very, very annoyed, because I know when
I’m trying hard to work on something, I can’t concentrate if there’s any
kind of noise going on... So I get very, very stressed about that (Post,

6.23-6.34).

Ms. Boone wanted to ensure that all of her students could concentrate and put for
their best efforts on the quizzes. As a result, she felt very annoyed when she couldn’t get
students who finished early to comply with her wish for silence while others were

finishing up.

127

Ms. Boone’s three remaining Main stresses that were not top stresses were:

Creating, aligping, modifying, or implementing curricula, Lack of student
interest/motivation, and After hours work/long hours. For Creating, aligping, modimpg,

 

or implementing curricula, Ms Boone mentioned, for example, how she is working on
creating the AP calculus curriculum and was also constantly modifying and reworking
her lessons to improve them in the Integrated courses that she had taught for several
years. For Lack of student interest/motivation, Ms. Boone mentioned that she felt
annoyed when her students were not listening or are bored with a lesson, which was
represented a few times in our observations. Ms. Boone’s challenges with Creating,
aligping, modifi'ng, or implementing curricula related to how hard she worked at
creating lessons for the AP calculus course that she taught, as well as reworking old
lessons that she felt could have been better structured, needed more hands-on activities or

additional content to meet her state’s mathematics standards.

Ms. Grant: Reported stresses.

Ms. Grant reported stresses in more categories than any other participant, with 15
of the 22 stress categories overall. She reported the median number of Main stress
categories with four, namely Teacher boredom, LLck of student interest/motivation,
Working with technology, and Relationships and communications with colljrgues. She
reported that two of those Main stress categories were top stresses, Teacher boredom and

Lack of student interest/motivation.

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-0
..l‘.

C02

“'1

Table 6

Ms. Grant’s Top, Main, and Mentioned Sources of Stress

 

Stress salience

Stress categories

 

Top stress(es)

Teacher boredom
Lack of student interest/motivation

 

Main stresses (M)

[Teacher boredom]

[Lack of student interest/ motivation]

Working with technology

Relationships and communications with colleagues

 

 

Mentioned stresses (m)

 

Directing student explorations of mathematics

Managing classroom discussions

Responding to unexpected student ideas

Creating, aligning, modifying, or implementing curricula
Planning lessons

Learning and teaching unfamiliar content

Relationships and communications with parents
Responding to problematic student behaviors

Preparing for, administering, and evaluating standardized tests
Finding and utilizing resources

Student diversity

 

Note. Brackets indicate stresses that were top, but then are necessarily also Main.

Ms. Grant said that teaching math is really boring for her, and although she is

willing to be there for the students, they don’t really enjoy or wish to engage with the

content readily. A passage relating to both of her top stresses, Teacher boredom and Lack

of student interest/motivation, follows:

Ms. G: I think like the biggest thing that might push me out of teaching
math, because I think about it sometimes, because I know what it’s like to
teach English. And I know what social studies teachers do, is that I’ll help
students be problem solvers and I’ll help those who need it, because I’m
helpful. And I ’11 just do this to be very helpful and encouraging and I want
to make them, not like math, but be successful at math when they maybe
haven’t in the past. And I’m just discouraged by how dull it is for me
sometimes... Teaching it can be very, very dull. And I can get into it, but
it’s so not authentic, I think, for the students. Like “It doesn’t make sense
for her to be all excited about solving for y.” And it drives me crazy that
like 4 weeks later, they still want me to solve for y and show the subtract 4

129

 

on both sides and then divide by 3, like if it was a linear equation. . . Like
that’s what frustrates me the most probably. Because they tune in and tune
out whenever they feel like it. And I’m like willing to be really committed
to them. But like it’s boring for me to stand up there... So if I could teach
solving linear equations for a month, or something, or two months. And I
could do it in a lot of ways, a lot of interesting ways, creative... then I
wouldn’t mind. But because I’m limited to this amount of time and these
students, all I can keep saying is you know, “Now subtract 3 on both
sides.” So that’s probably what would push me out [of teaching math]. . .
And that’s why I’m looking always (Post, 19.34-20.20).

This passage succinctly summarized Ms. Grant’s biggest complaints relating to

Teacher boredom, primarily that teaching math was boring compared to teaching English

 

(her teaching minor) or social studies (the subject her husband teaches at Maple High
School). Ms. Grant felt like it was so much easier to have meaningful conversations with
the students in English and social studies, while in mathematics, there were some topics
that just do not lend themselves well to whole-class discussion, like algebraic
manipulations (e. g., getting the x’s on one side and the numbers on the other).

With regards to Lack of student interest/motivation, Ms. Grant felt frustrated,
because she teaches mostly unsuccessful math students. They don’t engage with the
content, because “they’re not motivated... I teach mostly unsuccessful math students.
And so they find themselves as kind of losers at ma ” (Ms. G, Post, 15.10-15.37).

Ms. Grant also mentioned several challenges related to her other two main
stresses, Working with technology and Mationships and communications with
colleagpes. For Working with technology, neither the middle school teachers nor the
other high school teachers were training the students how to use graphing calculators, so
she had to teach them everything. That to her was very frustrating since even the middle

school teachers have graphing calculators, but they are more worried about how the

130

students treat the calculators than that they learn to use them. She felt like those teachers
had a professional obligation to teach the students about technology and that that
obligation was more important than the calculators, which were materials which could be
repurchased, if damaged. So because she wishes to use the graphing calculators in her
instruction, she has to go through the keystrokes step-by-step for students in each lesson,
often taking up a lot of time. I will share the specific quote when discussing stress
categories that are new to the literature.

For Relationships and communications with colleagues, Ms. Grant felt a little bit
let down by her experiences at Elm High School, particularly relating to the type of
conversations that they had in the lunch room. During her senior year (the year before her
5‘h year internship), she worked as a part-time sub at Hamilton High School, a local

professional development school.

Mr. Jones: Reported stresses.

Mr. Jones reported the second highest number of teaching stress categories
overall, 13 of the 22. He also reported the second highest number of main stresses, 5 of
his 13), namely Managing classroom discussions, Lack of student interest/motivation,
Assessing student understanding, Responding to problematic student behaviors, and
Dealing with class length, pace, or schedule. Of these five, Mr. Jones’ top stresses were
Lack of student interest/motivation and Managing classroom discussions. which I will

describe using examples from his interviews.

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While Managing classroom discussion; Mr. Jones found it challenging to present

content in terms that students could understand, as well as making sure that a great deal

of the ideas and information came fi'om the students rather than from himself.

Table 7

Mr. Jones’ Top, Main, and Mentioned Sources of Stress

 

Stress salience

Stress categories

 

Top stress(es)

Managing classroom discussions
Lack of student interest/motivation

 

Main stresses (M)

[Managing classroom discussions]

[Lack of student interest/motivation]
Responding to problematic student behaviors
Dealing with class length, pace, or schedule
Assessing student understanding

 

 

Mentioned stresses (m)

 

Directing student explorations of mathematics

Creating, aligning, modifying, or implementing curricula
Planning lessons

Teaching students of varying ability levels

Learning and teaching unfamiliar content

Preparing for, administering, and evaluating standardized tests
After hours work/long hours

Challenges associated with professional development

 

Note. Brackets indicate stresses that were top, but then are necessarily also Main.

 

Mr. J: Yeah, as a facilitator, as someone that’s trying to lead a discussion
or actually get them to start thinking about this path that they have to take,
it’s very hard to put [the idea of proof] in terms that they understand
besides—I wish I would have given more time for students to think about
and more students to think about, maybe they didn’t like this idea of a
path. Maybe they could have changed it. Maybe some students that were
really struggling with it, but finally got it, have them explain how they
understood exactly what this meant in order to prove these two angles are
equal. And I see on the test that I’m grading now, they did really struggle
with the proof, the proof part there... Thinking back now, I wish I would
have done something different, as far as having students talking about it
more than just, you know, me talking up there. I mean, I noticed from the
three video clips that I do a lot of work. I do more work than I should be
doing. And I should have students have more responsibility for what’s
being said in class. And I think that if they would have maybe described

132

what they were thinking, especially the struggling students once they did
figure it out... Maybe having them discuss that more. That’s what I’ll
change for next year (Post, 10.3-11.13).

Mr. Jones also explained that he wanted the students to be more engaged in
discussions and in-class activities, but maybe it wasn’t just the students, but also the
questions that he was posing that were creating the discrepancy between what he wanted
to see and what was happening in the classroom. He also mentioned that he wanted to be
doing less talking and acting more like a facilitator during discussion, but that that wasn’t
always what was happening in class.

For Lack of student interest/motivation, Mr. Jones mentioned that one of his
challenges in this area was getting students to engage in his slower-paced courses, in
particular. In that class, not only are students in the lower track, but they are also exposed
to the same content two to three days in a row. He felt like that could get a little boring
for them at times, as well as being difficult for the teacher to make interesting the second

or third day s/he covers that topic.

Mr. J: My first hour. . ., they’re challenging in a motivational kind of way.
They don’t seem to want to discuss mathematics. It’s first hour, but it’s
really hard to motivate them. They are on a lower, I guess, track you could
call [it]. They’re in a 1B, which is, if you take Integrated 1 and break it up
in two semesters, they’re taking the second semester and they spread that
out over the whole year. So they’re seeing—the material that a normal
class would see in just one semester, they’re seeing it over a whole year.
So it’s a lot slower pace. They have a lot of time to see material, which
could be boring sometimes. And it’s a real challenge to make it really
interesting for them and to get them excited about it when they don’t
really care, because they already know, “I’m in the slower track. Who
cares about me? I don’t care about math” (Pre, 3.32-3.42).

133

Here Mr. Jones identifies a challenge that other teachers, including Ms. Grant,
also mentioned. Specifically, he says that getting students engaged in mathematics
lessons in his lower-track courses was challenging. This appears to be a relatively
common issue for these teachers.

Mr. Jones’ three remaining Main stresses were: Responding to problemati_c
student maviors, Dealing with class length, pace, or schedule, and Assessing student

understanding. For Responding to problematic student behaviors, Mr. Jones mentioned

 

that he has one student whose misbehavior has led other students who were once
respectful to begin talking across the class during whole class discussions and in-class
work time. For Dealing with class length, pace, or schedule, Mr. Jones mentioned how
difficult it was to keep up with the schedule that he and the other teachers had agreed on
at the beginning of the semester, even though he was at the same place as the department
chair who he worked with jointly on planning.

For Assessing student understanding, Mr. Jones described how difficult the
performance assessments were at the end of the semester for him and the students. At
Maple High School, they have performance assessments where students prepare and
present a project in groups. Each project is challenging and has multiple parts, so that the
students must divide up the project to complete it. These assessments were difficult for
them, because each student has to prepare part of the project, so they have to rely on each
other for help. But it is also difficult, because every person in the group must have an
understanding of every part of the multi-problem project. The students complained a lot
about the projects and presentation, because they had to rely on classmates for their

grades, at least in part, because they were partly graded as a group and partly as

134

individuals. Also, Mr. Jones had to be prepared to ask questions that would help him

know whether the students truly understood the entire assignment and not just their part.

Ms. Price: Reported stresses.

Ms. Price reported about as many stress categories as the other teachers, 12 of the
22; however, she reported the fewest main stresses, only 2, namely Resmnding to
problemfl student behaviors and Lapkfiof student interest/motivation, where the former

was her single “top” stress.

Table 8

Ms. Price ’5 Top, Main, and Mentioned Sources of Stress

 

 

 

Stress salience Stress categories
Top stress(es) Responding to problematic student behaviors
Main stresses (M) [Responding to problematic student behaviors]

Lack of student interest/motivation

 

 

Mentioned stresses (m) Managing classroom discussions

Creating, aligning, modifying, or implementing curricula
Planning lessons

Teaching students of varying ability levels

Learning and teaching unfamiliar content

Relationships and communications with parents

Dealing with class length, pace, or schedule

After hours work/long hours

Assessing student understanding

Relationships and communications with administrators

 

 

Note. Brackets indicate stresses that were top, but then are necessarily also Main.

Ms. Price said that it was difficult to be consistent every time in Responding to
moblematic student beh_aviors. She also described how frustrated she became when she
did everything she could think of when dealing with student misbehavior and nothing

seems to work, because the student doesn’t care and their parents either don’t respond or

135

 

aren’t interested in correcting their children’s behavior. She said that it is a challenge that
she has become better at dealing with, but still continues to work on improving. Ms. Price

mentioned how difficult it was at times to get some students’ behaviors under control.

Ms. P: And sometimes dealing with student behaviors, you know it’s so
hard to be consistent every single time. It involves, I think it involves lots
of work, calling parents, following up on the kid, making sure they serve
their detentions—if they don’t, you’ve got to refer them to the
administrator—talk to the administrators about the kids, talking to the
parents, talking to the kid before or after class. I mean, it’s just really, it’s
hard, I feel like. And it’s exhausting. And sometimes I just feel like,
“Ugh!” You know like, it becomes tiring, I think. . .like, it’s not making
any progress. Nothing’s getting through to this kid. (Post, 11.40-12.06).

Clearly Ms. Price expressed struggling with student discipline, sometimes even
when she was using all of her resources.

With respect to her other Main stress, Lack of student interest/motivation. Ms.
Price mentioned how difficult it felt to get students engaged at times with all of the
outside things that they had to do, like early morning and after school athletic practices,

other classes, and so forth.

Ms. P: I mean, like you saw in my sixth hour. . .class. It’s kind of these
kids, you know, with too many friends in a class, their inability to just

focus, you know? They don’t like math. They’ve had a long, hard day.
And you have to somehow get them to do something for an hour. And

some days it seems like it’s just impossible. (Post, 11.34-11.40)

So Ms. Price reported that she felt like she could not always get her students to

engage with her mathematics lessons, to really do something in class.

136

Ms. Riley: Reported stresses.

Ms. Riley reported the fewest stress categories of any teacher with 8 of the 22;
however, she was judged to have experienced the median number of Main stresses with a
total of 4, including Lack of student interest/motivation, Dealing with class length, pace,
or schedule, Relationships and communications with administrators, and Managihg

classroom discussions.

Table 9

Ms. Riley’s Top, Main, and Mentioned Sources of Stress

 

 

 

Stress salience Stress caggories
Top stress(es) Lack of student interest/motivation
Main stresses (M) [Lack of student interest/motivation]

Dealing with class length, pace, or schedule
Managing classroom discussions
Relationships and communications with administrators

 

 

Mentioned stresses (m) Learning and teaching unfamiliar content

Relationships and communications with parents

Responding to problematic student behaviors

Preparing for, administering, and evaluating standardized tests

 

 

Note. Brackets indicate stresses that were top, but then are necessarily also Main.

Ms. Riley said that Lack of student interest/motivation was her top challenge. She
said that in at least one of her classes where the kids were really bright, it was hard to get
them to respond to her personality or to get them interested in the lessons. They would
also do their work quickly, but then she couldn’t move forward because of the way the

schedule is set up for her school’s trimester schedule, so they are often bored.

Ms. R: Yeah, [in my fourth hour class] they’re just, they’re smart. And
they just want to do the work and get it over with and move on. So they’re
a little bit bored. So they end up having time at the end of the class to just

137

 

pick their noses and you know, do nothing. Because I can’t really go on
and leave the other first and second hour behind, because those individuals
are so—they need to be in the same spot... Normally I would keep going.
I wouldn’t probably do a whole other section, but I would introduce the
next section. I would come up with more problems for them to do. You
know, just stuff like that so... And you know, they’re just naturally quiet
though. They’re bored during the lesson, too... Like I can’t get them to—
like normally, if I would be kind of like showy and clowny in fi'ont of the
class for everybody like I was in second hour, you know, they laugh and
they participate and they, you know, make jokes. And these guys would
just be like [silence]... You know, like they would have just no
expression. No, nothing, you know? Sometimes I feel like, “Is this thing
on? Is this thing on?” (Pre, 4.16-4.40)

For Dealing with class length, pace or schedule, Ms. Riley mentioned that one of
the challenges was trying to teach a semester’s worth of content in a single trimester due

to her school having adopted a trimester schedule.

Ms. R: So you’ve got three trimesters, but they’re like semesters. And
instead of having a class go all three [trimesters], you do it in two. And so
we have the same amount of material to do in two-thirds of the year. .. But
the exchange for that is that you get 75-minute classes, rather than 50-
whatever minute classes.

1: Okay. So you get one and a half times the class time?

Ms. R: Correct.

I: And 2/3 [of a year]. So 3/2 times 2/3 should equal out in theory.
Ms. R: In theory.

I: But you said you don’t love it.

Ms. R: It’s great on paper. [Laughter] What you get into is very
regimented schedules... You are very, very on schedule, on time (Pre,

3 .3 7-4.1 3).

Ms. Riley emphasized in this quote how she felt like she ended up with a very
regimented schedule as a result of the trimester schedule that her school had adopted.

This also dovetails with her concerns about Laclflf student interest/motivation. because

138

she mentioned that she felt very constrained by the trimester schedule that her school
operated under.

Ms. Riley’s challenges with Managing classroom discussions were related to
having difficulty explaining concepts in class, making mathematical mistakes in the
classes I observed and then trying to fix them, and being surprised by some things that
the students did and didn’t know during those discussions. In the following example, Ms.
Riley was struggling with helping the students understand why they used certain, specific

steps when completing the square.

Ms. R: I was challenged by the fact that I did not think that they were
getting it. And I was trying to come up with other ways to explain myself.
And I was having a lot of trouble. . .and it really, really was stumping me,
because they weren’t getting it at all...

I: Yeah. And how did that resolve itself?

Ms. R: I think how it resolved itself was I got to the point where I said,
like in my head, “We do not have enough time to tinker with ‘Do these
kids have deep, meaningful understanding of what’s going on? Or can
they just find h dividing by 2?”’ You know? And so I think that some of
them, hopefully a lot of them got the understanding of what’s going on
and why you divide h by 2. But I think it got to the point where I was like,
“Forget it... Just divide this number by 2 and square it. Just do it.”
[Laughs] ...I just dropped it, because I couldn’t handle it anymore...
Their faces were sheer terror... I feel like we got so off course with that,
so out of what I wanted to do. I mean it was ruined from there. (Post,
3.15-4.12).

Ms. Riley had difficulty explaining to students why completing the square
worked. She ended up just dropping the explanation, because her students were getting
confused and upset by her explanations of it, rather than gaining mathematical

understanding from it.

139

Ms. Riley’s challenges with Relationships and communications with
administrators related primarily to the new teacher orientation she attended, where high
expectations were voiced for the new teachers’ performances that made her feel very,

very nervous.

Ms. R: I am enjoying it more. At the beginning of the year, I was very,
very fiightened. Not of the students, but they have high, high expectations
here. . ., the administration and the parents and the school in general. And I
was really worried that I would not meet those expectations, that I was—
you know, they, I don’t want to say intimidate, but I was, after those six
days of new teacher training, I was definitely worried that I could not do
enough to be a good teacher at this district... It was basically, we were
given the impression that as new teachers, we would be watched very
closely, our progress and our, you know, style and everything would be
watched very closely. And it was very important on how many people we
were passing and how many people we were not passing. . . That would, I
would say, would be the biggest thing. And then there was a lot of work.
“Here’s this book. Read this. Here’s this book. Read this.” And there was
a lot of homework, too. And I was like, “Holy cow! I cannot do this all
year.” [But] that’s calmed down considerably (Pre, 13.40-14.24).

Ms. Riley was concerned that the expectations both inside and outside of the
classroom would be unreasonable and she would not be able to meet them, but eventually
she found out that the expectations were more reasonable than she had expected as the

school year got underway.

Ms. Wells: Reported stresses.
Of the 6 participants, Ms. Wells reported the second fewest number of stress
categories, 9 of the 22, and the second fewest number of Main stresses, 3, namely After

hours work/long hours, Responding to problematic student behaviors, and Lack of

140

student interest/motivation. Overall, she seemed to me to be least stressed teacher in the

sample.

Table 10

Ms. Wells’ Top, Main, and Mentioned Sources of Stress

 

Stress salience

Stress categories

 

Top stress(es)

After hours work/long hours

 

Main stresses (M)

[After hours work/long hours]
Responding to problematic student behaviors
Lack of student interest/motivation

 

 

Mentioned stresses (m)

 

Directing student explorations of mathematics

Creating, aligning, modifying, or implementing curricula
Relationships and communications with students
Learning and teaching unfamiliar content

Dealing with class length, pace, or schedule

Challenges associated with professional development

 

Note. Brackets indicate stresses that were top, but then are necessarily also Main.

For After hours work/long hours, Ms. Wells said that the long hours that she

worked was her top stress. She is often at school very late planning, grading, and helping

her students.

Ms. W: I try to get here by 7. And then I do random things in the
morning, whether it’s like making copies or getting the agenda on the
board or whatever it is before the kids come in at 7:50. You know, teach
my normal six-hour day. And then afterwards, I usually put in 2, 3, maybe
4 hours after school here, doing miscellaneous things, helping students,
planning for the next day, copies, whatever it is, checking e-mail, regular
stuff. And then I still end up taking a lot of it home. You know, 6:00 will
roll around. And I’ll say, “I’m ready to go home, but then I’ll still have to
take home a stack of papers to grade. Or I’ll have to take home some
plans or write a test when I get home. Or make a review. . .and then I’ll
usually stay up until 11:00 trying to get stuff done, just to stay on top of
everything. And by the time Friday rolls around, I usually don’t do
anything on Friday night. And Saturday, a lot of times, if I can pull myself
away, here and there I might take an hour out of the day to do a few

14]

 

grading things or whatever. But then on Sundays, that’s the day that it

kind of hits. And you’re like, “Okay, I’ve got to get ready for this week.

I’ve got to get all this grading done.” So you end up putting almost a full

day in on Sunday. And it’s just really time consuming outside... So that’s

really my biggest challenge is trying to find a balance... (Pre, 18.41-

21.20).

Ms. Wells worked late into the evening hours grading and planning at home
during the week, took a little time off on Saturday, and then worked all day Sunday trying
to get caught up on grading and planning.

In terms of Responding to student behaviors. Ms. Wells worried when students

are joking around that it will escalate into a fight. For her, that is stressful, because those

situations can escalate very quickly.

Ms. W: Okay. Student behaviors, I mean, that’s always a major
stress. I mean, when you’ve got kids joking around. And you’ve got other
things going on... But the students’ behavior is always a challenge,
because I mean, you’ve always got kids that are goofy and joking around
and, “Are you joking or are you really about to punch each other?” It’s
like, and it only takes a split-second for it to escalate. Whatever. So that’s
always a stressor (Post, 15.42-16.15).

Ms. Wells mentioned struggling with specific student behaviors other than
joking, such as student talking while she is talking at the front of the class, talking
while other students are trying to finish a quiz or test, students who will not work
unless she was physically present to answer every question that they had, etc. Her
frustration with student talking at inappropriate times also related to her
challenges with Lack of student interest/motivation in her mathematics class.

In discussing Lack of student interest/motivation, Ms. Wells also said that she

wishes that her homework tum-in rates, which are 30% or less in all of her classes, were

142

better. She also described how difficult it was, at times, to get them to work on

assignments in class.

Ms. W: [Students’ lack of motivation] is a big one at this school,
and in general, overall in my classes. I mean if you, you could kind of see
it from those graphs back there. . .. And those are goals that they set at the
beginning of the year... Almost all 5 of my classes said, “We want 80% of
the class to turn in homework every day.” So... then they should all have
all of their homework, right? 80% of the class should. And their
homework scores are awful... You’ve got maybe [listing off percentages
for each class period] 10[%], 30[%], 15[%], 10[%]. 30% of the class
turning in homework every day is just not acceptable. . . In every class, it’s
probably only about 30% of the kids that actually do their homework
every day consistently, bring it in complete. . .. And you limit it. I mean
half the time, I’m giving them... only like 12 problems a night. 12
problems should not even take them more than half an hour, if they paid
attention in class. And when I’m giving them 15 rrrinutes in class to get
started, there’s really no reason for them not to have it. So it’s just them
not doing it. It’s them being lazy... (Post, 16.16-17.21).

So getting students to meet their own goals for turning in homework was stressful
for Ms. Wells, as well as trying to keep them engaged in class. But later in the interviews,
she said that that stress has lightened up a bit since she implemented a ticket out policy
where students have to submit an assignment before they can leave her class.

The summaries above give the reader some sense of the factors that contributed to
each individual’s stress as a classroom teacher. But because these teachers were alike in
many ways, it also makes sense to examine their collective experience. In the next
section, I look across these novices’ stresses and consider which were salient (i.e. “top,”
and in some cases, “Main” stresses) for the group as a whole and which are common, but

not necessarily salient, for this group.

143

Salient Stresses Overall

In the analysis that follows, I define being a “salient” stress as being a “Main”
stress for each participant. For all participants, being a “Top” stress also implies being a
“Main” stress, even though my criteria for “Main” stresses did not overtly require it.

The first six stress categories listed in Table 11 are the most common stresses that
are salient for the six novices in this study taken as a group: Lacl_< of student
interest/motivation, Responding to problematic student behaviors, Dealing with class
le_ngth pace, or schedule, Managing classroom discussions, After hours work/longhours,
and Relationships and communications with administrators. Note that these 6 categories
collectively represent 8 of 10 “Top” stress categories and 18 of 24 “Main” stresses
reported by these novices. So there is good reason empirically for focusing on these 6
categories to understand the experiences of the group.

I will discuss each of these stresses only briefly, as most of them have been
described with examples in the previous section about each individual teacher’s salient
stresses. I refer the reader back to that section for specific quotes from the novices’
interviews. The first group of 6 stress categories in Table 11 contains those categories
that at least one teacher reported two novices reported as a Main stress. The second group
of 6 stress categories contains those that were Main stresses for exactly one novice. The
third group of stress categories represent those that were only “mentioned” stresses for
any novice reporting them.

Lg]; of student interest/motivation was the most common Main stress and was
also atop stress for more novices than any other category. This stress was very common

and relatively similar across participants. Novices tried to get student participation from

144

all of their students; in particular, they struggled to elicit participation of the students in

their lower-track courses.

Table l 1

Stress Categories Sorted by Frequency as Main Stresses

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stresses
Stress category names Top Main Mentioned
B, G, J,
Lack of student interest/motivation G, J, R R, P, W
B, P, J,
Responding to problematic student behaviors B, P W G, R
Dealing with class length, pace, or schedule J, R B, P, W
Managing classroom discussions J J, R G, P
After hours work/long hours W B, W J, P
Relationships and communications with
administrators B B, R P
Creating, aligning, modifying, or implementing
cunicula B G, J, P, W
Challenges associated with professional
development B B J, W
Teacher boredom G G B
Assessing student understanding I P
Working with technology G
Relationships and communications with collea ues G
B, G, J,
Learning and teaching unfamiliar content R, P, W
Relationships and communications with parents B, G, R, P
Planning lessons G, J, P
Directing student explorations of mathematics G, J, W
Teaching students of varying ability levels B, J, P
Preparing for, implementing, and evaluating
standardized tests G, J, R
Responding to unexpected student ideas B, G
Relationships and communications with students B, W
Finding and utilizing resources G
Student diversity issues G
Total 10 24 46

 

 

 

 

Note. First initial of last name represents each teacher (i.e. “B” represents Ms. Boone, etc.)

145

 

An example of Lack of student interest/motivation surfaced during Ms. Grant’s
interview, because her students didn’t want to engage with her teaching. She felt like she
didn’t enjoy teaching math as much as she might have enjoyed teaching another subject,
like her teaching minor, English, because it was easier to foment conversations that were
more interesting and relevant to the students’ lives. She said that she wanted to help her
students, but they wouldn’t put forth any effort.

Responding to problematic student bahaviors was both the second most common
Main teaching stress and the second most common top stress category that novices
mentioned. There were a variety of storylines here that varied from individual, irritating
student behaviors, like swearing or chattiness, to patterns of individual student behavior
that the novice couldn’t get the student to control. During Ms. Price’s stress story, she
said that she tried using all of her resources to deal with inappropriate student behaviors,
talking to the student, to the school administrators, and to the student’s parents, but
sometimes none of her resources helped.

I judged that both Ms. Riley and Mr. Jones experienced Dealing with class length,

pace, or schedule as a Main stress. Both said that they had agreed on a schedule at the

 

beginning of the year that was difficult to keep up with and that they were going to give a
uniform final exam with the rest of their department. But Ms. Riley was on the trimester
schedule and had to reach the exact same point in the material as her peers, while Mr.
Jones was teaching with his mentor and they had to make a reasonable amount of
progress by the end of the semester.

Mr. Jones and Ms. Riley were also the only two teachers who experienced

Managing classroom discussions as a Main stress as well. Both Mr. Jones and Ms. Riley

146

experienced stress related to challenges in getting participation fiom their students. Both
of their discussion went awry. But while Ms. Riley decided to bail on those discussions
and avoid them the following year, Mr. Jones continued to work during class and to
reflect on those challenges afterwards to improve the lessons for the following year.

For After hours work/long hours, both Ms. Boone and Ms. Wells expressed
similar concerns. They both had put in many hours outside of school to meet the demands
of their jobs. And while their workloads had become somewhat more reasonable, they
still required an inordinate amount of their time outside of school hours.

Finally, for Relationships and communications with administrators, Ms. Boone
and Ms. Riley were judged as experiencing Main stresses for very different reasons. Ms.
Boone described how frustrated she felt when the administrators sent her and her
colleagues to a first-year teacher orientation during her second year of teaching. Ms.
Riley, on the other hand, was very intimidated by the high expectations expressed by the
administration at her orientation before her first year teaching at Holly High School
which was her second year of certified teaching.

So it is clear that, while aspects of these experiences were common across this set
of teachers, there was also a great deal of diversity within each category of stresses, even ,
for the Main stresses that teachers experienced.

There were also several commonly reported stresses in Table 11 that were not
particularly salient for any teacher, namely Learningand teaching unfamiliar content,
Relationships and communications with parents, Planninghxsrfl, Directing student

explorations of mathematics, Teachirgstudents of varyingabilitv levels, and Preparing

147

fog implementipg, and evaluating standardized tests. This appears to suggest that some of
the most common stresses that teachers experience are not particularly poignant.

Now that I have reviewed the salient and common stresses in this case study, I
return to the categories in the teacher stress literature to compare these stresses with the
ones predicted by the literature to determine whether this research study uncovered any

new categories of teaching stress.

Stresses Named in the Literature and New

I initially based the definitions of these teacher stress categories loosely on the
existing categories in the teacher stress literature. I modified those categories during my
pilot study (Lewis, 2004) in iterative fashion as I analyzed that data set. In this study, I
continued to iteratively refine the categories created during the pilot study while
analyzing this new data set. As a result, some of the stress categories that I mention in
this study have not been described in the existing literature (see “New to literature”
column in Table 12), some match those reported in the literature very closely (see
“Existing” coltunn), and others only partially overlap with the literature and are partially
unique to this study (see “Partly new” column).

I list these categories in Table 12. As in Table l 1, the first group of 6 stress
categories in Table 12 consists of those categories that at least two novices reported as a
Main stress. The second group of 6 stress categories contains those that were Main
stresses for exactly one novice. The third group of stress categories represent those that
were only “mentioned” stresses for any novice reporting them. So these stress categories

are listed in terms of their salience for the novices in this study (see Table 12).

148

Table 12

Teacher Stress Categories Reported in or New to the Literature

 

Stress category names

Status of eat my

 

Existing

Partially
new

New to
literature

 

Lack of student interest/motivation

 

Responding to problematic student behaviors

 

Dealing with class length, pace, or schedule

 

After hours work/long hours

 

Relationships and communications with
administrators

>< ><><><><

 

Managing classroom discussions

 

Relationships and communications with
colleagues

><

 

Challenges associated with professional
development

 

Creating, aligning, modifying, or implementing
curricula

 

Assessing student understanding

><><

 

Working with technology

 

Teacher boredom

><><

 

Learning and teaching unfamiliar content

 

Relationships and communications with parents

 

Planning lessons

 

Teaching students of varying ability levels

 

Preparing for, implementing, and evaluating
standardized tests

 

Relationships and communications with students

 

Finding and utilizing resources

><><>< ><><><><

 

Student diversity issues

 

Directing student explorations of mathematics

X

 

 

Responding to unexpected student ideas

 

 

 

X

 

Note. First set of stress categories were Top stresses for at least one novice; second set were Main stresses
for at least one novice but not a Top stress; third set were only judged as mentioned stresses for novices.

While I could go into great detail about how these “Existing” categories overlap

with the stress categories listed in the related literature, the most important stress

categories to discuss appear to be those partially or completely new to the literature,

149

 

particularly those that were Top or Main stresses for these novices. It is those 5 categories
that I will now discuss.

Mmging classroom discussions was the only new or partially new stress that was
a Top stress for these novices. Managing classroom discnssions overlaps in part with
Poor student discipline because it describes how students can choose not to participate or
to be contentious in the classroom during whole-class discussions. But Manag'ng
classroom discussions also has the added expectation that much of the mathematically
meaningful content of lessons comes from the students, as well as the possibility of
opening up those ideas to mathematical scrutiny by the other students in the classroom
and the stresses that orchestrating such activities can impose on the teacher.

For Managing classroom discussions, recall that Mr. Jones felt frustrated by how
much of the talking that he was doing when he wanted more information to come from
the students. He felt like it was a combination of the questions he was posing and how the
students were responding to them and to each other that were making this challenging.

There were four stress categories that were Main stresses for some of these
novices but were not a Top stress for any of them that were also new or partly new to the
teacher stress literature. The two stresses that were new to the teacher stress literature
were Working with technology and Teacher boredom. The two stresses that were
partially new to the teacher stress literature were Creatifing, aligphrggmodifvirggor
implementing curricula and Assessing student understanding. I will discuss the former
two stress categories and share examples of them, while I will only briefly discuss the

latter two categories without examples.

150

Workianith technology_is a relatively new phenomenon primarily because
technology itself was not common in educational settings until the last few decades. For
Workingwith technology, Ms. Grant described how challenging it could be to get her

students to understand how to use calculators in her classroom.

Ms. G: Some of them think they did it all wrong when the graph doesn’t

appear on the screen. And they don’t realize that they aren’t looking at the

right window. And at this point, I feel like they should know the basic

keystrokes of entering an equation, using zoom efficiently, and finding a

good window. . .So I try to spend more time doing it. .. [And] they just

don’t know yet how to troubleshoot themselves. So I feel like I have to

wind around the room. And I have like people calling me all the time

(Post, 12.17-14.19).

So using calculators could make teaching more demanding and stressful for Ms.
Grant. But Ms. Grant also mentioned that she continued to engage in that struggle,
because it also allowed her to teach students useful skills and opened up possibilities for
mathematical discussions for which the mathematical operations that would need to
precede those discussions might have been too tedious to undertake.

Teacher boredom was also not in the existing literature, possibly because
boredom is not usually something that is considered to be stressful, although it was for
two of the novices in this study. For Teacher boredom, the reader may recall how Ms.
Grant described how boring teaching mathematics was for her compared to other
subjects, such as English (her teaching minor) or social studies (the subject that her

husband taught).

Creating, alignflg, modifying, or implementing curricula relates to Time pressure

 

and work overload. But there also exists the possibility of creating series of lessons and

151

activities that have exploratory activities and whole-class discussions at their core, where
students play a meaningful role in developing, explaining, and substantiating
mathematical concepts, as well as placing those ideas under the mathematical scrutiny of
the rest of the students in the class.

Assessing student understanding relates to possible conflicts with parents over
student achievement as Caspari (1976) mentioned, while it also introduces the idea that
assessment can be a formative experience. It can be stressful, because the students are
learning, as well as being responsible for the learning of other students in their group.
Both experiences can be frustrating for the students and, as a result, for their teachers.

In summary, many of the stresses reported in the teacher stress literature were also
reported in this study. In addition, there were four new categories to the literature and
four categories that contained at least some new types of stresses that have not been
reported in past studies of teacher stress. What this analysis does not speak about is how
any of those categories of teaching stress related to participants’ attempts at SBT, which

is the topic that I address next.

Stresses Related to SBT and Otherwise

It is unclear from a brief overview of the data on top, Main, and mentioned
stresses whether their attempts to enact some part of the vision of NCTM’s (1991)
Teaching Standards contributed to the stress that these teachers reported and, if it did,
how great was that contribution. Table 13 displays the same information as Table 11,
“top,” “Main,” and “mentioned” stress categories for each teacher, but when my analysis

of the interview data indicated a teacher’s attempts to enact some aspect of NCTM

152

Standards-based teaching (SBT) was linked the source of stress they reported, the

teacher’s initial is listed in boldface.

Table 13

Top, Main, and Mentioned Stresses with SBT Links

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stresses
Stress category names Top Main Mentioned
B, G, J,

Lack of student interest/motivation G, J, R R, P, W
Responding to problematic student behaviors B, P B, P, J, W G, R
Dealing with class length, pace, or schedule J, R B, P, W
Managing classroom discussions J J, R G, P
After hours work/long hours W B, W J, P
Relationships and communications
w/administrators B B, R P
Creating, aligning, modifying, or implementing
curricula B G, J, P, W
Challenges associated with professional
development B B J, W
Teacher boredom G G B
Assessing student understanding J P
Working with technology G
Relationships and communications w/colleagues G

B, G, J,
Learning and teaching unfamiliar content R, P, W
Relationships and communications with parents B, G, R, P
Planning lessons G, J, P
Directing student explorations of mathematics G, J, W
Teaching students of varying ability levels B, J, P
Preparing for, implementing, and evaluating
standardized tests G, J, R
Responding to unexpected student ideas B, G
Relationships and communications with students B, W
Finding and utilizing resources G
Student diversity issues G
Total 24 46 70
Number SBT-related ll 14 25
Percent SBT-related 45.8% 30.4% 35.7%
Note. First initial of last name represents each teacher (i.e. “B” represents Ms. Boone, etc.)

153

 

Table 13 also summarizes the number and percent of “top,” “Main,” and
“mentioned” stresses related to SBT. Summing teachers within categories, Table 13
shows that in approximately half of the cases of Main stress, there was some connection
to a teacher’s attempts at SBT, while only about one-third of the cases of the Mentioned
stress categories were so related. Using this view without further reflection, it would
appear that there is a powerful relationship between these novice teachers’ stresses and
their attempts at SBT. But if one keeps in mind that even one mention of an SBT link to a
stress category qualifies the category as relating to SBT, it is clear that further analysis is
needed to determine whether SBT is a prominent theme in these novices’ teaching
stresses.

The entries in Table 14 make it clearer why I am hesitant to state that SBT is a
prominent factor in these teachers’ stresses. As the reader may recall, I divided the data
into chunks where the novice talked about a single stress category wherever possible. As
long as the participant talked about the same source(s) of stress, that turn or sequence of
turns was coded as a single data chunk; therefore, data chunks could last for only part a
single turn in the conversation or for several turns or pages. One reference to SBT in the
data chunk implied that that chunk was related to attempts at SBT. The stress categories
shown in italics are those related to SBT. The most salient 6 categories are shown in
boldface. Note that one stress category was both strongly related to SBT (italicized

categories) and salient (bolded categories) for my 6 teachers.

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Table 14

Teacher Stress Categories Listed by Proportion Related to SBT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Teacher Stress Category SBT Total % SBT
Directing student explorations of mathematics 4 4 100. 0%
Planning lessons 3 3 I 00. 0%
Relationships and communications with colleagues 2 2 100. 0%
Responding to unexpected student ideas 2 2 100. 0%
‘ Managing classroom discussions I 0 1 7 58. 8%
Finding and utilizing resources I 2 50. 0%
Student diversity issues 1 2 50. 0%
Assessing student understanding 1 3 33.3%
Working with technology 1 4 25.0%
After hours work/long hours 2 10 20.0%
Creating, aligning, modifying, or implementing curricula 2 11 18.2%
Learning and teaching unfamiliar content 1 7 14.3%
Responding to problematic student behaviors 2 25 8.0%
Dealing with class length, pace, or schedule 1 13 7.7%
Lack of student interest/motivation l 29 3.4%
Preparing for, administering, and evaluating standardized tests 0 3 0.0%
Challenges associated with professional development 0 3 0.0%
Relationships and communications with administrators 0 5 0.0%
Relationships and communications with parents 0 4 0.0%
Relationships and communications with students 0 4 0.0%
Teacher boredom 0 2 0.0%
Teaching students of varying ability levels 0 4 0.0%
TOTAL 34 159 21.4%

 

 

 

 

 

 

Note. Italicized categories indicate those most strongly linked to novices’ attempts at SBT (i.e. _>_ 50% of
data chunks related to SBT). Bolded categories indicate those novices most commonly reported.

In Table 14, only the first 7 of the 22 teacher stress categories contain a
substantial proportion (Z 50%) of data chunks related to attempts at SBT. And of those 7
stress categories, only Managing classroom discussions was reported with relatively high
frequency (i.e. at least ten data chunks) compared with the other 22 stresses in the table. I
reported the example in the previous section about how Mr. Jones struggled to get
students to engage meaningfully in their whole class discussions. He wanted most of the

information to come from the students. This stress relates to Mr. Jones’ attempts to

155

implement Standard 3, Students’ role in discourse, because he was trying to bring
students into a more central role in the classroom where they actively contributed
meaningful mathematical ideas to the discussions.

Of the 7 categories in Table 14 that relate most strongly to attempts at SBT,
Planning lessons, Relationships and communications with colleagues, Finding and
utilizing resources, and Student diversity issues are interesting, because the definitions of
those categories do not necessarily suggest strong links to attempts at SBT. But none of
these were salient for these teachers. On the other hand, Relationships and
communications with colleagpes was a Main stress for Ms. Grant, primarily because she
had difficulty frnding teachers who thought the way that she did, particularly about
treating the students humanely when disciplining them. While this is a worthy goal, it is
not the primary domain of the NCTM (1991) Teaching Standards.

For the other 3 categories, Directingstudent explorations of rnathematics,
Respondifl to unexpected student ideas, and Managing classroom discussitms (which
was already discussed), the relationship to instruction that uses student inquiry and active
student participation in discourse is at least slightly more obvious. For example, if a
teacher is Dumfipg student explorations of mathematics, it means that the activity is
constructivist or discovery-based, so that the student is working at sense-making, which
would make the activity worthwhile, firlfilling Standard 1, Worthwhile mathematical
tasks. If a teacher did not intend to use unexpected student ideas as a meaningful part of
the lesson, Responding to unexpected student ideas would not be stressful, because they
would simply be dismissed. When a teacher treats such ideas as valid mathematical

conjectures, s/he is working at least to meet Standard 3, The students ’ role in discourse.

156

It is also interesting to note that of all of these seven categories of teacher stress,
only two were judged as Main stresses for at least one participant, namely Relationships
and communications with colleagpes and Managing classroom discussions (see Table
13). Relationships and communications with colleagrfi was judged to be a Main stress
for the only teacher who reported it as a stress, while Managing classroom discussions
was judged to be a Main stress by 2 of the 4 novices reporting that stress. Both of these
stress categories were related to SBT for all of the teachers reporting them.

Because it appears that only Managing classroom discussion_s was a salient stress
for the group of novices out of the seven stresses strongly related to attempts at SBT, it
appears that these novices’ attempts at SBT only contribute modestly to the teaching
stresses that they experience.

I will give an example of the most frequently reported SBT-related category,
Managing classroom discussions. This latter category was mentioned by four teachers, all
of whom related it at least once to their attempts at SBT. Two of those four described
their challenges with enough emphasis for this category to be judged as Main for them,
although it is unclear whether all of those statements related to their attempts at SBT.

I will also illustrate what these stresses looked like with examples fi'om two of the
categories with the largest proportion of SBT-related data, namely DnectLryg student
explorations of mathematics and Planning lessons, which were mentioned by 4 and 3
teachers, respectively and neither of which was a Main stress for those teachers.

For example, two teachers described the challenges they faced Directing student
explorations of mathematics, as students grappled with explorations of mathematical

problems in the classroom. For example, during student explorations of prospective

157

congruency properties, Mr. Jones found that they did not understand the reasoning behind
the instructions for the assignment, namely why they were attempting to create two
different triangles using a prospective congruence theorem like SSA. As a result, Mr.
Jones had to explain the assignment to several students individually, then to the class as a
whole with what he perceived as limited success. Implementing a lesson that was based

on student exploration of geometric concepts qualified this episode as relating to SBT.

Mr. J: The challenging part was probably trying to get them to understand
what they were doing, as far as why they were drawing two triangles, and
telling them that we’re trying to draw two triangles that are not congruent.
They didn’t really understand why. They didn’t really understand why we
cared about two congruent triangles. So maybe trying to do a better job of
explaining why we want to figure out about two congruent triangles, or
even why it was important, why we came to say they’re congruent. Why
do we have to have a minimum set of criteria? It would be very important
to lay that out before we even tried to have any kind of activity where they
had to figure out why the two triangles were congruent or not. . . And it’s
not an activity that’s necessarily completely—the idea of it as far as them
working with congruent triangles and seeing that there is a criteria that
they need in order to prove two things, two triangles are congruent. But
maybe a different activity. But it’s going to require some thought (Post,
2.42-4.17).

Teachers reporting Planning lessons as an SBT-related stress struggled to find
something interesting and engaging that would involve their students more in their
lessons and connect to their experiences more than the textbooks that they were teaching
from. For example, Ms. Price mentioned that she wanted to plan lessons to involve her
students more and was co-planning with a colleague while they were piloting a new

textbook with a more investigative approach to mathematics then their current textbook,

namely Discovering Algebra 2 by Key Curriculum Press.

158

Ms. P: Yeah, like I feel like I have more sort of time right now, in that I
have, I usually know where things are going. So I have more time to think
about my lessons, rather than just make sure I have a lesson ready to go.
So I can think more. My challenges now are just kind of making the
lessons better, a lot of them. I was thinking of better ways to approach
things or maybe hands on activities or computer lab, so it’s not so—you
know, to get the kids more involved. Things like that. That’s what I kind
of feel like I focus on a lot... And I’m also focusing on, because I’m
teaching a new book. I’m teaching algebra 2 before which I’ve not taught
before. And I’m teaching it out of a new book. I’m piloting that. So
another teacher and I are having ongoing conversations about things we
like about the book and things we don’t like. And I’m finding myself
having to supplement the book at certain points, and then skipping certain
parts. So that’s kind of a challenge, but hopefully it’ll pay off in the end,
when we finally use the book (Pre, 7.1-7.20).

Finally, an example of Managing classroom discussions comes fi’om Mr. Jones’
interviews. Mr. Jones was the only teacher who listed Managing classroom discussions as
a “top” stress. Mr. Jones had a difficult time explaining why the ASA condition was
sufficient to imply congruency conceptually. He had chosen to develop the proof
conceptually, but the students struggled to understand what he was talking about, which
made it more difficult for him to move forward with the discussion that he had planned.
He also felt frustrated that he had not adhered to his pedagogical goal of having the
students talk more than he did during the discussion. This frustration also appeared to be
related to his frustration at trying to set up the conversation and the instructions for the

task clearly enough so that the students could more meaningfully engage in that

conversation. But he also wasn’t entirely disappointed with the results of that discussion.

Mr. J: I think I had only heard from three students about their ideas from
the ASA criterion, but to me it was really hard to describe to all the
students exactly how that relationship was in fact enough information. So I
think that the students did a good job of talking about how the sides
related. And I think that’s what I wanted when I initially said, “Well, how

159

could you describe in your best words how this works?” . . . [But] I think

that I did a little bit more talking than I should have... I remember the

looks on the students’ faces. Some of them got it. Some of them didn’t.

But I think that was okay for them to be frustrated right away. It was our

first look at it. And I think it was okay for them to be fiustrated with that,

and maybe not understand exactly how the sides A, B matched up with the

angle, and how all the sides and angles had to match up.

Mr. J: I was frustrated with myself. And I think the students were

frustrated... That was criteria number 4 and I wanted to talk about all of

[the prospective congruence theorems] that day, so it was probably very

frustrating to see that. And the students were maybe not getting it. . . It was

a little frustrating that our conversation wasn’t as meaningful, I thought, as

it should have been (Post, 4.29-6.6).

F acilitative vs. Debilitative Stresses

I have described how these novices’ stresses intersected with the existing teacher
stress literature and how they interacted with their attempts at SBT, reporting that SBT
appeared to contribute modest additional stress to novices’ teaching lives. What I have
not described is what type of impact the stresses these novices described appeared to have
on them overall. That is what I attempt to address in the next section.

I asked five of the six participants which stresses were constructive or facilitative
and which were nonconstructive or debilitative5 . I gave the teachers examples of what
one teacher called good stress (e.g., kids fighting her when she tries to get them to discuss
ideas, concepts, and conjectures in mathematics class, because she feels she’s doing her
job well when she encourages this) and bad stress (e.g., when kids don’t turn in their
homework, because they can’t move forward and there was little or nothing she could do

to improve the situation). But I did not formally define these two constructs, because I

wanted teachers to give me examples using their own definitions of these constructs.

 

5 My interview with Ms. Boone went very long, so I either did not remember or did not choose to ask her
this question.

160

Table 15

Novices’ Facilitative and Debilitative Stresses

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stresses
Participant Facilitative Debilitative
Ms. Boone [Not asked] [Not asked]
Any challenge is constructive,
because he learns from them and
Mr. Jones faces them with a positive attitude. [None mentioned]
To be persistent with the students
and almost to trick them, so that
they can see that they can do math
and be successful [Lacl_( of student
interest/motivation]. Technology
issues, because they’re “fixable,”
or in other words, because the
students will work at becoming
better, even though their skills and
confidence are low |Working with
Ms. Grant technology]. [None mentioned]
Bad stress is when they come in
and haven’t attempted homework
Good stress is when they’ve or when they shut down and won’t
attempted the homework, but got even try [Lack of student interest/
all the answers wrong [opposite of motivationl. Stresses for Ms. Riley
Lack of student interest/ are all pretty much bad, because
Ms. Riley motivation]. stress takes it toll on her.
If a student asks a questions and it Behavioral issues, kids being off
catches her off guard and makes task, having to contact parents and
her think [Responding to write referrals. She says that these
unexpected student ideas]. Trying are things that she has no control
to come up with ways to get the over (e. g. a kid shouting out
students more engaged [Lack of something in class) |Resmnding to
Ms. Price student interest/motivation]. problematic student behaviors].
The ways that she has now
structured the grading system
(using stamps for full effort to cut
down on her grading and giving the
students a warm up and a ticket out
to assess understanding and as a
means of getting them to start their
homework in class) [After hours
Ms. Wells work/long hours]. [None mentioned]

 

161

 

All five novices described stresses that they felt were either constructive or
facilitative. But even after being given an example of a stress that a teacher in the
practicum or pilot study considered to be “bad stress” or debilitative, only two
participants, Ms. Riley and Ms. Price, offered stresses that they considered to be
nonconstructive. Table 15 summarizes the responses of the teachers to this question.

For the two teachers who offered examples of nonconstructive stress, both talked
about Laclpof student interest/motivation. Ms. Riley talked about students who haven’t
attempted their homework or when they shut down or won’t even try. Ms. Price talked
about students being off task. Ms. Price also talked behavioral issues, like a student
shouting out something during class that she has no control over, as “bad” stress. Ms.
Riley also said that all stress for her is bad, because they take their toll on her.

Of the five teachers who mentioned stresses that they considered constructive, one
teacher, only Mr. Jones talked about al_l of his teaching challenges as being constructive,
because he learns from them all. Ms. Wells said that her new method of grading has been
a positive outcome that has at least partially resolved the time challenges (After hours
work/long hours) that she faces. While it was not entirely clear that Ms. Wells understood
the question, it was clear that she felt like her new grading system was a positive
outgrth of her time management and student engagement issues.

Ms. Grant said that being persistent with students and tricking them into seeing
that they can be successful was a constructive stress for her (i.e. working on M
student interest/motivation). She also said that technology issues were constructive

stresses for her, because they were “fixable” (i.e. Workingwith technology).

162

Ms. Price talked about students’ ideas catching her off guard (i.e. Resp_onding to
unexpected student ideas) as good stress (which also relates to her attempts at SBT,
because that only causes stress if the teacher is attending to student ideas). She also
mentioned trying to get students more engaged, in other words, Lack of student

interest/motivation, as a positive and constructive challenge. Like Ms. Price, Ms. Riley’s

 

constructive stress also related to student engagement, or LackL of student
interest/motivation, describing positive stress as attempting all of the problems but
getting them wrong, while negative stress for her was when students hadn’t attempted
any problems at all.

Ms. Grant, Ms. Price, Ms. Riley, and to some degree Ms. Wells all talked
specifically about stresses related to Lack of student interest/motivation when discussing
which stresses were constructive and nonconstructive. Ms. Grant and Ms. Wells talked
about those issues as constructive. Ms. Riley talked about the Lack of student
interest/motivation as being nonconstructive. And Ms. Price talked about issues of
student engagement as being both nonconstructive and constructive. This strange
phenomenon appears to have more to do with Ms. Price’s assertion of how much control
she has over the situation. Ms. Grant described student engagement as something she
could control. Ms. Wells talked about how she responded to the challenge of motivating
students and managing her time by implementing bell work, ticket out, and stamping
homework. Ms. Riley described it as something that was frustrating; since she was
talking about lack of student homework completion, that too would be out of her control
once the students were in class. In Ms. Price’s case, it could be either. If it was related to

Responding to problematic student behaviors, Ms. Price was concerned that she could not

163

change it. But she did speak of the challenge of working to alter lessons to be more
engaging as a constructive stress. That was an aspect of Lack of student

interest/motivation that was clearly under her control.

Summary

In summary, these novices experienced many of the stresses predicted by the
literature and several others that are, in some cases partially and in some cases
completely, new to the literature. Also, as predicted by the literature, many of their salient
stresses appeared to be related to their attempts to keep students engaged in the subject
matter (in this case, mathematics) and to meet their classroom management goals. There I.
was no clear pattern relating a participant’s stresses to attempts at SBT. And it appeared
that attempting SBT contributed only very modestly (at greatest) to these participants’
teaching stresses.

Finally, there was some variance in the ways that novices viewed their challenges,
from being entirely positive as opportunities for growth to being entirely negative
because they took a toll on their resources. The novices generally identified the
challenges of getting students motivated and engaged in their classrooms as constructive.

But when students regularly misbehaved or chose not to participate, particularly if the

 

teacher felt powerless to correct the situation effectively, the teachers described that as
debilitative stress, because there was so little they could do about those challenges.
In the next chapter, I describe how novices coped with these challenges and, at

times, whether they viewed those coping resources as effective.

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Chapter 6: Coping Resources

In this second phase of the analysis, I examine and analyze the coping resources
that these six novices reported. I also consider how those resources connect to the sources
of teaching stress and to their reported and observed attempts at NCTM (1991)
Standards-based teaching (SBT).

As a reminder, I define coping resources as means of avoiding, alleviating, or
eliminating teaching stress; such resources take the form of physical assets, social
relationships, or self. These three types of resources are means of dealing with, avoiding,
or alleviating stress, whether targeted at the symptoms or at the sources of that stress.
These resources may change the classroom context or the teacher’s perceptions of that
context or their relationship to it. I provide a conceptual mapping that shows how teacher

stress is created and how coping resources mediate those stresses in Appendix C.

Coping Resource Framework: Categories of Resources and Examples

Before proceeding to the coping resources data analysis, I summarize the
framework that I used in analyzing the data set. I invite the reader to review the Methods
chapter for greater detail on this fiamework. Using the grounded or open coding method
described by Glaser and Strauss (1967), I developed coding categories. In beginning the
analysis, I looked for all of the teaching resources participants reported. As a reminder,
by teaching resources, I mean any physical or virtual (i.e. Intemet-derived) asset, social
interaction or intervention, strategy, idea, or psychological technique that had the

potential to help the teacher be more effective or comfortable in the act of teaching or to

165

alleviate stresses associated with teaching activities (see Appendix C). It is also important
to reemphasize here that I have defined teaching broadly, as all acts and thinking related
to classroom teaching, regardless of where or when those actions or thoughts took place.

After finding all teaching resources participants reported, I narrowed the list to
only those that teachers attempted to use to alleviate their teaching stresses. If the teacher
talked about the resource as alleviating stress generally, I placed that coping resource in
the “GENERAL” stress category, a miscellaneous category only used when coding for
coping resources. Then I sorted it into the four following categories that appeared to
describe trends in the data: Social, Collective, Self, and Physical.

As a reminder, Social resources consisted of obtaining help or advice from peers,
such as administrators, other teachers, fiiends, relatives, students, parents, etc. Collective
resources were a specific subclass of Social resources involving a group of peers that met
regularly in an organized fashion and with a specific purpose in mind (i.e. not for
informal venting or sharing of information about students). Self as a resource involved
using one’s own creative ideas, pedagogical strategies, management strategies, or
intrapsychic methods to alleviate stress. Physical coping resources involved using
existing physical materials to cope with stresses, including the Internet, books, other
teacher’s lesson plans, new seating arrangements, etc.

Clearly there are some overlaps between these categories. I invite the reader to
review the Methods chapter for a more thorough description of these categories and how
overlaps between them were resolved. But one particular overlap needs to be readdressed

at this time, namely the difference between Social and Collective coping resources.

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A teacher community (a Collective coping resource) can create interactions that
act as Social coping resources for teachers. During interviews, it was not always clear
whether the Social coping interactions teachers experienced would have occurred without
the framework of their teacher community. So it is possible that some coping resources
coded as Social should have been coded as Collective. Because of the strong and often
blurred relationship between these two categories, at times I will group them together as
“socially orient ” coping resources and at other times and at other times separately,
when creating a distinction between the two sheds more light on the novice’s coping.

Finally, I looked to see if there were links between the coping resources these
novices employed and their attempts at SBT. In the next section, I show the prominence

of these coping resource categories in alleviating the participants’ teaching stresses.

Results: Group Analysis

Before beginning to describe the results of the group analysis, I foreshadow
results presented in this chapter. I begin by looking at those coping resources that
participants reported most frequently, as well as those that they identified as their most
effective, or “top,” coping resources. I then consider for which categories of teaching
stress novices most commonly reported coping resources and what type of resources they
reported. I look across the group at how effective each participant found their coping
resources for teaching stress categories judged to be a Main stress for at least one novice.
I look at each participant’s case study individually to discuss which stresses they reported
coping resources and whether those coping resources supported or related to the

participant’s attempts at SBT. Finally, I discuss and summarize the results of this chapter.

167

Most frequently reported coping resources.

In looking across the results for each participant’s coping resources sorted by
category (see Table 16), some very striking results become evident. Clearly, Social is the
most frequently mentioned category of coping resources overall and for each individual
participant. The Self category is the second most frequently mentioned category for the
group as a whole as well as for each participant. The Physical and Collective categories
are both infrequently reported by all participants and their overall percentages are quite

small compared to the percentage of Social and Self coping resources.

Table 16

Frequency of Report of C oping Resource Categories

 

 

 

 

 

 

 

 

 

 

Social Collective Self Physical Total
Ms. B l l l 7 3 22
Ms. G 8 0 5 3 16
Mr. J 15 2 8 l 26
Ms. P 13 0 5 2 20
Ms. R 7 0 5 0 12
Ms. W 12 3 5 2 22
Total 66 6 35 11 l 18
Percent 55.9% 5.1% 29.7% 9.3% 100.0%

 

 

 

 

 

 

 

You will notice in Table 16 that I have chosen to list Collective next to Social
coping resources rather than keeping the categories in the order of frequency of report. I
digress to explain this choice. This is in keeping with the close ties that I previously

described between these two categories that I previously described.

Most effective, or “top, ” coping resources.

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When the participants were asked what their most effective coping or “top”
resources were in alleviating their teaching stresses, I judged that all of their answers
indicated that they judged their socially oriented coping resources as their most effective
and important. All of the novices except for Ms. Wells candidly and clearly stated that
their most effective coping resource was their teaching colleague(s).

Although Ms. Wells was not asked6 which coping resource was her most
effective, 15 of her 22 reported coping resources were socially-oriented (i.e. Social or
Collective) (see Table 16). This was the highest percentage of socially-oriented coping
resources (68.2%) of any participant in this study; therefore, she was judged by the
researcher as valuing those resources as most effective overall, as well. Because Ms.
Wells also said during our interviews how helpful all of her teaching peers were without
emphasizing any teacher over another, I judged that her teaching peers in general were
her most effective resource, particularly for dealing with curriculum-related stresses.

So Ms. Boone and Ms. Price reported and Ms. Wells was judged as rating their
teaching colleagues as their most effective teaching resources. All three of them
described many teachers with whom they conversed, but they did not rank one resource
above another when asked directly; indeed, Ms. Wells, in particular, specifically stated
that there was not one person that she valued as a resource more than another.

Ms. Riley and Mr. Jones reported that their mentors were their most important
coping resources. Ms. Riley reported a single mentor, while Mr. Jones circumstances
were unusual, so he actually had access to two mentors, his internship year mentor and

his formal teaching mentor. I will elaborate on this situation in Mr. Jones’ case study. Mr.

 

6 Ms. Wells was not asked this question either because her final interview ran long or due to interviewer
error.

169

Jones also volunteered (prior to being asked) a second top coping resource, namely
keeping himself and his students organized, which falls in the Self category.

So the top coping resources were generally socially oriented with one exception
where a teacher mentioned two “top” coping resources. In the next section, I discuss what

types of stresses each category of coping resources was employed to alleviate.

Coping resources overall.
Table 17

Coping Resource Category Frequency Listed by Connection to Teacher Stress Category

 

 

Stress categories Social Collective Self Physical Total

 

N
&

Responding to problematic student behaviors 31

 

\O
A

Creating, aligning, modifying, or implementing curricula 6 21

 

GENERAL

_
—

l4

 

Lack of student interest/motivation 1 12

 

Managing classroom discussions 1 l

 

Planning lessons 3 ll

 

O

Learning and teaching unfamiliar content

 

Working with technology

 

w—WNGMWNQ

After hours work/long hours

 

Challenges associated with professional development

 

~wNO\\lO\UtUI

H

Relationships and communications with students

 

Responding to unexpected student ideas 1

 

Relationships and communications with parents 1

 

Teaching students of varying abilities I

 

Dealing with class length, pace, or schedule 1

 

 

Student diversity issues 1

 

Assessing student understanding 1

 

Relationships and communications with administrators 1

 

Directing student explorations of mathematics

 

Relationships and communications with peers

 

Preparing for, administering and evaluating standardized
tests

 

Finding and utilizing resources

 

OOOOO—t—H———-—Nwm~)

Teacher boredom

 

 

 

 

 

 

 

 

TOTAL 81 5 37 11 134

 

Note. I judged coping resources as effective (E), somewhat effective (S), or ineffective (I), as listed in the
table for the Social, Collective, Self, and Physical categories of coping resources.

170

Table 17 lists the 22 categories of teaching stresses that the four different
categories of coping resources were employed to alleviate. One result that Table 17
suggests is that Social and Self coping resources were both used to alleviate a wide
variety of categories of teaching stress. It is also clear from Table 17 that, while less
commonly reported, Collective and Physical coping resources were primarily used for
alleviating stresses related to Creating, aligning, modifying, or implementihféurricula.
Physical coping resources also often relieved stresses related to Lesson planning, as
mentioned in discussions of the relevant categories of coping resources in this chapter.

The stress categories that teachers most often reported as being addressed by their
reported coping resources were Respondirg to problematic student behaviors, Creating,
aligning, modifih’ng, or implementing curricula and in general (i.e. the GENERAL
category in Table 17). They also commonly reported that coping resources addressed the
following stresses: Lacl_( of student interest/motivation, Manag'mg classroom discussions,
Planning lessons, and Learning and teaching unfamiliar content.

I will give an example of each of the two stress categories for which coping
resources were most often employed, namely Responding to problematic student
behaviors and Creating, aligning, modifying or implementing curricula. Participants
reported Social and Self resources when Responding to problematic student behyiors.

An example of a Self coping resource from Ms. Wells’ class follows:

Ms. W: In fifth hour. . .while we were going through [the exit
assignment], they were very, very talkative. And. . .I’ll stand up there and
be quiet, and I’ll wait. . .but as soon as I start to talk, they start talking
again... So today. . .instead of dealing with it, I had a select group. . .that

171

were really paying attention. So I went over the last example that I had to
go over... And made sure the ones that were paying attention really knew
how to do it. And then I said, “You know what? Clear your desks, because
this is a pop quiz.” And I turned their [exit assignment] into a pop quiz...
It’s just like, “Let their grade take a hit.” ...And a lot of parents check...
And if they’re not in line, we have a two-week break coming up. They’re
not going to see a lot of free time... (Post, 12.6-13.4).

In the previous example, Ms. Wells gave her students a pop quiz as punishment
when they wouldn’t stop talking during the discussion of an in-class assignment. The pop
quiz was a specific strategy, or Self resource, that she used to deal with flagrant student
talking. As a reminder, while such strategies may come from any source, I consider them
the teacher’s own once acquired, so I judged this to be a Self strategy.

Participants reported coping resources in all four categories to alleviate stresses

related to Creatin ali in modi in , or implementig curriculJa. An example of a

Collective coping resource used for Creating, aligning, modiM'ng, or implementing

curricula follows:

Ms. W: So we use [the Heath textbook]. And in all actuality, myself
and some of the other teachers, because we have the McDougal Littell
series for Algebra 2, we have a couple of floating copies of the geometry
one. And a lot of times we’ll go to the McDougal Littell one, because it
lays it out a little bit nicer. So we can kind of use both... And right now,
our algebra text is really outdated. But for now, I guess we have to stay
with our outdated one, because we’re working with. . .the Cognitive Tutor,
the Carnegie learning program [a computer-based algebra curriculum]...
As a department, we’re not too thrilled about it, [so] we kind of do

both. . . [Cognitive Tutor] has a computer component and then it also has
the workbook component with the student response and problem-based
learning approach... So as a department, we all use [the Heath Geometry]
text as our primary text... And we all just kind of share. “Oh, did you see
the Cognitive Tutor problems for this section?” Or “This unit’s really
good in the Cognitive Tutor book, so let’s use the Cognitive Tutor as our
primary text” (Pre, l . 1 5-3 .7).

172

Ms. Wells said that the department worked together regularly when Creating,
aligning, modifying, or implementing curricula. I judged this as a Collective rather than
Social coping resource, because there were five teachers that met. Ms. Wells mentioned
that her department met regularly to discuss teaching issues, including every day at lunch
(Post, 29.23 -29.36). She said that it was not just to gripe about students, but to talk about
management strategies and curriculum, so I judged this resource to be Collective.

An example of a Physical coping resource used by Ms. Boone to alleviate stresses

related to Cream, aligning. modifying, or implementing curricula follows:

Ms. B: Yeah. I don’t use the textbook very much at all. I hate our

textbooks... I have big issues with textbooks in general. I just think that

they’re too busy... So books, that’s kind of like my last resort. I really

enjoy utilizing the Internet. So I do that a lot... Right now, visual calculus

is very useful for me right now for my Calculus class, not for this class so

much. There’s a [website] called purple math—I can’t remember...

something like that. The Illuminations website for NCTM. I’ve gotten

some stuff off of there. .. There are other ones that I frequent (Pre, 7 .13-

7.40).

Ms. Boone didn’t like her textbook for calculus. She also reported that she didn’t
share much in common in teaching style with the previous calculus teacher, so she
resorted to looking on the Internet to find or create activities that helped make Calculus
more visual and hands on for her students. This helped alleviate stress related to Creating,
aligning, modifying, or implementing curricula in her AP Calculus course.

I now return to the whole group and look at the overall effectiveness of their
coping resources for each of their Main stresses (see Table 18). Since these stresses

appeared to be the most salient and significant for the participants, I focus my attention

on them to determine the effectiveness of these novices’ coping resources. In Table 18, I

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list only 12 stress categories, because only 12 of the 22 stress categories were Main
stresses for at least one participant.

In Table 18, notice that the coping resources are listed as Effective (E), Somewhat
effective (S), Ineffective (I), or Unclear (U) for each participant overall. For each
individual coping resource in each category, I made the judgment by first looking at each
resource and determining whether the teacher described the resource as being effective,
inconsistently or moderately effective which I have labeled as somewhat, or relatively
ineffective at alleviating stress. If no coping resource was mentioned or if its alleviating

influence on the stress was not clear, I judged that the effectiveness was Unclear.

Table 18

Main Stress Categories and Coping Resource Efiizctiveness Listed by Participant Initial

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stress categories Coping resource effectiveness
E S l U
Working with technology G
Creating, aligning, modifying, or implementing curricula B
Assessing student understanding J
Lack of student interest/motivation B, J, W P G R
Responding to problematic student behaviors B, J, P, W
Managing classroom discussions J, R
After hours work/long hours B, W
Relationships and communications with administrators R B
Challenges associated with professional development B
Dealing with class length, pace, or schedule J, R
Relationships and communications with colleagues G
Teacher boredom G

 

Note. Categories are listed in order of proportion of effective coping resources judged as Effective (E),
somewhat effective (S), Ineffective (I), or Unclear (U).

I judged the overall effectiveness of each participant’s coping resources in each
stress category by assigning values to each coping resource reported that was judged as

Effective (+1), Somewhat effective (0), or Ineffective (-1), then computing the average of

174

those scores. If the average effectiveness fell in the range of (1/2, 1], I judged that the
coping resources were effective for that category of stress. If it fell in [-1/2, +1/2], I
judged that the coping resources were somewhat effective for that stress. And if it fell in
[-l , -1/2), I judged that the coping resources were ineffective for that stress.

One notable trend in Table 18 is that teachers described coping resources for their
Main stresses with similar levels of effectiveness as other participants. For the four Main
stress categories with more than one teacher listed, all of the teachers employing coping
resources to alleviate those stresses did so with similar levels of effectiveness.

It is also clear from Table 18 that teachers had either effective or somewhat
effective coping resources for the majority of their Main stresses. Only 2 of the 18 Main
stresses novices reported were judged overall as having ineffective coping resources
associated with them. Notice also that there were an additional 6 stress categories for
which there was insufficient evidence to judge the effectiveness of their coping resources.

In Table 18, notice that there are four Main stress categories for which teachers
primarily reported effective coping resources, namely Wtfldng with techno—logy,

Creating, aligning, modifling, or implementing curricula, Assessing student

understanding, and Lack of student interest/motivation. I share an example from the most

 

 

commonly reported of these, Lack of student interest/motivation, from Ms. Wells’ class,

for which she reported effective coping resources:

Ms. W: . . .And then the kids also generate some ideas. We follow
the Baldridge model that we’ve been trying, as a school, to implement...
We ask the kids for feedback, like, “How would you like to learn these?
How would you like to learn this topic?” Or “What’s working for you?”
And like I said, that’s where I got the feedback from the kids saying, “We
need worksheets. We don’t like to do homework from the book, because

175

the questions are really confusing, so it’s easier when you give us a
worksheet.” ...So I get feedback from them, too, like and some of them
are like, “We like to do groupwork.” And so that steers my thinking, and
I’m like, “Well, how can I design things with a more group feel.” They
generate a lot of the ideas to help you think (Pre, 13.41-14.7).

Ms. Wells said that this strategy was effective at getting students more engaged in
her lessons, because she directly addressed students’ concerns and let them come up with
teaching strategies that were effective for them. She later reported being consistently
open to student suggestions about how to improve her teaching (Post 21.9-21.14).

Responding to problematic student behaviors, Managing classroom discussions,
After hours work/long hours, and Relationships and communications with administrators
were Main stresses for which participants appeared to have somewhat effective coping
resources. An example of how Ms. Price employed a somewhat effective Social coping

resource for the most commonly reported of these stress categories, namely Respgnding

to problematic student behaviors, follows:

Ms. P: I can’t just have a discipline plan that’s going to work for every
student. I kind of have to take it case by case... The administrators will be
supportive sometimes, too. Sometimes you’ll talk to an administrator
about a particular student and you’ll set up a plan where if this student
comes in and they’re not doing the things they’re supposed to be doing.
They’ll get sent down there right away, so they don’t become a problem.
I: Is there a particular administrator you generally talk to?

Ms. P: Well, it’s alphabetical for the kids, so it depends. We have three
assistant principals, so if my student has the last name “B,” I have to go to
this one. So I don’t really get to pick. I’ve talked to [the principal] about a
couple [of] students where the parents have called here or I’ve had to call
the parents. But usually it’s an assistant principal (Pre, 8.8-8.22).

Ms. Price expressed that the administrators were only sometimes supportive. She

also mentioned a plan for assigning students to an assistant principal that sorted them by

176

their last names. So she was dealing with different assistant principals, depending on the
student. So I judged that she was saying, at least in this case, that her administrators were
only somewhat effective, because they were “supportive sometimes.”

C_hallenges associated Mtlurrofessmd development is the only Main category
for which participants (in this case, Ms. Boone) reported having ineffective coping
resources. In Ms. Boone’s case study, I will share the specific quote involving her
Challenges associated with professional development and how she attempted to employ
her coping resources to deal with them in her case study. Here, I summarize those
explanations.

Ms. Boone was disappointed and frustrated that a district-sponsored workshop she
was required to attend as a second-year teacher was a first-year teacher orientation. She
and her peers had specifically asked the administration for a teambuilding experience.
The teachers went to the administration afterwards to talk about what they would like the
following year, but because the group couldn’t agree, the administration told them to take
courses at the university, which was also not a satisfying resolution for Ms. Boone.

Finally, there were three Main stress categories for which it was unclear whether
participants’ had any coping resources that helped them deal with those challenges,
namely Relationships and communicati_ons with CW3, Teacher boredom, and
Dealing with class legtjngrce, or schedule. Due to this lack of data, it was difficult to
know whether they had means of alleviating those stresses or not.

An example of one of these categories that did not have any coping resources
overtly linked to it was Ms. Riley’s struggles with Dealing with class length, pace, or

schedule. Ms. Riley clearly stated that the trimester schedule was challenging, because of

177

the very regimented schedule it caused her to keep. She said that she had to cover the
same number of topics in two-thirds the number of days each semester, but got longer
class periods in exchange. She did not report any coping resources for dealing with that
stress, nor did she report an absence of resources for dealing with that stress, except
perhaps for “very regimented schedules.” As a result, the effectiveness of her resources
for Dealingyvith class length, pace, or schedule were judged to be “Unclear.”

In summary, it was clear that these teachers felt that their coping resources were
effective or somewhat effective to meet nearly all of the Main stresses for which they
reported coping resources. Indeed, there was only 1 Main stress of the 12 listed in Table
18 for which teachers overall reported ineffective coping resources and 3 for which the
effectiveness of their resources were unclear.

I now turn to consider each novice’s coping resources individually, reflecting on
how the participants described coping with the Main stresses that they experienced, how
effective those resources were, and whether those coping resources supported any of the

novices’ attempts at SBT.

Coping Resources: Results by Participant

In the following participant summaries, I describe and share examples of their top
coping resource(s). Then I examine how effective their coping resources were at
alleviating their Main stresses (which implies, as a reminder, all of their top stresses, as
well). Finally, I attempt to determine whether their coping resources appeared to support

their attempts at SBT from the available data.

178

Ms. Boone.

Ms. Boone reported that her most important coping resources were socially
oriented. While it was unclear whether she meant Social or Collective, Ms. Boone did
report coping resources in both areas. The following quote illustrates Ms. Boone’s report

of her most effective coping resources:

1: Which of the resources that you’ve talked about have been most
effective?

Ms. B: I’d say my peers, teachers. I’ve got a lot of friends that happen to

be teachers that teach here. So they’re my resources as far as like little

things. If I’m having a big issue, I have other people in the building that I

can go to. And for me, talking things out helps so much... So

communication with my fellow peers and teachers and colleagues is

definitely the biggest thing that helps relieve that stress and the biggest

resource that I have to fall back on (Post, 15.20-15.34).

In this passage, Ms. Boone’s stresses were coded as GENERAL stresses. The
coping resource(s) that Ms. Boone employed in meeting those stresses were her fellow
peers, teachers, and colleagues.

In Table 19, Ms. Boone’s reported stresses are listed with the coping resources
she used to alleviate them and the frequency of report and effectiveness of those
resources. The stresses are sorted by average overall effectiveness of the coping resources
employed to alleviate them. I eliminated ties by listing categories with the most coping
resource statements first. I used this same methodology for all novices’ tables in this
chapter.

Ms. Boone mentioned effective coping resources for two of her six Main stresses,

Creating, aligning, modifying, or implementing curricula and Lamh of student

interest/motivation. She mentioned having somewhat effective resources for dealing with

179

Responding to problematic student behaviors and After hours work/long hours. Ms.

Boone reported ineffective coping resources for dealing with her Challenges associated

 

with professigal development. She did not report any coping resources for Relationships
and communications with administrators7. I give examples of each of these stress

categories and the coping resources she employed to alleviate them.

Table 19

Coping Resource Eflectiveness for Ms. Boone ’s Main Stresses

 

 

 

 

 

 

 

 

 

 

 

Coping Resource
, Fr uenc and :3
Stress categones for Ms. Boone Effqectivefress g
E S I U
Creating, aligning, modifying, or implementing curricula 4 E
Lack of student interest/motivation l E
Responding to problematic student behaviors 2 2 S
After hours work/long hours 1 l S
Challenges associated with professional development 2 1
Relationships and communications with administrators U
TOTAL 14 5 3 0 N/A

 

 

 

 

 

 

Note. Coping resource effectiveness is rated above as Effective (E), Somewhat effective (S), Ineffective (I),
or Unclear (U), then judged their overall effectiveness (“Overall” column), as previously described.

For Creating, aligning, modifying, or implementingncurricula, Ms. Boone was

judged as having effective coping resources, including her math colleagues.

Ms. B: We generally are very collaborative. So a lot of what we come up
with comes from us talking it out and creating our own problems. . . We
used to [talk] a lot more last year, because Ms. Horne and I used to have
the same prep... Ideally, [this year] the grand plan was to meet once every
one to two weeks. We’ve been more on a 3-week schedule. Pretty much
whenever a unit starts, we’ll get together and talk (Pre, 7.43-8.33).

 

7 Because coping resources were asked for generally, but not specifically related to any teaching stress, it is
difficult to judge exactly what the lack of data means for any given teaching stress.

180

Ms. Boone later identified Ms. Horne, Ms. Knowles, and Mr. Jones (also a
participant in this study) as specific colleagues with whom she shares ideas. They
are Social coping resources, because Ms. Boone did not describe them as meeting
as a group, so the resource was not necessarily Collective.

For Lack of student interest/motivation, Ms. Boone reported effective

coping resources. An example of a Self coping resource she reported follows:

Ms. B: And I’ve just found the best way to address it is to address it with
that student right away. You know, just call them out on it. “I see you’re
not doing your work,” you know. And I think that that helps so much... It
can be so easy if you have a kid there that’s not motivated and not causing

a distraction to ignore them. But that’s not doing anybody any good, so

(Post, 12.40-13.12).

While she realized that it would be easy to ignore a disengaged student
who was not causing any distractions, Ms. Boone chose to address those issues
immediately and directly to motivate the student to participate. Because she said
that that it was the best way to address the behavior and that “it helped so much,”
I judged this resource as effective at helping her deal with student engagement.

For both Respondingto problematic student behaviors and After hours
worn/lonwurs, Ms. Boone’s coping resources were only somewhat effective
overall (see Table 19). In discussing Responding to problematic student

behaviors, she described how she calmed herself down when she felt like the

students’ behaviors were stressing her out.

Ms. B: As far as discipline goes, that can be stressful sometimes. But if I
find myself getting stressed out about it, I try to remind myself that they

181

are high school students. And that they are young. And that this is how

they act. And that I’m the adult. And I need to respond to it in a mature

way. And that calms me down (Post, 11.13-11.17).

I judged this coping resource as somewhat effective, because it did not appear to
be a long-term plan for dealing with this stress. It seemed like it helped Ms. Boone deal
with the immediate impact of the stress, but did not actually changing student behavior.

An example of a Self coping resource that was only somewhat effective at alleviating

stresses in the category of After hours wmong hours follows:

Ms. B: [I need help with]...the amount of time I spend doing things. Like
if somehow they could find out a way to give me more time or
resources... [But] I have noticed within myself, I’ve gotten faster at doing
certain types of things. And I don’t him and haw and change and mess
with the font and this and that, you know, quite as much as I used to (Post,
15.40-16.6).

While it appeared Ms. Boone was developing strategies to alleviate her stresses
related to After hours work/long hours, she said that she still had trouble with the amount
of time that, in particular, planning took her, even though things had improved over time.

Finally, one stress category for which Ms. Boone appeared to have relatively

ineffective coping resources was gallenges associated with professional development.

She specifically mentioned those Social resources in the following excerpt:

Ms. B: We had two first year teachers. And the rest of us. . .were all in our
second or third year. And we felt like it was such a cop out to [send us to a
new teacher orientation] ...So we went to the principal and expressed our
frustration... We had all these great ideas. Why not require us to go to a
conference in our subject area? ...Maybe we should go to [a] website
class. . .We were like, why don’t we do a book review... And they took

182

down all these ideas, [but]. . .it just never really went anywhere (Post, 9.23-

10.2).

Ms. Boone and her colleagues tried to come up with a better professional
development plan, but they couldn’t agree on one, so they ended up taking MU
courses the next year. So I judged that her Social coping resources for dealing
with her Qhallengs associated with professional development were ineffective.

Three of Ms. Boone’s six Main stresses were also related to her attempts at SBT,
namely Creating, aligninnmodifying and implementingurricula, Respondingfl
problematic student behaviors, and After hours wont/long hours.

For Responding to problematic student behaviors and After hours work/long
now, there were no clear instances where coping resources helped resolved stresses
related to her attempts at SBT. However, for Creating, aligning, modifying and

implementing curricula, Ms. Boone’s struggles were related to her attempts at SBT in at

 

least one of her descriptions of the related stresses.

Ms. Boone was trying to teach in hands-on, exploratory ways to develop intuitive
mathematical concepts in her Calculus class, so she looked for resources on the Internet,
particularly at the visual calculus and Java applets that could make her Calculus class
more discovery-oriented. This related to her attempts at SBT, because she was trying to
engage the students in worthwhile mathematical activities (N CTM Standard 1) that
would develop their understanding of the mathematical concepts in Calculus.

Overall, Ms. Boone’s coping resources appeared to be only somewhat effective,
because the effectiveness of her resources were quite mixed (in terms of being effective,

somewhat effective, and ineffective) for her Main stresses.

183

13"“
1‘

Ms. Grant.

Like Ms. Boone, Ms. Grant’s most important resources were socially oriented.
While she mentioned several teaching colleagues and relatives that she interacted with
about her teaching stresses, she named her department chair as her top coping resource. A

quote that describes her relationship with her department chair follows:

Ms. G: Probably my department chair is my best support, just because he

needs support from me, too, a lot. We’re good at like bouncing things off

each other. . .and he’s gone through the MU program (Post, 22.26-24.18).

Interestingly, Ms. Grant felt like her department chair was a good support,
because they both helped and supported each other, rather than feeling like that support
was only in her service. Even though they were not teaching similar courses, she could go
to him to share ideas and to talk about her teaching.

Like her peers, Ms. Grant reported Social and Self coping resources, in that order,
with the greatest frequency for dealing with her teaching stresses. For Social resources,
Ms. Grant says she talks to different people depending on the problem. For example, she
vented to her husband, got technical help and teaching ideas from the computer teacher, {
got teaching ideas from the department chair, and talked to the principal about teaching
and discipline. Her Self category included several strategies, such as creative lesson
planning, palliation, exploring cultural differences to allow students to teach her

something, and moving away from tasks that went awry during in-class discussions.

184

Table 20

Coping Resource Effectiveness for Ms. Grant’s Main Stresses

 

 

 

 

 

 

 

 

 

 

 

Coping Resource
Stress categories for Ms. Grant Fgefgéfaifizgf i
0
E S I U
Working with technology 4 3 E
Lack of studentfiterest/motivation l l S
Relationships and communications with colleagues U
Teacher boredom U
TOTAL 4 4 1 0 N/A

 

 

 

 

Note. Coping resource effectiveness is rated above as Effective (E), Somewhat effective (S), Ineffective (I),
or Unclear (U), then judged their overall effectiveness (“Overall” column), as previously described.

Ms. Grant’s four Main challenges were Working with technology, Lacl_( of student
interest/motivation, Relationships and communications with colleagnes, and TM
boredom (see Table 20). For the last two, Relationships and communications with
colleagnes and Teacher boredom, it was unclear whether she had any coping resources
for dealing with her challenges in those categories.

For Worl_(ing with technology, her coping resources were effective at dealing with
this category of stress, with Social coping resources being the most frequently mentioned.

An example of an effective Social coping resource for Working with technology follows:

Ms. G: And at this point, I feel like they should know the basic keystrokes
of entering an equation, using zoom efficiently, and finding a good
window. . .and they just don’t know yet how to troubleshoot themselves.
So I feel like I have to wind around the room. And I have like people
calling me all the time.

Ms. G: ...And I actually had to talk to the computer teacher about it,
because I thought, “Geez, he teaches this stuff all the time, like step by
step things. You know, how does he not go crazy?” And he suggested
having people who are really proficient actually act as kind of like
monitors while it’s going on. It’s a good idea, you know, helping people.
It helps when they have friends next to them, you know. The more I use it,

185

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ti

the better I can point things out before they’re lost in CalculatorLand

(Post, 12.17-14.29).

So Ms. Grant felt fiustrated by how little knowledge her students had of the
calculator, even though they were supposed to have learned how to use them in middle
school. But she got help from the computer teacher who suggested that she use proficient
students as teachers’ aides to help her get her other students’ questions answered in a
more timely fashion and with less running around. And she pointed out that it was a
helpful strategy that worked even better the more that she used it. Because she talked
about it as positive and improving, I judged that this coping resource was effective.

For Ms. Grant’s remaining Main challenge, Lacl_< of student interest/motivm,
she had few coping resources. Her coping resources were only somewhat effective at
alleviating her stress. An example of a Physical coping resource that was somewhat

effective at alleviating stress due to Lackfiof student interest/motivation follows:

Ms. G: I’m looking for published, engaging [resources] on the Internet. ..
[But] so much of the things they call engaging lessons are still just kind of
different ways to do notes. Or like just a little piece of something. It’s not
really pushing them to the next level that I want. The book provides
projects and things, but those again aren’t pushing them really. It’s like
you’re going to make a carnival, so choose some rides and how much
would it cost? It’s [just] not there... My most successfirl spots are the
virtual manipulatives, so that way I can plan a lesson and they have
something to do during it (Post, 16.35-17.16).

Clearly Ms. Grant found many different types of resources on the Internet, but
only a few of them, particularly virtual manipulatives, were effective at helping her to do

the kind of teaching that she wanted to do. Because so few of the things that she found

186

were useful to her, I judged that these Physical resources were only somewhat effective at
alleviating her stresses related to Lank of student interest/motivation.

Two of Ms. Grant’s four Main stresses, namely Working with technolngy and
Relationships and communications with colleaguies, related to her attempts at SBT. There
were no instances that I found relating Relationships and communications with
colleagnes to Ms. Grant’s attempts at SBT.

There were at least two instances where Working with technology appeared to
relate Ms. Grant’s coping resources to her attempts at SBT. First, the computer teacher
advised her to use student as monitors who were advanced technology users to help her
answer student questions. This allowed her to use technology in her classroom in ways
where she and the class would explore concepts with the calculator (Post, 2.16-2.30).

The second instance, also shared in a quote above, related to Ms. Grant’s attempts
to find resources online. She found that many of the things online were only different
ways for students to take notes (i.e. used the lecture format) or were not worthwhile
mathematical tasks, like the carnival projects. She felt like the virtual manipulatives were
some of the only engaging activities that pushed her students mathematically. Since Ms.
Grant describes the virtual manipulatives as engaging tasks that push her students
mathematically, she meets the first NCTM (1991) Standard, Worthwhile mathematical
tasks, so it appears that these resources supported her attempts at SBT.

Overall, because Ms. Grant’s coping resources for the only two Main challenges
for which she identified resources were effective in one case and somewhat effective in

the other, I judged that her coping resources were somewhat effective.

187

Mr. Jones.

Mr. Jones reported that his top coping resource were working with his mentor
teachers, which is a Social coping resource, and keeping himself and his students
organized, which is a Self coping resource. Because Mr. Jones was hired by the school
where he interned, he continued to seek help from his intemship-year mentor, as well as
seeking out his current, school-assigned teaching mentor for help and advice. A quote

describing his interactions with these two mentors follows:

1: Which of your resources are most effective in dealing with these
things?

Mr. J: . . .If I’m really struggling or really frustrated, I like to try to figure
things out for myself. But if I get to the point that I can’t do it, I usually go
to my mentor teachers. My mentor this year, Ms. Knowles, I talk to quite a
bit. And you know, if she’s not there, I talk to my mentor that I had when I
interned here, [Ms. Home] (Post, 23.10-23.18).

So Mr. Jones said that he liked to go to his mentor teachers if he was really
struggling or frustrated. He generally went to talk with his current mentor teacher, Ms.
Knowles, and if she was not available, he would talk with his mentor teacher fi'om his
internship at Maple High School, Ms. Horne.

Mr. Jones also talked about a second top coping resource, keeping himself and his

students organized.

Mr. J: The best thing that helps me to deal with my stress on a daily basis
is probably my organization. I’m kind of a stickler about being organized.
And I make sure my students are organized, so that helps me and it helps
them. So it does help the stress level that I’m organized about my work
[and do] good planning... It [keeps] me from worrying about “What do I
have to do tomorrow? Where do I look for things?” (Pre, 1.14-1.33).

188

Mr. Jones said that his organization helped him deal with daily teaching stresses,
so he didn’t have to wonder where things were or what his plans were for the next day.

While Mr. Jones reported that his Social and Self coping resources were his most
effective coping resources, he, like the other novices, reported Social resources with
greater frequency than any other category (see Table 16). In addition to receiving help
from his mentors, he also mentioned how administrators helped him with management

issues, observed his teaching, and gave him constructive criticism.

Table 21

Coping Resource Eflectiveness for Mr. Jones’ Main Stresses

 

Coping Resource

 

 

 

 

 

 

 

 

, Fre uenc and =

Stress categorres for Mr. Jones Eff‘bctivefress g
E s r U §_

Lack of student interest/motivation 4 2 E

Assessing student understanding I 1 E

Responding to problematic student behaviors 2 l 3 S

Managing classroom discussions 3 S

Dealing with class length, pace, or schedule U

 

TOTAL 7 5 l 4 N/A

 

 

 

 

 

 

 

Note. Coping resource effectiveness is rated above as Effective (E), Somewhat effective (S), Ineffective (I),
or Unclear (U), then judged their overall effectiveness (“Overall” column), as previously described.

Mr. Jones’ five Main stresses were Lack of student interest/motivation, Assesshrg
student understanding, Responding to problematic student @aviors, Managing
cl_assroom discussions, and Dealing with class, length, pace, or schedule (see Table 21).
For Dealing with class lengthnpace, or schedule, Mr. Jones did not report whether he had
any coping resources to address those concerns.

For Lack of student interest/motivation, Mr. Jones’ mentioned Social, Collective,

and Self coping resources which were effective overall in alleviating those stresses. An

189

 

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example of an effective Collective coping resource for the stress category of Lack of

student interest/motivation follows:

Mr. J: My first hour [is] challenging in a motivational kind of

way. . .They’re in a 1B, which is, if you take Integrated 1 and break it up in
two semesters, they’re taking the second semester, and they spread that
out over the whole year. . .so it’s a lot slower-pace. They have a lot of time
to see material, which could be boring sometimes. And it’s a real
challenge to make it really interesting for them and to get them excited
about it when they don’t really care, because they already know, “I’m in
the slower track. Who cares about me? I don’t care about math.” So. ..[for]
the 1B, we just pull things from anywhere, so we use the textbook, but we
come up with a lot of things on our own... As a math department, we
probably work together every single day [during] lunch time, between
classes, before and after school for 20 or 30 minutes (Pre, 3.32-4.18).

So Mr. Jones’ Collective resource involved working with his department pretty
much every day, talking about how to make lessons interesting for their students,
particularly for those in the slow-paced sections of the Integrated courses that he taught.

For Mr. Jones’ stresses while Assessing student understanding, his Self coping
resources appeared to be effective at helping him deal with those stresses. An example of

a Self coping resource that alleviated stresses in several categories, including the

Assessing student understanding category, follows:

Mr. J: Well, I’d say [my organization] eliminates me from worrying
about “What do I have to do tomorrow? Where do I look for things?” I
have three different systems that I use to organize all of my different
plans. I have the system up here with the hanging folders with all of the
assignments up there for myself, labeled by subject. . .and for each unit. So
for the Integrated 2 course that you’re going to be looking at, I had the
first three units in there and all of the worksheets that they’ve done (Pre,
1.14-1.33).

190

The stresses alleviated by Mr. Jones’ organization include Planning lessons,
Assessing student undefinding, and GENERAL, but here we are focusing on the Main
stress of Assessing student understanding and how Mr. Jones’ organization helped
alleviate that stress for him. It appeared that being able to find hard the blank and
completed assignments helped to alleviate Mr. Jones’ stresses in this area.

For Responding to problematic student behaviors, Mr. Jones’ only resources were
Social. And they appeared to be effective at alleviating those stresses. An example of a

Social coping resource for Responding to problematic student behaviors follows:

Mr. J: I usually talk to the assistant principal, Mr. Thomas. He’s a former
teacher in the Inner-City School District. And he has a lot of different
strategies for discipline. I usually go talk to him about strategies for that.

And with my former mentor teacher when I interned here, Ms. Knowles,

we worked really hard on class management. And so I think I have a good

strategy for class management, as far as discipline, behavior. I am pretty

strict about that. . ., so I usually don’t have too big of a problem (Pre, 5.40-

6.2).

Mr. Jones said that he had a good strategy for classroom management, so I
judged that his resources for Respondingto problematic student behaviors were
effective. While Mr. Jones said discipline wasn’t usually a big problem, at other
points during our interviews he talked about the ongoing discipline challenges
that he still faced, particularly during his first and sixth hour classes (Post, 18.24-
18.31) and later named it as his third biggest teaching challenge (Post, 21 .41-

22.2), so there is evidence that classroom management was a challenge for him.

191

Mr. Jones’ coping resources were only somewhat successful at alleviating his
stresses related to Managing classroom discussions. An example of a somewhat effective

Self coping resource for the stress category of Managing classroom dimuLflons follows:

Mr. J: I step back and—even in the middle of a lesson—I look at things.
And I take 30 seconds or a minute [while] students are working. And I
think “What could be done differently right now?” . . .Say second hour, I
do one thing. And I take a look back. And maybe during my prep, during
third hour, I think, “Okay. This is what I was going to change for 5th hour
and 6th hour.” . ..I need to make sure that [the students] are actually doing
the talking. I need to change the lesson some way... Next year, I’ll have a
better idea fiom this year what needs to be done to help students the best
(Post, 12.23-12.39).

So when Mr. Jones felt like he was doing too much of the talking during a lesson,
he would mentally step back, think about his original lesson plan, and decide what he
could do differently that would get the students more centrally involved in the discussion.

Four of Mr. Jones’ five Main stresses, namely Managing classrpom discussions

 

Responding to problematic student behaviors, Lacl_( of student interest/motivation, and
Assessing student understanding, related to his attempts at SBT. Of those four, I could
not find a clear link between attempts at SBT and coping resources for Resmnding to
problematic student behayiors or Assessingstudent understanding. For Managing

classroom discussions and Lack of student interest/motivation, I found coping resources

 

that supported his attempts at SBT while he experienced teaching stress(es).

For Managing classroom discussions, Mr. Jones mentioned two coping resources
related to his attempts at SBT. First, he mentioned using the analogy of a path which he
described as only somewhat effective at helping the students understand proof during

class discussions. For similar reasons, I judged that it was only somewhat effective at

192

relieving the associated teaching stresses. Second, as illustrated in one of the previous
quotes, Mr. Jones mentioned that if he felt like he was doing too much of the talking
during a discussion, he would reflect on how to get the students more involved.

For Larch of student interest/motivation, Mr. Jones works on one lesson a week to
try to make it engaging, as a way of bringing students into the classroom discussions that
he tries to incite. So it is clear that Mr. Jones did have some coping resources that
supported his attempts at SBT. Overall, Mr. Jones’ resources were judged to be effective

in alleviating his Main challenges.

Ms. Price.

Ms. Price reported that her “top” or most effective coping resource(s) were Social.
She talked about other teachers helping her in general, but did not identify any colleague
specifically as the most helpful. When asked about her mentor teacher, she said that she
was assigned one, but their teaching styles were so different that she rarely went to talk
with him about any of her issues or concerns. He follows the book very closely, while she

is more interested in discovery-based approaches to teaching and learning.

Table 22

Coping Resource Eflectiveness for Ms. Price ’s Main Stresses

 

 

 

 

 

 

 

 

 

Coping Resource
. , Fr uenc and =
Stress categorres for Ms. Prrce Efi‘ictivefress s
E s I U L
Responding to problematic student behaviors 11 S
Lack of student interest/motivation 2 S
TOTAL 0 l3 0 0 N/A

 

 

 

 

Note. Coping resource effectiveness is rated above as Effective (E), Somewhat effective (S), Ineffective (I),
or Unclear (U), then judged their overall effectiveness (“Overall” column), as previously described.

193

 

Ms. Price reported the category of Social coping resources more frequently than
any of the other categories (see Table 22). She mainly talked with other teachers about
Planning lessons and Responding to problernatic student behaviors and also talked to
administrators about Responding to problematic student behaviors.

Ms. Price’s two Main stresses were Responding to problematic student behaviors
and Lack of student interest/motivation (see Table 22). For Responding to problemaLic

student behaviors, the Social and Self resources she reported were only somewhat

 

effective. For Lgh of student interest/motivation, the Self resources she reported were
also only somewhat effective.

I previously shared an example of a somewhat effective Social coping resource
for Responding to problematic student behaviors. Ms. Price said that when she needed
help with disciplining her students, the administrators are supportive sometimes. My
judgment that this describes administrators as only somewhat effective at alleviating
stress was reinforced by her expressions of concern about the administrators’
interventions. She said that sometimes an administrator only gave students a verbal
reprimand for a serious issue, like loud arguing in class, and then sends them back to her
room. But she wanted the students out of the class for the rest of the hour, due to the risk
of a physical fight. So I judged that this coping resource was only somewhat effective at
alleviating her stresses related to Responding to problematic student behaviors.

An example of a somewhat effective Self coping resource for the stress category

of Lack of student interest/motivation follows:

194

Ms. P: One challenge that’s probably going to be ongoing is getting kids

genuinely motivated or actually wanting to do whatever it is you’re doing

in your class on that particular day. Because sometimes they’d rather

sleep. Sometimes there’s an assembly. Sometimes they have something

going on after school. And just trying to get them to at least focus for that

hour on what they need to do, trying to make the most of it, [is difficult].

But I don’t know if that’s something that necessarily has an answer, other

than, the better the lesson plans are, the more engaged the kids... (Pre,

8.27-9.9).

So Ms. Price had a continuing struggle to get students engaged in her classes. She
said that she felt like there wasn’t a solution, except that the better she could make her
lesson plans, the more engaged the kids would be. Because of how she phrased the l
situation here as not being completely solvable, I judged that this coping resource was it
only somewhat effective at alleviating her concerns relating to the Lack of student
interest/motivation.

Ms. Price did not mention any coping resources linked to SBT-related Main

stresses. Overall, Ms. Price’s coping resources were judged to be somewhat effective at

helping her deal with her two Main teaching stresses.

Ms. Riley.

Ms. Riley said that her top coping resources were Social; in particular, she

 

mentioned how helpful her mentor teacher was at Holly High School. They talked
frequently after school to discuss any issues that Ms. Riley was having and met for lunch
once a week to discuss any issues that had come up in her teaching, as well. Ms. Riley
reported the fewest different categories of coping resources, citing only two, Social and

Self (see Table 16). She reported them nearly the same number of times, as well.

195

Table 23

Coping Resource Effectiveness for Ms. Riley ’s Main Stresses

 

Coping Resource
Frequency and
Effectiveness

E S I U

Stress categories for Ms. Riley

 

 

Relationships and communications with administrators 1

 

Managing classroom discussions 1 2

 

Lack of student interest/motivation

 

c c: m mIOvmu

Dealing with class length, pace, or schedule

 

 

TOTAL 1 l 2 0 N/A

 

 

 

 

 

 

 

Note. Coping resource effectiveness is rated above as Effective (E), Somewhat effective (S), Ineffective (I),
or Unclear (U), then judged their overall effectiveness (“Overall” column), as previously described.

Ms. Riley’s four Main stresses were Relationships and communications with
administrators, Managing classroom discussions, LLkof student interest/motivation, and
Dealing with class length, pace, or schedule (see Table 23). For the last two categories,
Lack of student interest/motivation and M with class lengthnace, or schedule. it
was unclear whether Ms. Riley had any resources for coping with her stresses.

For Relationships and communications with administrators Ms. Riley reported a

 

single somewhat effective Social coping resource. An example of that resource follows:

Ms. R: This is the first year of the two schools [being linked as one]... So
there were a ton of problems. And actually at the beginning [of the year],
they weren’t letting the kids go four minutes early. They were supposed to
just leave. There was no bell. We were just supposed to let them go two
minutes early and then let them come two minutes late... And it just, the
teachers basically were like, “No! We can’t do this anymore.” And so the
administrators came up with the 4-minute bell at the end. It’s pretty good.
Because by the end, everybody’s working and doing stuff. So that’s
working well. So then I can take tardies. And the kids have 9 minutes to
get over, plenty of time (Pre, 133-29).

196

 

 

So Ms. Riley’s coping resource in this case was the administration changing the
bell system that started and ended class. While her wording here might lead the reader to
think that this coping resource was effective, just prior to explaining this situation, Ms.
Riley complained that at the end of class, she can’t really do anything, so the last four
minutes of class are “shot” (Pre, 1.14-1.21). So I coded this coping resource as only
somewhat effective.

Overall, I judged that her resources were somewhat effective at helping her to
deal with stresses related to Managing classroom discussions. Stuprisingly, Ms. Riley’s
Social coping resources were effective at helping her deal with Managing classroom
discussions, while her Self resources were ineffective. An example of an ineffective Self

coping resource for the stress category of Managing classroom discussiw follows:

Ms. R: . . .Well, I was challenged by the fact that I did not think that they
were getting [why you need to complete the square]. And I was trying to
come up with other ways to explain myself. And I was having a lot of
trouble... And they’re good at telling me when they don’t get it. They
shake their head, “No, don’t go on.”

1: Yeah. And how did that resolve itself?

Ms. R: I don’t know if it ever did... I just dropped it, because I couldn’t
handle it anymore... I think how it resolved itself was I got to the point
where I said, like in my head, “We do not have enough time to tinker with
[this]... Forget it... Just divide this number by 2 and square it. Just do it.”
[Laughs] ...I feel like we got so off course with that, so out of what I
wanted to do. I mean it was ruined from there (Post, 3.15-4.12).

So Ms. Riley’s Self resource for dealing with her challenge with Managing

classroom discussions here was to discontinue the discussion and to revert to direct

 

instruction. Since this diverged from the major goal of her lesson, namely to help students

understand why they were completing the square, and because Ms. Riley said the lesson

197

was ruined from there, I judged that this coping resource was ineffective at helping Ms.
Riley cope with her teaching stress in this instance.

Two of Ms. Riley’s four Main stresses, namely Managing classroom discussions
and Dealing with class length, pace, or schedule related to her attempts at SBT. Ms. Riley
did not report resources for dealing with either category of teaching stresses as they
related to her attempts at SBT.

Overall, I judged that Ms. Riley’s coping resources were somewhat effective at

alleviating her stresses.

Ms. Wells.

Although Ms. Wells was not directly asked what her top coping resource(s) were,
she was judged as having her socially oriented coping resources as her most effective or
top coping resources. I based this judgment on how frequently she mentioned those
resources, more often than any other participant. She talked about other teachers in
general as being resources, without heavily emphasizing any one person, with the
possible exception of her department chair who led their group of teachers. She said that
her mentor teacher was a resource for her, but no more than any of the other teacher in
the department with whom she worked and shared ideas and resources.

Ms. Wells mentioned how she regularly met with her peers at lunch every day to
talk. They also talked before and after school. Much of it was informal, but they bounced
ideas off each other and shared resources, lesson plans, etc. She also mentioned that they
got together sometimes to talk about curriculum and work on it, although the structure

appeared loose from her comments. She said that her department was very cohesive, even

198

compared to other departments at her school, meeting together each day to talk about
meaningful and constructive ways of dealing with students, as well as “hash out their
differences” on the curriculum at lunch (Pre, 4.28-4.30).

Ms. Wells reported experiencing three Main stresses, Lacl_( of student
interest/motivation, Responding to problematic student behaviors, and After hours

work/long hours (see Table 24). For Lack of student interest/motivation, she reported that

 

her Social coping resources were effective. I shared an example of an effective Social
coping resource for the stress category of Lag of student interest/motivation previously.
Ms. Wells felt like the feedback that she got from her students was very helpful in getting
them more engaged in the classroom. I judged that this Social coping resource was

effective at alleviating stresses due to Lack of student interest/motivation.

Table 24

Coping Resource Eflectiveness for Ms. Wells ’ Main Stresses

 

 

 

 

 

 

 

 

 

 

Coping Resource
, F uenc and =
Stress categories for Ms. Wells Erffcbctivehess g
E S I U
Lack of student interest/motivation l E
Responding to problematic student behaviors 3 3 l S
After hours work/long hours 3 S
TOTAL 4 6 l 0 N/A

 

 

 

 

Note. Coping resource effectiveness is rated above as Effective (E), Somewhat effective (S), Ineffective (I),
or Unclear (U), then judged their overall effectiveness (“Overall” column), as previously described.

For Responding to problematic student behaviors, Ms. Wells reported that both
her Social and Self coping resources were only somewhat effective. An example of
somewhat effective Self and Social coping resources for the stress category of

Responding to problematic student behaviors follows:

199

Ms. W: We have what we call a Student Responsibility Center

[SRC]. .. It’s an actual room where they go... If two kids are having a

verbal confrontation and somebody needs to go, you can send them down

there. And it’s basically to cool off... They sit down with the teacher in

there whose job it is to run the SRC. .. And...once they’ve been to the

SRC, they’re not allowed to come back to the classroom until

they’ve. . .had a discussion about their plan... I don’t have to use [the

SRC] that often. I probably should in some of my classes... I tend to be a

little bit more lenient with things like giving the kids more warnings and

things like that. I probably could be more firm in sending them out... I use

it for more extreme cases... (Pre, 15.20-16.39).

Ms. Wells described the Student Responsibility Center as a place where she could
send students who were having a verbal confiontation so that they could cool down. This
was a Social resource, since the teacher there dealt with more severe student disciplinary
issues. Since she called it okay and said that she tends to be more lenient and try to
resolve things in her own classroom, I judged that this resource was only somewhat
effective. It appeared to be too harsh for most situations that she faced with her students.

Clearly, Ms. Wells also describes a Self coping resource here, namely, issuing
warnings. But again, she also described herself as probably needing to be more firm in
this area. It appeared that neither of these strategies were ideal for Ms. Wells’ self-
perceived needs when Responding to problematic student behafviors.

For After hours work/long hours, Ms. Wells reported that both her Social and Self

coping resources were only somewhat effective. An example of a somewhat effective

Self coping resource for the stress category of After hours wonk/long hours follows:

Ms. W: I try to get here by 7... I make copies or get the agenda on
the board. . .before the kids come in at 7:50. [I] teach my normal six-hour
day. Then I usually put in 2, 3, maybe 4 hours after school. . .helping

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students. planning for the next day, copies, checking e-mail. .. And then I

still end up taking a lot of it home... [And I] end up putting a full day in

on Sunday... But then. . .I came into this year thinking, “Okay. What can I

do to alleviate some of my grading stress?” So. . .now I stamp the

homework [for completeness] so I don’t have to bring it home. . .And

then. . .I feel comfortable going over it in class, because. . .the ones that

have tried it get credit for it... So then we can go over it... So it’s gotten

better, but I still do put in a lot of time outside of school (Pre, 18.41-

21.20).

Ms. Wells began stamping homework for completeness, so that she didn’t have so
much to take home to grade. But she also mentioned that she still finds her job very time
consuming outside of school hours, so I judged that this coping resource was only
somewhat effective at alleviating stresses related to After hours worl_(/long hours.

Because Ms. Wells had no stresses related to her attempts at SBT, there was also

no overlap between her coping resources and her attempts at SBT. Ms. Wells’ coping

resources for alleviating her Main stresses were judged as somewhat effective overall.

Discussion

Social resources, particularly these novices’ teaching colleagues appeared to be
the most important means of coping with teaching stresses, particularly when they were
attempting to change the environment, rather than just alleviate the symptoms. This also
included Collective coping resources that were related to Social resources, since many of
the social interactions were with people that participated in the teacher collaborative.
While all teachers mentioned social interactions as helpful regardless of whether they had
access to a teacher collaborative group, there may have been some building of those
relationships and interactions that made them more effective as coping resources due to

the existence or structure of the teacher collaborative; this conjecture lacks adequate

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support in my data, but the result is suggested by the very positive comments teachers
made about their teacher collaboratives, as well as by the teacher collaboratives literature.

Self as a coping resource was also an important means of dealing with teaching
stresses. Using one’s creative abilities, experiences, and known management and
pedagogical strategies were important tools in resolving the sources of teaching stress in
the environment. Self was also a means of diminishing teaching stress by reframing the
issue, like saying “that’s the way kids are” or remembering that the student is not an adult
and “I need to respond in a mature manner.”

Physical resources was possibly the least mentioned coping resource (if you
consider collective resources as a category of the Social category), even though all but
one teacher mentioned them.

Nearly all of the participant cases mirror these overall frequency patterns for
coping resources. The case studies also identify marked differences in which coping
resources each teacher employed and how they selected those resources. In particular,
Ms. Grant picked and chose among the teachers at her school, a less cohesive context
than most in this study, to find teachers who shared similar ideas about classroom
management or pedagogy, or had stronger ability than her in certain areas, like
technology. Ms. Price was similar in this respect. But Ms. Boone and Ms. Riley tended to
look for teachers who they had relationships with as mentors or colleagues for help with
difficult problems. Similarly, Mr. Jones tended to talk with teachers who were teaching
the same sections of the class, but also with administrators with whom he had strong
relationships. On the other hand, Ms. Wells felt comfortable talking with any of the other

math teachers at her school, likely due to the highly cohesive nature of their department.

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While such departments are highly desirable, it is unclear whether they can be
created or whether they are organic and must simply be enjoyed when encountered. Ms.
Wells reported that other departments in her school were not nearly as cohesive as hers.
Research on middle and high school academic departments reinforces what she suggests,
that cohesiveness and collaboration in one department generally does not imply such
cordial relations in other departments at the same school; moreover, high school
departments, schools, and districts play a role in supporting or undermining a shared
technical culture, strong service ethic, and professional commitment. In other words, such
activities are generally fostered in organizations such as teacher learning commrurities
(Talbert & McLaughlin, 1994).

From these case studies, it appears that novices had few supports for dealing with
Main stresses related to attempts at SBT. But what is even clearer from the previous
chapter is that few of their Main stresses related to their attempts at SBT. So while they
have little support for SBT-related stresses, these stresses also appeared to play only a
very small role in the big picture of the stresses that these teachers experienced.

On the other hand, the teachers I noticed making the most visible attempts at SBT,
namely, Ms. Boone, Ms. Grant, and Mr. Jones, also reported more SBT-related coping
resources than the other three teachers. This suggests that novices require coping
resources to make meaningful attempts at implementing aspects of SBT in their
classrooms.

Finally, when panning out to look at the overall picture of all of the stresses that

these novices reported, it is clear that these novices were dealing effectively or somewhat

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effectively with nearly all of the stresses that they mentioned having coping resources to

attempt to alleviate, including their stresses related to SBT.

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Chapter 7: Discussion and Conclusions

As I conclude this dissertation, I review the major findings of this study, including
which stresses novices reported, how those stresses compared to categories reported in
the existing research literature, how those stresses related to novices’ attempts at NCTM
(1991) Standards-based teaching (SBT), and which coping resources novices reported. I
do so to summarize the results of this dissertation in preparation for the discussion of
research literature and significance for teacher educators and firture colleagues of novice
teachers that follow in this chapter. After broadly reviewing the findings of this study, I
will discuss how those findings relate to the existing research literature on teacher stress,
NCTM (1991) Standards-based teaching, and coping resources with a focus on teachers’

concerns. Finally, I consider follow-up research that the findings of this study suggest.

T op-Level Summary of Major Findings

Novices experienced many stresses previously reported by the literature and
several others that are, in some cases partially and in some cases completely, new to the
literature. In the existing literature, stresses were listed in the following categories: m
motivation of students, poor student discipline, mor worlfig conditions, time pressure
and work overload, low status and opportunities—including!!!“ promotiomand canneg

development, and poor school ethos—including conflict with colleagues a_nc_l

 

administrators. These categories entirely subsumed 14 of the 22 categories, as I
previously reported in Chapter 5 (see Table 12). Of the remaining eight categories, four

were partially new to the literature, namely Managing classroom discussions, Creating,

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a_ligning, modifying, and implementing curricula, Assessing student understanding, and
Student diversity issues. The other four categories were new to the literature, namely
Directing student explorations of rnathematics, Respondinnnto unexpected student ideas,
Working with technology, and Teacher boredom.

Of these eight partially and entirely “new” stress categories, all but Iflchnr
boredom related at least in one instance to at least one novice’s attempts to implement
SBT. Briefly, Managingclassroom discussions related to attempting the types of
conversations about mathematics that the NCTM (1991) Standards advocates, that opens
students’ mathematical ideas and conjectures to the class for discussion and mathematical
verification which allows students to develop greater insight into underlying
mathematical concepts, generally before learning algorithms and procedures. Creating,
a_ligning, modifying, and implementinfiurricula related to attempts at SBT, because
many of these teachers were striving to modify their curricula in ways to better align the
pedagogy with the NCTM Standards. Assessing student understanding related to SBT,
because teachers assessed students on their presentation of mathematical concepts to the
class and/or teacher in ways that exposed their thinking to public mathematical scrutiny.
Directing student exploratiogns of mathernatics related to novice teachers’ attempts to
engage students in meaningful explorations of deep mathematical tasks from which they
could formulate conjectures and often verify those conjectures as a whole class
afterwards, as advocated in the NCTM Standards.

Directing student explorations of @thematics related to the NCTM (1991)
Standards because many of these activities required students to explore deep

mathematical content and to develop and verify mathematical conjectures. Resp_onding to

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unexpected student ideas generally was only stressful for teachers who were attempting
to use student ideas in meaningful ways in classroom discourse, rather than simply
dismissing them, thus reinforcing the active intellectual role for students that the NCTM
Standards advocates. Workinflith technology related to teachers’ attempts to implement
technology in ways that allowed students to engage in exploration and discussions of
mathematical concepts that they could not readily identify without such tools, as
advocated by the NCTM Standards.

It appeared that attempting SBT contributed only modestly to these participants’
overall teaching stress. As a reminder, most of the stresses that were salient to the
teachers were not strongly related to SBT except for one, Managing classroom
discussions. Also, of those stresses that were most often related to participants’ attempts
at SBT, the only one that was cited with any reasonable frequency to show that it was
common in these participants’ experiences was Managing classroom discussions. While
the contribution of SBT to overall stress was modest, so were participants’ overall
attempts at SBT. But what was surprising was how many categories of teaching stress,
particularly among the new categories, related to novices’ attempts at SBT. Of course, I
was looking for evidence of such concerns, but these categories were linked with very
different teaching activities from the categories listed in the existing literature.

There was some variance in the ways that novices viewed their challenges, from
being entirely positive as opportunities for growth to being entirely negative, because all
challenges took a toll on their resources. According to the existing literature, this could be
due to the amount of stress that they experienced (i.e. their teaching contexts) and/or to

their personalities (Abouserie, 1994; Pithers, 1995). The literature predicts that both are

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factors in how humans perceive and experience stress, so both of these could be factors in
these teachers’ perceptions of their teaching challenges.

These novices’ top coping resources were Social, whether they resulted from
interactions in a teacher community (i.e. Collaborative resources) or were based on
individual relationships and interactions (i.e. Social resources). Participants in highly
cohesive departments listed the department among their greatest resources. This is not
particularly surprising, given how teachers involved in teacher learning communities and
in highly cohesive departments valued those resources. The importance of teacher
learning communities is also a central theme in the research literature (e. g. McLaughlin,
1993). But it is not clear whether such departments can be constructed in any setting with
any group of teachers or what the constraints would be to create such an environment.
This issue requires further research.

That Self was also an important coping resource for these novices is not
surprising, given the high amount of autonomy and expectations for individual
accountability and initiative in US. schools today.

These novices were dealing effectively or somewhat effectively with nearly all of
the Main stresses that they mentioned having coping resources to attempt to alleviate,
including their Main stresses related to SBT. Most of those resources related, in at least
one instance, to stresses related to SBT.

Of the six novice teachers in this study, three (Ms. Boone, Ms. Grant, and Mr.
Jones) appeared to be making more attempts and more effective attempts at SBT than the
other three participants (and more than, of course, the other five prospective participants

who did not qualify for participation in this study, because they were not observed

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making meaningful attempts at SBT). In other words, I was more likely to see whole
class discussions involving presentation of students ideas, mathematical conjecturing and
mathematical justification during these three novices’ mathematics classes than during
the other three novices’ classes (or, for that matter, during the other teachers’ classes who
were screened for participation but who I did not observe making meaningful attempts at
SBT). It also appeared unlikely that I would have observed more meaningful attempts at
SBT in many other teachers’ classes in Ms. Boone’s, Ms. Grant’s, or Ms. Jones’ cohorts,
given my method for selecting prospective participants, as described in Chapter 3.

It is not entirely clear why Ms. Boone, Ms. Grant, and Mr. Jones appeared to be
making more successful attempts at SBT than their peers. They did not appear to have
any more social supports than their peers for such teaching; indeed, all six participants
talked about socially-oriented (i.e. Social and/or Collective) coping resources in 50% to
70% of the passages that related to their coping resources, with the three novices under
consideration spread across that range.

As a complicating factor, I did not ask directly or specifically how these novices’
coping resources related to their attempts at SBT8. As a result, I could not code
systematically to determine which and what proportion of coping resources supported
these novices’ attempts at SBT; however, Ms. Boone, Ms. Grant, and Mr. Jones spoke
more specifically and pointedly about how their coping resources related to their attempts
at SBT than did the other three teachers. For example, in Ms. Boone’s and Mr. Jones’
cases, they were deeply enmeshed in a teacher learning community that openly

encouraged and supported their attempts to teach in the spirit of the NCTM (1991)

 

8 Given the strong feelings discussing SBT tends to incite, I avoided specific probing about how novices’
coping resources related to SBT. While that lessens the analytic impact of these statements, it also suggests
that the connections these novices made to SBT derived from their commitments to SBT, rather than mine.

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Standards. And while Ms. Grant’s context appeared (by far) the least conducive to
attempting such teaching, she also appeared to be the most selective of the group in
implementing the resources that she had in meeting her goals and educational
commitments, primarily because there were few people that shared all of her educational
goals and commitments, including (but not limited to) a desire to enact the NCTM
Standards in her teaching. As a reminder, my classroom observations tended to confirm
that they were making more meaningful attempts at such teaching.

I would like to suggest several possible causes for the varying number of SBT
attempts that I observed in these participants’ classrooms. One possibility is that these
three novices (Ms. Boone, Ms. Grant, and Mr. Jones) may have held stronger
commitments to attempting SBT than did their peers. Their successes in attempting SBT
may have been primarily due to how deeply they held their educational goals and, as a
result, how systematically they attempted to implement those goals. There is at least
some evidence to support this conjecture. For example, Ms. Grant sought out supports
actively and selectively to support her SBT attempts, even though her lack of success in
attempting meaningful mathematical discussions appeared to be taking its toll on her
desire to continue teaching mathematics (as opposed to teaching English, where students
expected and more readily engaged in deep, meaningful conversations). She mentioned
on more than one occasion that she was considering switching to teaching English instead
of mathematics. She reported that her fatigue and boredom with teaching was at least
partly due to how her students resisted engaging in meaningful mathematics discussions.

Another example is that Mr. Jones attended a high school where his teachers

readily and fully embraced a pedagogy that could reasonably be judged as meaningfully

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aligned with the NCTM (1991) Standards; specifically, it would easily clear the modest
criteria defining meaningful attempts at SBT in this studyg. In other words, he had the
unusual, but increasingly more common, experience of viewing SBT as part of his
“apprenticeship of observation” (Lortie, 1975) as a high school student and possibly
earlier, as some of the junior high schools in that district were also attempting such
teaching. His commitments may have been prompted by those relatively early and
formative experiences in his education.

On the other hand, it is also possible that the educational contexts in which these
novices taught may have either influenced them or may have been influenced by them in
one of three ways. First, Ms. Boone’s, Ms. Grant’s, and Mr. Jones’ school contexts that
led or allowed them to attempt SBT more efficiently than many of their other peers, and
if such events occurred, what their character might be. Having a network of social
supports for teaching in general may have allowed them to make more meaningful
attempts at SBT. Second, attempting SBT more arnbitiously may have caused teachers to
look for and build up supports and resources for their ongoing attempts at such teaching.
Third, the environment at the school, which may have included such elements as a pre-
existing teacher learning community, forward-thinking administrators (i.e. principal,
assistant principal(s), department chair, curriculum coordinator, etc.), like-minded
colleagues, etc. could have created an environment where meaningful SBT attempts were
both encouraged and actively supported.

If the context were considered to be the significant element in why these

participants appeared to be making more SBT attempts than their peers, then Ms. Grant’s

 

9 Given the extensive contact that I had with the professional development school for Midwestern
University that Mr. Jones attended as a secondary student, 1 can judge from my observations in those
classrooms that they undoubtedly met and surpassed the modest criteria in this study for attempting SBT.

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case may have been an example of the second of these three possibilities; in other words,
she was a teacher with ambitious teaching goals and decidedly competent social skills
who sought out resources specifically to help her meet her pedagogical (and other) goals.
On the other hand, Mr. Jones and Ms. Boone were harder to judge. While they were in a
context that was arguably very supportive of their attempts at SBT, it is unclear whether
they would have done so on their own or whether they could have made less meaningful
attempts at such teaching if they had chosen to do otherwise. In other words, it was
unclear whether the number of social supports allowed them to meet their own goals,
whether the expectations of the commrmity encouraged them to reach for those goals, or
whether they looked in the school for these resources because they already had
pedagogical goals aligned with SBT. So this remains an open question for them and for
all of the novices in this study.

But I must say that there is a good deal of evidence to support that both of these
conjectures. These novices held commitments deeply that aligned with the NCTM
Standards. And they were very capable and accomplished at finding and implementing
resources to support their ongoing attempts to persevere in attempting to enact their
pedagogical goals that aligned with the NCTM (1991) Standards. In particular, Ms. Grant
showed a great deal of social skill for networking in a less-than-ideal teaching context to
support her ongoing efforts to teach according to her deeply held beliefs about education

that included pedagogical goals aligned with the NCTM (1991) Standards.

Contribution to the Research Literature

Teacher stress literature.

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As stated previously, the novices in this study reported many of the categories of
stress reported in the existing teacher stress literature. They also reported some new
stresses. In particular, Managing classroom discussions was the most salient stress that
was (at least partially) new to the literature. It was a Main stress for two participants and
was mentioned by two others; moreover, it was related to SBT attempts in at least one
instance for all four of these participants. This category of teacher stress also clearly
related, in many cases, to novices’ attempts at SBT.

The remaining categories were Main for exactly one participant, as follows:
Creating, aligning, modifying, or implementing curricula, Teacher boredom, Assessnrg
student understanding, and Working with technology. These categories were also
“mentioned” categories for at least one other teacher, except for Working with
technology. As a reminder, all of these categories also related to at least one novice’s
attempts or reported attempts at SBT, except for Ember boredom.

Creatifl, aligning, modifling, or implementing curricula were related at times to

 

trying to align one’s curriculum with state content standards, but at other times, those
efforts related to teachers’ desires to implement a pedagogy more consonant with the
NCTM (1991) Standards. This theme is certainly reflected in the many studies relating to
more experienced teachers’ (e.g. Romagnano, 1994), novices’ (e.g. Schweitzer, 1996),
and interns’ (e.g. Van Zoest & Bohl, 2000, 2002) experiences, including their challenges,
while attempting SBT.

Teacher boredom is a surprising addition to the literature, since teachers do not
usually talk about being bored, but more often about having too much to do and deriving

pleasure from their work with children. This is not reflected in the mathematics education

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research literature relating to SBT either. There is some work relating to teacher burnout
(e. g. Farber, 1984) that suggests that teachers who burn out invest less and less in their
teaching over time. So this may describe the beginning of that phenomenon, but, if so, it
is not well documented in the literature.

Assessingstudent understanding relates to SBT in that novices described their
attempts to implement a performance—based group presentation for the class where their
mathematical work and knowledge were exposed to public scrutiny, generally by their
classmates. While assessment is discussed in the literature from the perspective of the
students or from that of a general observer (e. g. Darling-Hammond, Ancess, & Falk,
1995), it is rarely discussed from the teacher’s perspective; therefore, this is also an
addition to the mathematics education literature on teacher stress.

Working with technology is clearly related to the rise of technology in society,
and particularly, in schools during the past few decades. Surprisingly, the literature on
novices’ SBT teaching attempts talks about this topic very little, if at all, even though
technology plays a central role in many of the NSF-funded textbook series that arose
from the NCTM (1991) Standards movement, such as CPMP (Coxford, Fey, Hirsch, &
Schoen, 1996).

The three remaining previously cited stresses that were new or partially new to
the literature, Directingtudents’ exploratinrs of matheflrtics, Responding to unexpected
student ideas, and Student diversity issues, were not Main stresses for any teacher. As
previously stated, all three of these stress categories were also related to at least one

participant’s attempts at SBT.

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N C T M Standards-Based Teaching Literature

This study suggests that SBT is still hard to find (Wilcox et al., 1991), even
among the graduates of the progressive mathematics teacher education program at
Midwestern University (MU). MU has an arguably NCTM (1991) Standards-oriented
mathematics teacher education program, so that teachers in this study were given many
opportunities to understand, experience, and observe how the NCTM (1991) Standards
can be implemented in secondary classrooms. In many (but unfortunately, not in all)
cases, the program gave these interns mentors who were selected based on their ability to
implement such teaching. And while the set of novices chosen for this study was
screened from a carefully selected subset of two subsequent teaching cohorts (see
Methods chapter), these novices’ observed and reported attempts at SBT as a whole
group were relatively modest in number and in character.

The categories of teacher stress identified by this study related to SBT attempts
were distributed unsystematically across many different categories for the most part,
rather than being confined to a few stress categories and/or teaching activities. So
generally, there was not a simple pattern for how SBT affected these novices teaching
stresses, except that it could surface in many different ways.

Most stresses reported by the novices in this study related to at least one novice’s
SBT attempts, but few of those stresses were both salient and common for this group of
participants with the single exception of Managing classroom discnsnions. This suggests
that a specific activity that is very challenging for novices relating to their efforts to
implement SBT is Managing classroom discussions. While Managing classroom

discussions, Smith (1996) pointed out that it is harder and more elusive for teachers to

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feel that they are successfully directing learning than during a lecture. There is a great
deal of teacher uncertainty inherent in whole-class discussions where students take an
active role in sharing their mathematical ideas, offering conjectures, and verifying their
own and other students’ ideas mathematically. Such a role for students gives them an
active voice in suggesting the direction of classroom events. Teachers need a deep
understanding of mathematics, pedagogy, pedagogical content knowledge, students’
known and likely conceptions of the content, and strong social skills to navigate such
discussions. They must maintain social norms while choosing among the many different
mathematical themes and concepts that may arise and direct the class in the most fiuitful
directions to solidify students’ blossoming understandings of those concepts. Teachers’
deep knowledge of mathematics needs to include a variety of representations for each
mathematical concept, multiple ways to describe each mathematical concept, and an
understanding of how students may be thinking about each mathematical concept during
these discussions. Such a knowledge base appears easier (and much more likely) to
develop over time than to acquire from a teacher education program, although a
disposition that is open to meaningfirlly attempting such teaching is most likely acquired
during one’s K-12 education or early in one’s teaching career. That is why it appears that
the teacher education program experiences provide the ideal opportunity to have an
impact on novices’ teaching.

Those novices who were most effectively attempting SBT were generally found
in strong departments that supported their pedagogical efforts, namely Mr. Jones and Ms.
Boone. Ms. Grant was the only novice making surprisingly effective attempts at such

teaching outside of a strong, supportive department that promoted SBT. While other

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teachers also talked about having strong departments or many peer resources, such as Ms.
Wells and Ms. Price, respectively, they did not often portray those supports as reinforcing
their efforts at SBT, but as general resources for more traditional teaching activities and
concerns.

On the other hand, it is surprising and perhaps runs counter to McLaughlin’s
(1993) observations during her study that all six of these novices were making
meaningful attempts at SBT, but most of those attempts were outside of teacher learning
communities that directly supported SBT. While no teacher reported a school context that
discouraged SBT in an organized way, Ms. Grant did talk about a school environment
that was clearly a challenging context for making such attempts. Her observations here
echo those of Wilcox et al. (1991) who found that few of their novices were still making
any meaningful attempts at SBT after leaving their progressive teacher education
program, primarily because they lacked strong teaching communities to support their
attempts to implement a pedagogy that they valued but was relatively new to them.

While Ms. Grant was making such efforts, it is difficult to say how long she will
continue unless she finds more organized and/or effective supports for her blossoming
pedagogical skills, dispositions, and habits of mind. Ms. Grant was surprisingly one of
the few in her cohort making the most effective SBT attempts, but she was also possibly
the most discouraged of the group. As a reminder, she mentioned more than once that she
was considering a switch to teaching English in order to find a context where the type of
conversations that she wished to have with her students were better supported by the
content. She also spoke about how selectively she had to look for supports among her

peers, depending on whether she needed help with classroom management, pedagogy,

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technology, etc. So the social relationships in her context also added to the challenges and

complexity of her teaching at Elm High School.

Coping Resources Literature

The most salient resources for these novices were the socially-oriented categories
of coping resources (including the Social and Collective categories). The reader may
recall that it was often difficult to tell when a resource existed because of the teacher
learning community, so that category was relatively thin. But given the potential of
teacher learning communities to quickly and efficiently forge (and give direction to)
professional social relationships, we cannot overlook the importance or potential in
particular of the Collective category.

That Self was also a salient resource for these novices was not particularly
surprising, given the focus in American schooling on independence in teachers' work.
Teachers generally do value themselves as resources, but the content of the Self category
of coping resources for each novice depended primarily on the experiences that these
teachers had had in their educations, both K-12 and post-secondary. As teacher educators,
we have an opportunity to have an impact on the content of this category of resources by
teaching novices new ways of thinking and of learning about teaching and by giving them
new educational experiences that they may not have previously considered and by
allowing them to observe teachers, hopefully including ourselves, whose teaching
embodies to some degree specific elements of the NCTM (1991) Standards.

Finally, it is interesting that Physical resources were not particularly valued by

this group of novices as coping resources. But the research suggests that the value they

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placed on one of those physical resources, the textbook, rrright have been greater if they
had been using one of the NSF -fimded curricula, such as the CPMP (Coxford, Fey,
Hirsch, & Schoen, 1996) materials, as Alice did in Van Zoest and Bohl’s (2000, 2002)
study.

The coping resources that these teachers mentioned most often included several
already described by the coping resources literature (e. g. Lazarus, 1976), but their
relationships to the classes of resources that I describe above are not completely clear. I
will attempt to relate them, at least in a cursory fashion, to the coping resources which I
observed and heard about during my observations and interviews.

For example, Preparation against harm relates to novices’ efforts to prepare for
classroom events by careful planning to avoid difficult classroom events or situations and
by creating discipline and management strategies that help them and students know what
to expect when students choose undesirable behaviors. For example, Ms. Price wanted to
prepare better mathematics lessons to get her students more interested and engaged in her
classroom.

There also appeared to be some Intellectualization that occurred as teachers
reflected on and talked to others about classroom events and situations. For example, Ms.
Boone mentioned that she was the adult, the students are children, and she had to respond
in a mature way, which may have been Intellectualization.

Teachers also may have practiced Identification to some degree in meeting the
demands of their teaching, particularly in strong departments. But such a process could

have had been synergistic (as appeared to have occurred in Ms. Boone’s and Mr. Jones’

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cases) or quenching (as may have occurred in Ms. Wells’ or Ms. Riley’s cases) for their
SBT attempts.

Novices also talked about mild forms of Displacement, as when Ms. Grant and
Ms. Boone vented about their teaching stresses to a husband and to an administrator and
peers, respectively. I also heard of Encapa as a strategy, when Ms. Boone described a
difficult confrontation with a parent. She chose not to return to her classroom that
afternoon, while she was processing the experience with an assistant principal.

There are some strategies that I would have had difficulty identifying.
Specifically, Suppression, Repression, Denial, and Projection are all ways that humans
avoid reflecting on or acknowledging stress. Since I primarily judged coping resources as
those perceived and reported by the teachers, I would not have been able to identify such
responses to stress. Not surprisingly, the data did not substantiate that such responses to
stress existed for this group of novices.

Reaction formation would also be difficult to identify, because it involves
expressing the opposite of what one is feeling. Since I took these teachers at their word
and they did not mention misrepresenting events to anyone else (nor were they likely to
in a professional interview setting), I did not identify any indication of this coping
response.

Likely due to the risk of professional embarrassment, I did not hear of any of the
more embarrassing physical Palliation activities, such as drinking or taking drugs, nor did
participants report more socially acceptable behaviors in this category, like exercise,

meditation, or yoga. Aggiession would also be embarrassing for most professionals to

220

admit in an interview setting with a representative of the teacher education program; not

surprisingly, no teacher mentioned a coping response fitting this category either.

Future Research Steps

As I consider future research that might be undertaken to follow up on my
dissertation, I feel like this study has covered a lot of the groundwork about the stresses
that novice teachers experience. First, it says that those stresses are not particularly acute
as they relate to attempts to implement aspects of the NCTM (1991) Standards. One
possible exception to this statement may be that attempting the type of classroom
discourse that the NCTM (1991) Standards advocates may be a universal and salient
stress for novices, and possibly all teachers (Smith, 1996), attempting this type of
teaching. This is an area that both begs to be further explored and is enjoying
considerable attention as researchers engaged in discourse analysis explore classroom
interactions relating to innovative teaching and, in some cases, SBT.

While some important exploratory work has been done in by this study, it is
unclear whether these results hold for large groups of participants. And it is also unclear
whether this is symptomatic of the alumni of MU ’s mathematics teacher education
program or whether it is true on a broader scale for all such programs. So there is still
some work to be considered by other researchers in exploring the how generalizable these
results are to the alumni of other progressive mathematics teacher education programs.

As far as how I personally might follow up on this research project, given my
personal interest in learning to attempt “ambitious teaching,” I am drawn to explore how

student and novice teachers begin acquiring the skills, dispositions, and capacities that

221

help novices and interns develop their teaching in the spirit of the NCTM (1989, 1991,
2000) Standards. Wilcox et al. (1991) partially answered the question as to what
mechanisms lead novices to gain a disposition towards working on such interesting
teaching, while others retained their traditional beliefs. Their program led novices to
believe that they had learned a new way of thinking about mathematics that was
important and valid for themselves, but did not necessarily apply to K-12 students.
Wilcox et al. reported that they felt like their teachers did not persevere in the face of
contextual obstacles at their first jobs.

These observations lead us to a series of questions about how to prepare teacher
candidates for such activities. What drives some novices to persevere in their SBT
attempts, while others readily abandon them when challenges arise or their pedagogy
doesn’t yield the expected or desired results? Why do some novices persevere in
modifying pedagogically interesting lessons, while others move towards a more
traditional pedagogy when a lesson based on developing student understanding, which
may include student explorations, conjecturing, and/or whole class discussions, fails?
How do we get SBT-minded novices to meaningfully reflect on their teaching, even
lessons that appear to have failed, and teach them to turn those into successful efforts to
engage students in deep discussions and investigations of significant mathematics? And
how can teacher educators, mentors, administrators, and colleagues help support novices
in attempting SBT and to learn to persevere in the face of some of these obstacles? While
some interesting research has been done in this area (e.g. Van Zoest & Bohl, 2002; Vacc

& Bright, 1999; Schweitzer, 1996), there is still much work to do in deciding how best to

222

support interns and novices as they acquire these teaching skills, dispositions, and
capacities.

While I have identified social relationships broadly as being salient in SBT-
minded novices’ experiences as other researchers have found (e. g. Vacc & Bright, 1999;
McLaughlin, 1993), there is much to be understood about how and under what
circumstances such structures can be created and strengthened in schools, how to give
novices access to such resources, and how to train them to use those resources
effectively. There is also the open question of how to help novices develop an interest in

these types of activities, as many teacher educators across the nation are researching at a

121”“ A» -

formal or an informal level. Given the considerable social skills that novices need to
implement SBT and to create and make use of the resources around them, the question of
how to train novices to value and develop those social skills also arises. Is it something
that should be made explicit in their programs and in the schools where they teach? Or is
that something that people in these programs need to keep in mind in order to effectively
implement the type of teaching that they desire? These questions need to be considered as
we look to how to continue supporting interns’ and novices’ attempts to implement

aspects of the NCTM (1991) Standards in their teaching.

 

223

APPENDICES

 

224

Appendix A

Protocol for Identifying Attempts at SBT during Classroom Observations

 

Standard 2:
The teacher’s role in discourse

Operationalized

[Novice
name]

 

The teacher of mathematics should orchestrate discourse by-

 

A.*posing questions and tasks that elicit,
engage, and challenge each student's
thinking;

A.*eliciting, engaging, and challenging
each student's thinking;

 

B.*listening carefully to students' ideas;

B.*listening carefully to students' ideas;

 

C.*asking students to clarify and justify their
ideas orally and in writing;

C.*asking students to clarify and justify
their ideas orally and in writing;

 

D.*deciding what to pursue in depth from
among the ideas that students bring up
during a discussion;

D.*following up on the ideas that
students bring up during a discussion;

 

E.*deciding when and how to attach
mathematical notation and language to
students' ideas;

E.*expressing students' ideas using
mathematical notation and language;

 

F .*deciding when to provide information,
when to clarify an issue, when to model,
when to lead, and when to let a student
struggle with a difficulty;

F.*letting a student or letting the students
as a class struggle with a difficulty;

 

G.*monitoring students' participation in
discussions and deciding when and how to
encourage each student to participate.

G.*encouraging each student to
participate and be engaged in speaking
and listening to ideas.

 

 

Standard 3:
Students’ role in discourse

 

Onerationalized

 

 

The teacher of mathematics should promote classroom discourse in which students-

 

A.*listen to, respond to, and question the
teacher and one another;

A.*listen to, respond to, and question the
teacher and one another;

 

B.*use a variety of tools to reason, make
connections, solve problems, and
communicate;

B.*use a variety of tools to reason, make
connections, solve problems, and
communicate;

 

C.*initiate problems and questions;

C.*initiate problems and questions;

 

D.*make conjectures and present solutions;

D.*make conjectures and present
solutions;

 

E.*explore examples and counterexamples
to investigate a conjecture;

E.*explore examples and
counterexamples to investigate a
conjecture;

 

F .*try to convince themselves and one
another of the validity of particular
representations, solutions, conjectures, and
answers;

F.*communicate to convince themselves
and one another of the validity of
particular representations, solutions,
cgrjectures, and answers;

 

 

G.*rely on mathematical evidence and
ar ment to determine validity.

 

G.*rely on mathematical evidence and
argument to determine validity.

 

 

225

 

 

Appendix A (continued)

 

Standard 5:
Learning environment

 

Operationalized

 

 

The teacher of mathematics should create a learning environment that fosters

development of each student's mathematical

power by-

 

A.*providing and structuring the time
necessary to explore sound mathematics and
grapple with significant ideas and problems;

A.*providing and structuring the time
necessary to explore and grapple with
significant mathematical ideas and
problems;

 

B.*using the physical space and materials in
ways that facilitate students' learning of
mathematics;

B.*using the physical space and
materials in ways that facilitate students'
learning of mathematics;

 

C.*providing a context that encourages the
development of mathematical skill and
proficiency;

C.*posing questions and tasks that
develop students’ mathematical skill,
proficiency, and understanding;

 

D.*respecting and valuing students' ideas,
ways of thinking, and mathematical
dispositions;

D.*respecting and valuing students'
ideas, ways of thinking, and
mathematical dispositions;

 

 

 

and by consistently expecting and encouraging students to-

 

E.*work independently or collaboratively to
make sense of mathematics;

E.*work independently or collaboratively
to make sense of mathematics;

 

F.*take intellectual risks by raising questions
and formulating conjectures;

F .*raise questions and formulate
conjectures;

 

G.*display a sense of mathematical
competence by validating and supporting
ideas with mathematical argument.

G.*validate and support ideas with
mathematical argument.

 

 

 

 

226

‘N

 

Appendix B

Teacher Stress Coding Categories, Definitions, and Examples from the Data

 

 

Code Title Code Definition/Description Examples from the Data
Managing Stresses deriving from [Ms. R discusses when she asked the
classroom teachers’ attempts to involve students to attempt a completing the

discussions

students actively in classroom
discussions and contributing
ideas that the teacher
anticipated or hoped to elicit in
that discussion, while the
teacher primarily acted as a
facilitator. (If the teacher had
difficulty getting students to
participate in conversation and
called it a shared problem or it
was unclear why students did
not participate, it belonged in
this category. If the teacher
characterized students as
resisting participation or
lacking interest, I placed the
passage in Lack of student
interest/motivanion.)

square problem during a class
discussion with a number other than
one in front of the x2 term.]

Ms. R: We were going to complete the
square. And it was the first time that
they’d ever seen that at all. And I
didn’t give them enough examples of
the easy, easy ones. We went virtually
right into a hard one. And we
drowned, because we didn’t have the
basics of it... After that day, I actually
sat down and counted how many steps
it would take me in order to do that...
And then it was like 8 steps. And I
was like, “You know what? I should
not have attempted to do this with
them”...

Ms. R: I feel like the kids should
know how it works. You know, just
telling them, like we did the quadratic
formula yesterday. And there isn’t a
ton, at least I don’t know, of things
you can do other than say, “This is the
formula. Just use it and trust me.” And
I just don’t like that, you know? And I
wish that they would understand what
was going on (Post, 4.46-7.25).*

 

 

Responding to
unexpected student
ideas

 

Stresses deriving from
teachers’ attempts to engage
with and pursue unexpected
student ideas offered during
classroom discussions (i.e. this
is a special case of Managing
disroom discussions).
(Teachers often reported
experiencing such events as
more surprising and more
stressful than simply
facilitating discussions, pushing
with immediacy on their
content and pedagogical
content knowledge.)

 

[A student said that when you have 8
places that you need to connect with
roads, you must have at least 7 roads]
Ms. B: ...When she said that, like I
looked, because I was like, “Okay, I’d
better figure out right now if this is
true or not.” So I sat there and I
looked. And I was thinking through a
couple of examples really fast in my
head. And I was like, “Okay, that
would be true.” So then I gave them
that as an assignment to think of
“Well, why would that be true?”. . .[It
was challenging] trying to figure it out
within 30 seconds to see if it’s right or
not! (Post, 5.28-5.42)*

 

227

 

 

 

 

 

 

 

Appendix B (continued)

 

Directing students’
explorations of
mathematics

Stresses deriving from
engaging students in activities
where they explored, alone or
in pairs or small groups, a
problem or situation. (If the
teacher characterized students
as not participating and
described it as or a shared
problem or did not explain
why, I placed it here; if the
teacher characterized it as
student lack of interest or
resistance to participation, I
placed it under Lack of student
interest/motivation.)

[Mr. J assigned problems where
students tried to create two different
triangles that met a specific criterion,
such as ASA or SSA, to see whether
the condition always implied
congruence]

Mr. J: Yeah... The challenging part
was probably trying to get them to
understand what they were doing, as
far as why they were drawing two
triangles. . .that are not congruent...
They didn’t really understand why we
cared about two congruent triangles.
So maybe trying to do a better job of
explaining why we want to figure out
about two congruent triangles, or even
why it was important, why we came to
say they’re congruent. Why do we
have to have a minimum set of
criteria? It would be very important to
lay that out before we even tried to
have any kind of activity where they
had to figure out why the two triangles
were congruent... (Post, 2.42-4.17).*

 

 

Creating, aligning,
modifying, or
implementing
curricula

 

Stresses deriving from
teachers’ attempts to organize,
create, modify, and implement
the school’s chosen curriculum,
or to align it with the NCTM
Standards or Michigan’s State
Standards. These stresses
included how well the chosen
textbook or curriculum fit the
teacher’s pedagogical goals.

 

Ms. W: Our official text. . .is the
Larson Boswell... So we use that
one... We have the McDougal Littell
series for Algebra 2. .. And a lot of
times we’ll go to the McDougal Littell
one, because it lays it out a little bit
nicer. So we can kind of use both. It’s
very, it’s like they’re very parallel...
And right now, our algebra text is
really outdated. But for now, I guess
we have to stay with our outdated
one. . ., because we’re working with
that program, ...the Cognitive Tutor,
the Carnegie learning [computer-
based algebra curriculum]... So our
board recognizes that as one of
them... Because that was supposed to
be the new curriculum... As a
department, we’re not too thrilled
about it. We kind of do [all three]...
So we’re all over the board for our
high school [curriculum]. It’s kind of
bafihe, 1.15-3.7).

 

228

 

Appendix B (continued)

 

Working with
technology

Stresses deriving from
teachers’ attempts to integrate
technology into the curriculum.
These stresses could be related
to the pedagogy they wished to
employ, the time that teaching
students how to use technology
took, the lack of availability of
resources to perform such
teaching, or the teachers’ lack
of knowledge about the
technology that they wished to
employ.

Ms. G: At first, he hit intersect, I
think. [Pause] ...I think I was just
like, I’m just going to go through one
at a time and show them, because . . .it
is fi'ustrating, really frustrating... At
this point, I feel like they should know
the basic keystrokes of entering an
equation, using zoom efficiently, and
finding a good window. And that’s
what middle school’s not preparing
them for... I know the middle schools
have them, .. .but they’ll get taken
away for weeks, because maybe like a
kid lost one or dropped it on the
floor... So I feel like I have to wind
around the room. And I have like
people calling me all the time (Post,
12.17-14.l9).

 

 

Relationships and
communications
with colleagues

 

Stresses deriving from
teachers’ interactions with their
peers. Such stresses often
related to differences in beliefs
about classroom management
or “teaching style,” including
pedagogy, collaboration, and
classroom management issues.

 

Ms. G: And then I did a six-week-long
long-term sub thing at Hamilton [High
School], which was another like
ideal—like they brought me in, and I
was with the math department and
doing these amazing things... It was
my senior year, but I got hired as a
long-term sub. So I taught 2 or 3
sections of math at Hamilton and
spent my lunch hours with the
Hamilton teachers [collaborating]...
So math is different there.

I: That did set your expectations pretty
high.

Ms. G: Yeah. And what kinds of
conversations we should be having in
the lunch room, you know. They are
very focused. So coming here, it is a
bit of a let down (Post, 27.42-28.12).*

 

 

229

 

Appendix B (continued)

 

Lack of student
interest/motivation

Stresses deriving from
teachers’ attempts to engage
students in their lessons and/or
students’ resistance to engaging
in those lessons in a non-
superficial way. (If it is clear
that chattiness is slowing
students’ or the class’ progress,
I coded the passage here;
otherwise, I coded it as
Responding to problemati_c
student behaviors. Also, when
the challenge is student interest
or motivation during
discussions or student
explorations and the teacher
described the responsibility as
shared, I coded it as Managing
mssroom discussions or

 

 

Directing students’
explorations of mathematics,
respectively.)

Ms. P: I think one challenge that’s
probably going to be ongoing is just
getting kids genuinely motivated or
actually wanting to do whatever it is
you’re doing in your class on that
particular day. Because sometimes
they’d rather sleep, [or] there’s an
assembly, [or] they have something
going on after school. And I guess just
trying to get them to at least focus for
that hour on what they need to do,
trying to make the most of it. But I
don’t know if that’s something that
necessarily has an answer, other than,
the better, I guess, the lesson plans
are, the more engaged the kids (Pre,
8.27-9.9).

 

 

Learning and
teaching unfamiliar
content

 

Stresses deriving from
teachers’ attempts to teach
content that they had never
seen before (e.g., graph theory
or statistics), had not seen
recently (e.g., geometry), or
had had limited opportunities to
learn (e.g., calculus).

 

Ms. W: 80 next year might be kind of
challenging, because I think they
might try and put me in at either
Precalc or Algebra 2. And that will
definitely be a challenge, because... I
would almost prefer to be at a middle
school. . ., just because the content is...
at a different level. ...When I did my
internship, there were nights that I
could go home and I really could
leave it at [school]... And I could still
go in and teach. At the middle school
content, it’s so much easier to wing it
on the fly, you know?

Ms. W: ...When I took over that
Precalc class [for a few weeks], the
night before...l was sitting down and
saying, “Okay, let me make sure I go
through all these homework problems
to make sure I know how to do them,
because when they ask me, I want to
make sure I can.” . . .I want to know it,
so that they’re not, “Okay, she doesn’t
even know what she’s talking about.”
Because that goes so far with them
(Post, 22.26-23.21).

 

 

230

 

Appendix B (continued)

 

Planning lessons

Stresses deriving from
teachers’ attempts to prepare
individual lessons. This
generally involved creating
new lessons or adapting
existing lessons to their
curricular objectives. (If the
stress related to tailoring
lessons for students of varying
ability levels, the passage was
placed in the Teaching students
of vnyingjnrility levels
category. If teachers related
planning interesting lessons to
lack of student motivation, it
went in Lack of student
interest/motivation.)

Ms. G: No, no, no. My whole
internship year, I wrote out a lot of
things. But I found that like in the
“fast-pacedness” of school, I don’t
necessarily have time to reflect on all
of those lesson plans. Or all of those
lessons.

I: For five or six classes every day.
Ms. G: Yeah, yeah. And that is
frustrating (Pre, 4.16—4.20).

 

 

 

Responding to
problematic student
behaviors

 

Stresses deriving from
teachers’ attempts to deal with
student behaviors that were
inappropriate for the classroom
or irritating to the teacher, such
as loud or excessive talking,
disrespectful remarks to the
teacher or other students,
whining about an assignment or
lesson, etc. (If the teacher said
that the talking or chattiness
was delaying progress or
occurred while the teacher or
other students talked to the
class, the passage was coded as
Lack of student
interest/motivation. If the issue
was talked about generally or
the timing was unclear, this
was the default code.)

Ms. P: The students... came in that
day and they decided that they were
going to talk and whatever. . . I mean
pretty much one of them knows
what’s going on. And the other one
doesn’t care. So they talk to each
other.. .And the day you came, I’d just
moved their seats. We’d just got new
seats there... So like that’s been an
issue (Post, 1.30-1.40).

 

 

Ms. R: I have not had so many kids
not answer. . .questions on the test...
They’re doing horribly. And not on
the ones that they tried and got partial
credit for... I’m grading these tests
and... in the first hour three kids tried
every single problem... I don’t know
when that became acceptable, to not
try... It’s not like they had a bunch of
chicken scratch and then couldn’t get
to an answer. Completely

blank. . .They’re not even attempting
to jog their memory. They’re just
looking at it... And that’s the only
thing that peeves me is that it’s
exactly like [the practice test]. I mean,
one of the questions, even the
numbers were the same (Post, 10.1 1-
10.29)

 

231

 

 

 

Appendix B (continued)

 

Finding and
utilizing resources

Stresses deriving from
teachers’ attempts to find
physical, curricular, or human
resources to meet their
pedagogical goals. Often these
resources involved Internet
(and sometimes library or
curricular) searches that met
with limited or low rates of
success. This category also
included teachers’ unsuccessful
attempts to get students to be
resources for each other.

I: Do you find you’re pretty successful
at finding things that you like [through
lntemet searches]?

Ms. G: I’m not, actually... So much of
it is like tutorials of straight up
algebra... [and] notes. I’m looking for
more engaging things. . . And so much
of the things they call engaging
lessons are still just kind of different
ways to do notes. .. It’s not really
pushing them to the next level. . . My
most successful spots are the virtual
manipulatives. . . (Post, 16.35-17.14).

 

Ms. G: I guess I struggled with the
resources that I don’t have in the
classroom student-to-student. .. In
general, I would say 40% of my
students are absent. And it’s not the
same 40%... So when that population
who’s absent is shifting all the time,
there’s no continuity. It’s a whole
different approach to teaching than I
thought I would have... Doing things
in chunks of days is not very good,
except like those 10 who show up
regularly. Things really have to be day
to day (Pre, 7.45-8.18)"

 

 

After hours work /
long hours

 

Stresses deriving from
teachers’ attempts to manage
their extracurricular work, such
as completing class
preparations and grading,
thinking about management
issues, etc. (If professional
development took a lot of time,
the passage was coded as
C_hallenges associated with
professiorfl development.)

 

Ms. B: Man. The amount of time I
spend doing things. Like if somehow
they could find out a way to give me
more time or resources... Ms. K can
sit down and create a lesson or create
a new document that we’re using in
literally 15 minutes. And it will take
me an hour and a half to do the exact
same thing. And I just think that that
comes with time and maturity and
knowing how you like to organize
things (Post, 1545-166).

 

232

 

Appendix B (continued)

 

Challenges
associated with
professional
development

Stresses deriving from teacher
perceptions of professional
development experiences as
time consuming or inadequate.
This frustration often related to
the number of professional
development hours required by
their state or the quality of the
school- or district-provided
professional development
experiences. (If professional
development took a lot of time,
it was still coded as Challenges
assoginted with profession!

development.)

Ms. B: The first year, we had two days
required at the beginning of the year,
kind of in-service type days that. . .the
novice teachers were required to go to.
We got to go to [a teambuilding
experience]. It was so fun... It was a
really great way to build some
camaraderie between the new
teachers... The next year we came
back. And we weren’t doing
[teambuilding], even though every one
of us said, “This is great! We want to
do this again next year.” But they
didn’t listen... [They sent the second-
year teachers to a first-year teacher
orientation instead] And it was just,
[with] everything that was going on,
we got really frustrated (Post, 9.1-
9.15).

 

 

Student diversity
issues

 

Stresses deriving from
teachers’ attempts to relate to
and involve all students,
including those whose racial,
linguistic and/or ethnic
background was different from
the teacher’s and/or some of
their peers.

 

Ms. G: And then this year, instead of
like freaking out about what is [the]
constitution of the class, the challenge
is thinking about who I’m reaching
today. And then who different can I
reach tomorrow by making a change
in what I’m doing. You know, because
I have two [or three] days to teach a
lesson in the C-series. ..for one simple
topic. How many different ways can I
do it so I can reach those different
types of students, those_different
levels and those different languages
and those different types of learners?...
There’s like 24 languages... I think
10% of our population is ESL (Pre,
9.45-10.25).

 

233

 

Appendix B (continued)

 

Dealing with class

length, pace, or
schedule

Stresses deriving from
teachers’ attempts to deal with
challenges related to the length
of class periods, the pace at
which they felt obliged to teach
due to an agreed upon teaching
curriculum or schedule, or the
demands of their particular
schedule, including the number
of preps, types of classes, room
changes, unexpected events
(like fire drills, team practices,
competitions, and assemblies),
etc. (Note: Pace issues related
to Teaching students of vying
ability levels were placed in
that category and not here.)

Mr. J: So I struggle with pace, as far
as “Well, what do I do? How do I
accommodate all students?” as far as
that. So I’ve kept it. Pretty much
where it’s at right now is where it
needs to be, as far as getting material
done. But I always offer extra
challenges for the ones that think it’s
too slow. “Here are extra challenges
for you to do.” For going too fast,
come in to get help or have someone
tutor you. Do whatever it takes. You
know, there are a lot of resources
around the school, especially if you
need to get help, so make sure you
come in to get help and get caught up
if you’re behind (Post, 16.4-16.10).

 

 

Assessing student
understanding

 

Stresses deriving from trying to
assess whether students
understood the mathematics
that they were learning,
whether formally or informally.
This category did not include
standardized tests, as defined in

Preparing for, administering,

evaluating, and assessing
standardized tests category.

 

Ms. P: I guess another [challenge] is
always like assessing where the
students are, like during the class, like
trying to feel out. Because especially
if the class is dead, it’s like, “Do they
understand? Or just?” Do you know
what I mean?

Ms. P: Kind of both [during
discussions and when I go around to
their desks]. When I go around to their
desks, I can tell [if they understand],
but if I’m teaching them something
new, then sometimes it’s hard to tell.
You know? (Post, 15.45-16.13

 

234

 

Appendix B (continued)

 

Teaching students
of varying ability
levels

Stresses deriving from

teachers’ attempts to effectively
teach students with a variety of

perceived or measured ability
levels within a single class.

Mr. J: As opposed to Integrated 1
which takes two semesters, the
semester’s broken up. The first
semester of Integrated 1 is actually
1A, and it’s a year. And 18 is the
second semester of Integrated 1. So it
is a lower track. .. A lot of them are in
there, because the way they tested in,
they need a slower pace. . . I do have a
lot of former 1B students in Integrated
2 this year. And they’re really
struggling with the pace, as far as how
the material is presented. So I’ve been
working a lot with pace. I know some
students in Integrated 2 feel that the
pace is extremely slow and they want
it sped up, or for a couple of students,
too fast... So I struggle with pace, as
far as “Well, what do I do? How do I
accommodate all students?” ...Pretty
much where it’s at right now is where
it needs to be, as far as getting
material done. But I always offer extra
challenges for the ones that think it’s
too slow... For going too fast, come in
to get help or have someone tutor you.
Do whatever it takes. ...There are a lot
of resources around the school... if
you’re behind (Post, 15.37-16.16).

 

 

Preparing for,
administering, and
evaluating
standardized test

 

Stresses deriving from
teachers’ attempts to prepare
students for standardized tests,
including modifying lesson
plans and curriculum,
administering those tests,
evaluating the tests (where
applicable), and determining
how to utilize feedback from
those tests to inform one’s
teaching. Such tests included
the Federal- and State-
mandated tests, as well as
school- or district-created
and/or -mandated tests.

 

Ms. R: Another way they’re following
up, and it’s actually for all teachers, is
we are going to be analyzing our test
scores. Not so much to say, “You’re a
bad teacher. You’re a good teacher.”
But “Your kids seem to have done
better on linear equations. What types
of things did you do that I didn’t do
that can help me out?”. . . [Grimace]
Ms. R: ...I get nervous as a new
teacher that they are going to look at
it. And if my kids do poorly, I think
they’re going to think that I’m a bad
teacher. Or it just makes me nervous
as a new teacher who doesn’t know
anything... to have my scores
compared to a teacher who has been
doing this for fifteen years (Pre,
15.24-15.37).

 

235

 

Appendix B (continued)

 

Relationships and
communications
with parents

Stresses deriving from
teachers’ interactions with
parents. Often, these stressful
events involved parental
disapproval of the teacher’s
responses to student
misbehaviors or the parent’s
reaction to their child’s low
grades.

Ms. B: And I had a parent who was
absolutely awfirl to me, ...like
ridiculously horrible. .. That was the
first time I’d ever had a parent belittle
me. And really make me feel like,
“Oh, you’ve only been teaching for so
long? Oh, you’re awfully young!

. . .Oh, you’re a female?” You know,
that kind of stuff, so that was the first
experience I had with that. And that
was very unpleasant, so that was very
stressful (Pre, 1 1.34-1 may

 

Teacher boredom

Stresses deriving from trying to
deal with one’s own boredom
while teaching because the
content, lesson format, or
students were not particularly
engaging for the teacher. These
stresses could be short-lived or
persistent.

Ms. G: I think like the biggest thing
that might push me out of teaching
math, because I think about it
sometimes, because I know what it’s
like to teach English. . . I want to make
them—not like math—but be
successful at math when they maybe
haven’t in the past. And I’m just
discouraged by how dull it is for me
sometimes gPost, l9.34-l9.39).

 

 

Relationships and
communications
with administrators

 

Stresses deriving from
administrators’ decisions that
made the working environment
less comfortable for the teacher
or from teachers’ attempts to
enlist administrators help with
classroom management,
professional development, and
pedagogical concerns.

 

Ms. R: I am enjoying it more. At the
beginning of the year, I was very, very
frightened. Not of the students, but
they have high, high expectations
here... And I was really worried that I
would not meet those expectations,
that I was—you know, they, I don’t
want to say intimidate, but I was,_after
those six days of new teacher training,
I was definitely worried that I could
not do enough to be a good teacher at
this district.

Ms. R: We were given the impression
that as new teachers, we would be
watched very closely, our progress
and our style and everything would be
watched very closely. And it was very
important on how many people we
were passing and how many people
we were not passing (Pre, 13.40-
14.24).

 

236

 

Appendix B (continued)

 

 

Relationships with
students

 

Stresses deriving from
maintaining or lacking

relationships with students.

 

Ms. W: My mentor [from my
internship] is always calling me like,
“We might have a position in the
district, a middle school position.”
...I’m always “If you get a middle
school position... and I can work next
to you guys, definitely let me know,
because that’s one that I would
consider.” You know, because 1 love
the middle school... So it would be a
toss up. But if there’s nothing that
comes up, I’d have to just deal with it
and take it as it goes.

Ms. W: ...It’s hard. As much as the
connections that I’ve made here. . .
With the 7th graders, ...they love to
cling onto you... They love to have
that connection. And they were so
much fun, too. And they buy in to so
many things. I can be like, “Okay,
guys, let’s do this today.” (Post,
23.30-24.35).

 

Note. The “*” after a quote indicates that the content of that quote (as listed in this table) is related to the
teacher’s attempts at SBT.

237

 

 

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