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BECOMING A REF ORM-ORIENTED TEACHER

By

Lauren Claire Pfeifi‘er

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Counseling, Educational Psychology, and
Special Education

1998

 

 

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ABSTRACT

BECOMING A REFORM-ORIENTED TEACHER

By

Lauren Claire Pfeiffer

In this study, I explored some of what it takes for a teacher to support her
continued, self-directed professional development; what helps and what hinders her
development as a reforrn-oriented teacher in a period of intense educational change.

The context of this study was my collaboration with Lisa Pasek, a sixth grade
teacher in a mid-size, Midwestem school district. One way Lisa chose to pursue her
development of a sixth-grade teaching practice was to experiment with how she might use
videotapes of her own classroom to learn about her mathematics teaching. She was
interested in how the videotapes might inform her efforts to develop a discourse with
children in which they explore multiple perspectives on solving particular mathematical
problems and look to themselves and to their peers as sources of support for their own
learning. Lisa was also curious about how she might use videotapes of her teaching to
talk with her faculty colleagues and administrators about her practice.

To explore the question, What and how does a teacher learn from conversations

around videotapes of her own teaching?, Lisa and I met regularly during the 1992-93

school year. The activities of our work included videotaping her sixth grade mathematics
classes, talking in preparation for her to share the tapes with colleagues, reflecting (in
writing and in dialogue) about occassions when she showed videotape to other teachers
and talked about her practice, and individual and joint presentations of our work at
workshops and conferences. I gathered the following data: (1) videotapes of Lisa’s
mathematics classes; (2) audiotapes and transcripts of Lisa’s conversations around these
video records; (3) my fieldnotes and journal; (4) Lisa’s journal; and (5) audiotapes and
transcripts of conversations and interviews with Lisa.

The analysis focuses on three contexts in which Lisa engaged in conversations
around videotapes of her teaching: discussion in a teachers’ group, dialogue with me, and
a classroom discussion with her sixth grade students. Through my study of these sets of
interactions, I learned that Lisa’s educative use of videotaped records of her teaching
required that she construct and employ new kinds of knowledge about teaching and
learning. The kinds of knowledge needed to support Lisa in critical examination and
articulation of her understandings, beliefs, and her practices are of a different order than
the knowledge of learners, subject matter, pedagogy, for example, identified as part of a
knowledge base for teaching. Specifically, Lisa’s learning in this study reflects her
development and use of professional participation knowledge, a domain of knowledge for
a teaching practice that supports her capacities to work with colleagues on individual and

collective inquiry into teaching and learning.

Copyright by
LAUREN CLAIRE PFEIFFER
1998

T o my parents
Oaire and David Heifer

My first and most cherished teachers

ACKNOWLEDGENIENTS

I was standing with a long time fiiend and colleague, admiring the work of an artist
who combines her watercolor painting and calligraphy with the literary work of well-

6‘

known authors. My friend turned to me, pointing to Thoreau’s words: ...to live
intentionally...,” and commented that they reminded her of me. I was touched by her
words. I was also taken aback by the reflection she offered me. With the writing of this
dissertation I am deeply grateful for an opportunity to acknowledge many of those who
have taught me the importance of living and learning intentionally, some who have shown
me what it looks like, and others who have joined me in the adventure.

I begin with my gratitude and admiration for Lisa Pasek. She made our work
together intriguing, absorbing, challenging, and at times, great fiin. She shared openly her
gift of speaking and writing intellectually from her heart. I earnestly offer my thanks to
her for all she has taught me about the challenge of becoming a reforrn-oriented teacher.

My gratitude for the Investigating Mathematics Teaching group is immeasurable. I
thank Helen Featherstone, Stephen Smith, Debi Corbin, Carole Shank, Kathy Beasley,
Marian Shears, Jan Derksen, and Teri Keusch, (and Lisa, too) for helping me to hold on to
my identity as an elementary classroom teacher while I explored and developed new ways

of becoming a reform-oriented educator. I cherish the opportunity to learn about learning

and teaching in their good company.

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I acknowledge and thank the members of my doctoral committee. I am gratefirl to
my director, Christopher M. Clark, for his commitment and support throughout my
doctoral studies. His vision of reforms in teaching and learning and his passion for real
change that supports authentic learning in caring communities continues to be an
important source of inspiration for my work. His experience, insight, and capacity for
taking a different perspective provided me with valuable tools during the dissertation
project and on into new work. I am grateful to Helen Featherstone and Deborah Ball for
their committed support in helping me puzzle through complex aspects of my analyses. I
am grateful for Helen’s careful resolve to help deepen my work, for her enthusiasm in
joining me as a learner of the work, and for, still now, her writing lessons. I value
Deborah’s hard questions, her modeling of “confident uncertainty,” and her thoughtful
perspective on the work and lives of classroom teachers. I thank Evelyn Oka and Patrick
Dickson for their supportive inquiries and responses to the work in progress.

The opportunity to acknowledge my graduate school “family” is long awaited. To
Julie Ricks-Doneen, Carol Crumbaugh, Troy Mariage, and Garnet Hauger: If formal
education can be likened to a runner’s marathon, replete with jagged hills, smooth
stretches, and mini-breaks for the necessities of living, and if graduate school begins at the
twenty-five mile marker, I could not have been blessed with a more caring, supportive,
insightfirl, and funny team with whom to “run” the last, most challenging mile. For their
perspectives, their questions, their commitment, and their love, I value deeply the critical
colleagueship we have created and sustained these many years. I thank them for their

individual gifts and our collective life in a very special time.

I was blessed, too, with an opportunity to live and learn in a graduate school
community that crossed disciplines and generations of graduate students. In an era of
professional learning that presses beyond seminars and cofi’eehouses, I am grateful to a
enormous group of graduate school colleagues, including: Michelle Parker, Lynn Cavazos,
Ruth Heaton, Ginny Goatley, Janet Navarro, Paul Vellom, Randi Nevins, Jordy Whitmer,
Neli Wolf, Martial Dembele, Tammy Lantz, Lynn Brice, and Dan Schultz. I thank them
for their generous and varied contributions to my learning. I extend special gratitude to
my colleague and fiiend, Jenny Denyer, for her wisdom, her care, and her guidance. I
cherish the joy we share that comes with our commitment to educative experiences.

As my time at Michigan State University criss-crossed a territory of instructional
design, educational technology, professional learning, and educational psychology, a
special group of educators contributed to my learning and development. I wish to
acknowledge in particular the teaching and mentorship of Joseph L. Byers, Cassandra L.
Book, Stephen Yelon, Norman Bell, Sharon Feirnan-Nemser, Susan Florio-Ruane, and
Magdalene Larnpert. These faculty members shared with me their perspectives, their
experiences, and their wisdom in ways that have truly guided my professional life. I
extend to each of them my deep and sincere gratitude.

My family is a continuing source of strength and joy-——my first and most cherished
learning community. My parents, Claire and David Pfeiffer, have never wavered in their
unquestioning love for me nor their belief in my potential. I am especially gratefirl to them
for knowing how to support me “at a distance," for sharing my delight that “life is what

happens while we are making all the plans," and for never really doubting that “I would be

viii

fine.” I am gratefirl for the many ways my family cared for me during the course of this
work. My brother and sister-in-law, Craig and Cissy Pfeifi‘er, provided a haven in the
woods for reading and writing and thinking. My brother and sister-in—law, Tim and Susan
Pfeifi’er, provided a haven in the mountains for rest and renewal. My sister, Julie Pfeiffer,
provided a unique haven in our relationship for my head and my heart. Her genius for
asking good questions, listening deeply, and nurturing me through the creative process,
supported me in ways that only she could as both sister and colleague.

My husband, Gary Childs, crossed my path as I was riding the last stretches of this
particular trail. I am grateful for his capacity to listen, watch, and wait, with endearing
patience as I closed the book on this important part of my life’s journey. I admire his
energy and enthusiasm for learning—and his commitment to share what he learns with
others. I cherish our choosing to continue our journeys together and to help each other

live and learn intentionally.

TABLE OF CONTENTS

List Of Tables .............................................................................................................. xiv
List Of Figures ............................................................................................................. xv
Prologue ...................................................................................................................... xvi
CHAPTER ONE ............................................................................................................ 1
Teachers’ Professional Development In The Context Of Reform -- - - - 1

 

Responding To The Call For Critical Colleagueship: A Social Constructivist

 

Perspective ..................................................................................................................... 4
Teacher Groups ........................................................................................................... 8
Challenges To The Reform Of Professional Development ........................................... 9
The Culture of Teaching .............................................................................................. 9
Critical Awareness of the Culture of Teaching ............................................................ 11
Teachers’ Conversations ............................................................................................ 13
Self as Learner and Self as Teacher ............................................................................ 19
Becoming A Reform-Oriented Teacher ...................................................................... 22
Teacher Reflection and Learning from Practice .......................................................... 23
A Teacher and A Researcher Explore What’s Possible ............................................... 27
Overview of this document ........................................................................................ 29
CHAPTER TWO ......................................................................................................... 31
Lisa - - - - ................................................................................................ 31
Lisa's Story .................................................................................................................. 35

A Teacher, A Researcher, And A Method Of Inquiry- - - - - - - - - - -...44

 

 

 

 

 

 

A Web of Questions ................................................................................................... 44
Mustering Resources .............................................................................................. 46
Creating a Partnership ............................................................................................ 47
A Week of Videotaping .......................................................................................... 48
Notes on the Week ................................................................................................. 51

A Method Of Inquiry: Investigating Experience As We Live It ................................... 56
Gathering the Materials of Lived Experience .......................................................... 58
Reflecting on the Materials of Lived Experience ..................................................... 61
Interpretation as Conversation ................................................................................ 64
What Have I Learned? How Might I Show Others? ............................................... 66

CHAPTER THREE - - - - - - - - - ______ -- 70
Learning New Norms For Making Practice Public - - 70
Sharing Her Own Videotape Of Teaching - - _ -- _ - - - 76

Earlier Preparation for Sharing ................................................................................... 78

Showing and Talking about Practice .......................................................................... 82

Lisa’s Four Conjectures about Showing Videotape .................................................... 91

Making Practice Public - - - - -- - - -- - _ _ 92
“A Kind Of Coming Out Party” - -- ..... - __ ---_-92

Reflections on Sharing Videotape .............................................................................. 95

A Question of My Own .............................................................................................. 98

Shared Experience with Sharing Videotape .............................................................. 100

Making Practice Public and Problematic and Shared ................................................ 102

Boundaries On Conversation, Boundaries On Learning About Teaching ............. 104

The Rights and Duties in the IMT Conversation around Videotape .......................... 107

Segment Two: A Pattern of Questions and Answers ................................................ 108

Segment Four: A Break in the Pattern of Questions and Answers ............................. 114

Segment Six: A Possible Shift in the Conversational Rights and Duties ..................... 118

Sharing The Relational Work Of Creating New Norms .......................................... 121

 

Building and Standing on the Trust of Colleagues .................................................... 122
Trust and Dialogue .................................................................................................. 123
Relational Work In Dialogue And Reforming The Culture Of Teaching .................... 124
Learning About The Culture Of Teaching ............................................................... 127
CHAPTER FOUR A AA A A A . A- AA A . . AAAAAA A 131
Learning A New Kind Of Conversation About Teaching. ...... ............. 131

 

Conversational Workspace 1: Learning To Articulate Questions About Practice . 134
Conversational Workspace 2: Learning To Be One’s Own Knowledgeable Other 143

Conversational Workspace 3: Learning New Meaning For Familiar Language 152

 

 

 

What Counts as a Conversation Around One’s Videotape? ...................................... 158
Learning About Teachers' Conversations ................................................................ 160
CHAPTER FIVE AAAAA A A A A A A - A . -A - A A A A 162
Learning About Oneself In Learning To Teach........- A - AA A A 162
The Grouping Experiment ........................................................................................ 165

Raising Questions about Practice ............................................................................. 168

Origins of the Grouping Experiment ......................................................................... 169

The Connections Continue ....................................................................................... 174

Students and Teachers as Researchers and Colleagues in Learning to Learn ............. 175
Lisa’s Reflections On Learning From Her Practice: - A A AA 177
The “Rut” Is No Longer A Threat ............................................................................ 177

A Conversation about Learning from Experience ..................................................... 181
Learning About Self As Learner And Self As Teacher ............................................ 188

xii

CHAPTER SIX

Constructing Professional Participation Knowledge For A Teaching Practice ......

Learning In A Different Domain Of Knowledge
Professional Participation Knowledge For Teaching In The Context Of Reform ......
Knowledge of Conversational Rights and Duties ......................................................
Knowledge of language use and meaning in dialogue ................................................
Knowledge of self as teacher: relation of beliefs to actions .......................................

Knowledge of self as learner: reflection on personal/professional growth ..................

Continuing The Reform Of Teachers’ Professional Development

New Questions For New Work

REFERENCES

 

 

xiii

191
191

193
198
203
203
204
205

206

210

213

List Of Tables

Table 1. Reciprocal Rights and Duties for Segment Two of the Group's Discussion 112
Table 2. Reciprocal Rights and Duties for Segment Four of the Group's Discussion. 117
Table 3. Reciprocal Rights and Duties for Segment Six of the Group's Discussion ....... 119

Table 4. Possible Rights and Duties for Lisa and the IMT members ............................. 120

xiv

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.

Figure 10.

List Of Figures

Calendar of Early Events in the Project ....................................................... 51
Two approaches to multiplying two-digit numbers discussed

in IMT meeting ........................................................................................... 83
Base ten block shaded to show .515 ............................................................ 88
Three segments of the discussion following group’s viewing

of Lisa's videotape. .................................................................................. 107
Connections between trust and a new culture of teaching. ......................... 127
Visions of the students’ role in discourse ................................................... 141
Visions of the teachers’ role in discourse. .................................................. 144
Events highlighted in Lisa's inquiry into groupwork ................................... 173
A Framework for Teachers’ Knowledge for Practice. ................................ 197

A view of the contexts of reform: education reform, school reform,
and professional development reform. ....................................................... 207

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Prologue

My principal teacher was experience; I learned to teach through trial and error in
the classroom. As a classroom teacher, I lived the self-socialization Daniel Lortie (19 75)
describes as personal experience, supplemented by collegial assistance that I screened
and adapted to my individual practice. For six years I survived, and in some ways
thrived, in a culture of individualism and mutual assistance. Then came a time when I
started to ask hard questions about my work in schools and about my own development
as an educator—as a learner. What are we teaching? What are they learning? What
does it really mean to say “I am a teacher? ” This time is marked for me by the memory
of a conversation with a colleague:
Sitting in her car in my driveway, I listened to Nan speak the same words of
fiustration, disillusionment, and undirected determination that had been stuck in my own
head for some time. The ungraded math papers on my dining room table tugged at my
conscience, but my sharp awareness that this was a kind of conversation I had never had
before kept me riveted to the seat as the ideas and the words and the questions came
pouring forth.
Nan and I were both elementary classroom teachers. We met when we enrolled in
a Masters course in elementary language arts at a small university in Indiana. During

the last half of the term we traveled together to the nearby campus for a Tuesday night

xvi

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class that ofl'ered lots of ideas and activities related to whole language curriculum, active
child participation, and meaningful assessments of student learning. I can 't remember
much about the course now. What I remember is talking with Nan. I remember the
striking sense that I was talking with another teacher in a way that was rare during my
first five years of teaching. We sat in my driveway and tried to make sense of the vague
“hungty " feeling we had in common. We sat there a long time. My conversation with
Nan was the first occasion on which either of us spoke openly and thoughtfully about
these big questions and the implications of our lack of answers. We wondered how we
would ever stay motivated to teach in our respective settings year after year. In the
middle of another school year, our immediate futures were quite predictable and that in
itself was unsettling. Aside from the reward of personal relationships with the children,
the work and the accomplishments of the teaching year would be similar to last year 's
and to next year's. It was good, but it wasn't good enough. “I want more, " we each
confided “but, I don 't really know what 'more ’ is or how to get it. " More than all the talk
in the course sessions, this was the conversation that pushed me to think and to wonder
and to question my own professional development. Later, I would learn that educational
researchers have studied teachers' career paths (F eiman-Nemser and F laden, 1986;
Huberman, 1989; Ball and Goodson, I 985) and I would find language and ways of
thinking about experiences and questions I could only describe then as a kind of hunger.
I tried to describe for Nan the intellectual high I experienced when I participated

in the university class sessions—the conversations, the descriptions of alternative

approaches to instruction, the debates that were launched when we spoke of our

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experiences in classrooms. I also told her how it seemed that the intellectual high was
tied to those Tuesday night sessions and it stayed locked up in the university classroom.
It didn't seem connected to the tasks and issues that awaited me the next morning. The
intellectual high would tease me. I would hear myself talk in this class and I would want
to continue the conversations, but such talking, such thinking wasn ’t part of my work at
the elementary school.

I saw Nan only two or three times after we finished the course. As our separate
lives continued to unfold, it became clear to me that this December conversation was the
beginning of a transition. For me, it was a critical event in making sense of my
experience as a classroom teacher and wondering what my place in the field of education
could be. After another year of teaching, I chose fiill time graduate study as my
“something more. " I came to graduate school an experienced classroom teacher. By

then, I was very hungry.

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CHAPTER ONE

Teachers’ Professional Development In The Context 0f Reform

We are living and teaching in times when the struggle to affect changes in the
professional development of teachers is more conscious and more visible than ever.
Understanding that current reform agendas (see, for example, NCTM, 1989, 1991) require
enormous and complex learning on the part of teachers, some reformers are calling for
new forms of professional development (Ball & Cohen, 1996; Lord, 1994). Such
innovations call for teachers to situate their continued learning in their ongoing practices,
and to talk openly and in detail about their beliefs, decisions, and actions as teachers
(Little, 1993). Examples of these innovations include participation in teacher groups,
collaborations with university based researchers, the use of videotapes, stories, and
conversations about the complexity of teaching and learning in schools. Whether the
function of the teachers' group is to engage teachers as writers in and out of the
classroom, to support teachers’ development of alternative approaches to assessment, or
to assist teachers' investigations of the psychology and pedagogy of teaching mathematics
for conceptual understanding, the burgeoning reports of teachers meeting and talking
together in groups suggest a shared view that conversations about teaching and learning
can support teachers’ efl’orts to teach in the context of reform. (see for example, Schram,

et al, 1995; Harris, 1995', Florio-Ruane & deTar, 1995; Cavazos, 1993; Nathan, 1991).

 

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Researchers argue that talking together in groups is a powerful medium for
learning (Moll, 1990; Tharp and Gallimore, 1988; Bruner, 1986; Vygotsky, 1978; Dewey,
1938; 1902). The theories of learning guiding most of the current reforms propose
learning as a social process by which we come to new understanding through our
interactions with others. The notions that we learn through our interactions with others,
that we take pieces of those interactions into subsequent interactions, that we use these
interactions to construct meaning, and that we use our meanings to make sense of our
experiences—both past and present-~continue to press nationwide efforts to change the
way we interact with children in classrooms. This perspective on learning has been part of
the last fifieen years of educational reform, raising difficult questions about what it means
for children to learn school subjects. This perspective has contributed to the creation of
new subject matter standards that call for children to be active participants and responsible
owners of their own learning (NCTM, 1989,1991; NCTE, 1996).

These notions of learning are also influencing the field of teacher learning.
Researchers and teacher educators are asking difficult questions about the design,
development and implementation of professional development activities for teachers.
Many are interested in grounding these activities, too, in theoretical frames of learning
through social constructivism (Ball & Cohen, 1996; Cohen, et al., 1993; Calderhead,
1993; Leiberman & Miller, 1992). Judith Warren Little (1993) argues that teachers’
professional development must shift from a dominant model of teacher training to teacher

learning, where teachers’ intellectual curiosity is acknowledged and their contributions to

knowledge and practice are credited. She points out:

Compared with the complexity, subtlety, and uncertainties of classrooms,
professional development is often a remarkably low-intensity enterprise. It
requires little in the way of intellectual struggle or emotional engagement
and takes only superficial account of the teachers' histories or
circumstances (p. 148).

Reflective of reformers’ efforts to address the poverty of intellectual engagement

as an integral part of teacher’s continued learning is Brian Lord’s (1994) concept of

critical colleagueship. Critical colleagueship is an alternative professional stance held and
acted upon by teachers. Through their interactions, teachers reflect this stance of critical
colleagueship when they move beyond sharing ideas and supporting one another through
the change process “to confronting traditional practice-the teacher’s own and that of his
or her colleagues-with an eye toward wholesale revision.” In prompting educators to

shift from a paradigm of teacher training to teacher learning, Lord outlines six elements

included in the development of critical colleagueship:

1. Creating and sustaining productive disequilibrium through self-reflection,

2.

collegial dialogue, and on-going critique.

Embracing fiindamental intellectual virtues. Among these are openness
to new ideas, willingness to reject weak practices or flimsy reasoning
when faced with countervailing evidence and sound arguments,
accepting responsibility for acquiring and using relevant information in
the construction of technical arguments, willingness to seek out the best
ideas or the best knowledge from within the subject-matter
communities, greater reliance on organized and deliberate investigations
rather than learning by accident, and assuming collective responsibility
for creating a professional record of teachers research and
experimentation.

. Increasing the capacity for empathetic understanding (placing oneself in

a colleague’s shoes). That is, understanding a colleague’s dilemma in the
terms he or she understands it.

4. Developing and honing the skills and attributes associated with
negotiation, improved communication, and the resolution of competing
interests.

5. Increasing teachers’ comfort with high levels of ambiguity and
uncertainty, which will be regular features of teaching for understanding.

6. Achieving collective generativity—“knowing how to go on”

(“Wittgenstein 1958) as a goal of successful inquiry and practice (p. 193).

While Lord outlined these elements as part of a holistic casting of what is involved
in critical colleagueship, I see them as a good starter set of ideas salient to the focus of the
study reported here. These elements refer to the skills of inquiry and the stance of
uncertainty a teacher must acquire in order to engage in an approach to teaching that is
quite different from any approach she may have studied as a preservice teacher or as a
beginner.

What these elements call for is complex, difficult to model—let alone guide—as
teachers engage in changing their practices. There is much practice and study to be
conducted if we are to understand Lord’s concept in context, and identify the challenges,
as well as the achievements, it proposes. By nature of the call itself, I think classroom

teachers must play a key role in creating this complex and difficult new work.

Responding To The Call For Critical Colleagueship: A Social Constructivist Perspective
Thinking about classroom teachers as learners in the context of their work means
thinking about the creation of opportunities, resources, and strategies that can facilitate

their development of new knowledge, new skills, and new stances to be employed across

the variety of contexts that comprise a teacher’s practice. The work requires a kind of
engagement in which teachers explore what they think they know; for example, how they
make sense of why it is difficult to sustain a conversation with fourth graders about
negative numbers.

We have all experienced the frustration that occurs when we have difiiculty
explaining an idea that we thought we understood. Further, we know the excitement that
occurs when we find that in explaining our idea to someone else, we actually gain a better
understanding for ourselves. Duckworth (1987) describes the power of having learners
explain verbally what they think as a means of sense making:

1. Trying to make their thoughts clearer for someone else, learners achieve greater

clarity for themselves.

2. Learners determine what they want to understand. The explanation they give

also provides them with the questions they want to ask.

3. Learners come to depend on themselves as judges of what they know and

believe.

4. Learners experience the power of having their ideas taken seriously.

5. They learn enormous amounts from other learners.

6. Learners come to recognize that they have constructed their own knowledge.

The theories of learning that guide Duckworth and other reformers describe
learning as a social process by which we come to new understanding through
conversational interactions with others.

Currently, many educational psychologists, particularly those involved in

educational reform work, have turned their attention to theories of learning and

development that come from the sociohistorical school of psychology. Russian theorist

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Lev S. Vygotsky led the study of social origins and cultural bases of individual
development (Cole, 1985; Wertsch, 1990; Scribner, 1985). Vygotsky’s work is centered
on a foundational concept of individual development. The range between what we can do
alone and what we can do with the help of others sets the boundaries of our zone of
proximal development: “What the [learner] is able to do in collaboration today, he will be
able to do independently tomorrow” (Vygotsky, 1987, p. 211).

The implications of this view of learning are manifested in significant and visible
changes in what “doing school” looks like. In “The Teacher and the Taught,” Clark
(1990) points out an important shift in the role of the teacher :

In neo-Vygotskian theory, the aim of good teaching is to give the game

away to the learners. Through “scafi’olding”--the gradual transfer of

responsibility and control to the group of students-the adult teacher moves

away fi'om center stage to become a coparticipant or even an outsider in

the learning community. The course may be about algebra or art or history

or English, but in this framework, schooling is also about collectively

initiating, creating, and sustaining an inclusive learning community. In the

long run, this community-building feature of inclusive teaching may be of

as much social, developmental, and educational value as are the learning
and remembering of academic content (p. 263).

Social constructivist views of psychology prompt us to think about both the child
and the teacher as learners working together in classrooms. Luis M011 (1990) describes
Vygotsky as unusual because he was an educator turned psychologist. He cites the
observation of Vygotsky's collaborators: “Vygotsky demanded that psychology become
more than a scientific study of education and go beyond abstract theoretical knowledge

and intervene in human life and actively help in shaping it”(Leontiev and Luria, 1968, p.

367). Vygotsky's conviction that a psychologist must be not only a thinker, but a
practitioner as well, can be reversed: a teacher must not only be a practitioner but a
thinker as well. The two roles are inextricably linked and mutually dependent. This
relationship is readily recognized as the age old problem of connecting theory and practice
in learning to teach; of relating language, thought, and action in making sense of human
development.

A radical shift in what counts as learning changes everything about understanding
learning to teach. If learning is social and much of what is being learned resides in the
collective, what does it mean to be prepared and named as a teacher, or to maintain and
enhance the generic skills and inert knowledge first encountered in preservice training? Is
it even possible to think of school learning as a firndamentally social endeavor and still
think of teaching as an individualistic practice? The organization of schooling may still
treat teaching as a private practice. But learning to teach and learning from experience by
veteran teachers must begin to break with this reductionistic and disempowering pattern,
especially when the leading edge reforms of classroom teaching and curriculum are
founded in social constructivist learning theory.

Reforms underway incorporate social constructivist understandings of learning into
the design and practice of teachers' professional development, though these are few and
undersupported (Little, 1993). The aim of these reforms is to support new students of
teaching in continual learning to teach in the company of their colleagues. “The newest

approach to teacher education is less about certifying finished products and more about

getting something started-—a complex of learning, discourse, inquiry and action that will
thrive and evolve for thirty years” (C. M. Clark, personal communication, 1994).
Investigating and reframing their wisdom of practice can lead teachers to new
ways of thinking about children, subject matter, and self, and can encourage teachers to
act in new ways. Through this work they may come to see their teaching--and themselves

and others—in a new light.

T ch r u

Teacher educators organize and facilitate teacher groups, in part, as alternatives to
traditional inservice programming. Teachers join teachers’ groups-~and in some places,
organize them on their own--in pursuit of resources and support for their work in
classrooms (F eatherstone, 1996; Cochran-Smith and Lytle, 1993; Featherstone, Pfeifl’er, &
Smith, 1993; 19953; Schifter & Fosnot, 1993a).

Reforrners are calling for new norms of professional work where teachers talk
about teaching, observe and critique each other's practices in the classroom, work together
to design and prepare curriculum and actively pursue together real instructional
improvement (Little, 1990; Lord, 1994; Ball & Cohen,l996; Johnson, 1990; Lieberman &
Miller 1992; Little &McLaughlin, 1993) . These "critical practices" (Little, 1982) are
features of settings where the intellectual and professional growth of teachers is as much

an expected condition of school life as the intellectual development of children. What does

it take for teachers to participate in these new forms of professional work in ways that
align with the reforms of school learning and support their eli’orts to make changes in their

practices?

Challenges To The Reform Of Professional Development
Before describing the design of the study, I want to sketch a framework of three
aspects of current professional development reforms: (1) the culture of teaching,
(2) teachers’ conversations, and (3) self as learner and self as teacher. I believe these
aspects to be critical influences on the new work I’ve described above. In what follows, I
draw on literature that addresses these aspects as challenges to real change and as

constructs for understanding the complexity of teacher learning in the context of reform.

The Culture of Teaching

Teachers entering firlly into their local teaching practices meet with long standing
patterns of social interaction in schools. These norms of interaction support a culture of
sameness where teachers present their similarities and hide their differences as they relate
to their perspectives, experiences, and skills in teaching. The culture of teaching is
premised largely on a notion that a teacher’s practice is private, that what a teacher does
in her classroom with her students is largely an individual endeavor shielded by a shared

sense that an individual practice also means a private practice. When we, as teachers, talk

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about our teaching, from behind a social shield of privacy, we talk about it in ways that
serve to protect that privacy. This allows us to tell stories of our practice that reinforce
the notion that one teacher’s practice is more similar to than different from another’s. We
tend to reinforce a cultural belief that the ways one teacher thinks about curriculum, thinks
about instruction, and acts on assessment, is pretty much, more or less, the same as the
next teacher down the hall. Or, we accept differences as personal preferences and take a
hands-ofi’, non-interference approach to each other's work. When difi‘erences arise in
conversations about teaching practices we find ways to work around them. It is more
common to hear choruses of agreement around the lunch table than to hear bursts of
disagreement, debate, or even wondering about challenges and complexities about good
teaching. Little (1982) has described the culture and the relations of teachers within it in
this way:

This conception of collegial relations is consonant with portraits of
teachers' work that have altered little over decades (Waller, 1961[193 2];
Fuchs, 1969; Lortie, 1975). One cannot examine the boundaries of
teachers' professional relations without taking account of [the] pervasive
“ordinary reality” of sporadic and informal exchange. A school's staff may
be described as “close,” offering large doses of camaraderie, sympathy, and
moral support, but the texture of collegial relations is woven principally of
social and interpersonal interests. Teacher autonomy rests on freedom
from scrutiny and the largely unexarnined right to exercise personal
preference; teachers acknowledge and tolerate the individual preferences or
styles of others. Independent trial and error serves as the principal route to
competence In all these ways, the modal conception of collegiality is both
characteristic and reinforcing of a culture of individualism, presentism, and
conservatism (p. 513).

10

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For the most part teachers have lived and worked without active knowledge of or
attention to their culture of teaching. Traditionally, the body of knowledge constructed
and shared about the culture of teaching has been acquired by researchers: observing from
the outside, at times participating in, documenting, and describing the roles and
relationships which shape and govern the culture of schools. 1 Researchers have been the
ones to develop theoretical frames and vocabulary for talking about the culture of
teaching. While numerous former classroom teachers may have insight that is powerful for
examining culture, many practicing teachers do not attend actively or critically to the
norms and structures that shape their professional lives. Sources of knowledge about the
culture of teaching and uses of this knowledge have remained largely outside the culture.

I do not intend to suggest teachers are unaware of their culture, but the extent to
which they explicitly refer to it, examine it, and challenge it, has been limited and at times,
dismissed as the way things are. Now, in the context of reform, classroom teachers are
beginning to attend critically to the culture that surrounds their work. The press to engage
in collaborative work with colleagues, to talk about one’s teaching and to actively attend
to the features of one another’s practices is making visible norms of interaction,
relationships, and structures that can support or stifle productive dialogue among
educators. As I think the study reported here will show, teachers responding to the

current reforms in education are engaged in learning about the culture of teaching and are

 

‘ See Floden and Feiman Nemser, 1986 for a review of the literature on the culture of teaching.

11

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constructing for themselves new knowledge of the ways, norms, and relationships that
shape their work with colleagues and in turn, their work with students. For perhaps the
first time, teachers are becoming conscious—and vocal—about these features of their
work lives.

As this critical awareness emerges, reformers and teacher educators, and teachers
as well, face a powerfirl issue in their efforts to foster and support new collegial relations
in the name of professional development: the norms of interaction—~ways of being—called
for in reformed professional development activities, those guided by theories of social
constructivism are diametrically opposed to the norms of interaction in the traditional
culture of teaching. Several researchers have described and analyzed the problem of fit
between the reforms and the cultures of schools (e. g., Little, 1982; Lieberman, 1988;
Liston & Zeichner, 1990; Hargreaves, 1992). Many of these analysts take as their
starting point the organizational features of schools and teaching culture. In contrast, I
think this study takes as a starting point innovative forms of professional interactions
among teachers grounded in principles of learning. That is, principles that emphasize the
importance of making explicit one's understanding and one's uncertainties about the
practice of teaching and drawing on the richness of multiple perspectives as a resource for
continued learning (Cohen, Talbert, and McLaughlin, 1993).

Teachers committed to enacting current reforms in the existing culture of teaching
experience the problem of non-interference with the personal preferences of colleagues as

an unresolvable tension. They struggle to balance a sense of belonging to the local culture

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of teaching with a conscious sense of becoming a teacher who raises questions of her own
practice, opens her practice to the scrutiny of others, and seeks collegial help in engaging

in inquiries and experimentations in teaching. A culture of teaching that reinforces norms
of privacy and sameness among its members presents a direct barrier to the teacher who

seeks a community of learners where differences can be educative.

Teaghers’ Conversations

A second challenge to the reform of teachers’ professional development is the
nature and purpose of teachers’ conversations. Anyone closely associated with teachers
and teaching has learned that teachers carry with them ready to share stories of life in the
classroom. Talk of classroom life, “teacher talk”, fills the stafiioom, the hallways, and the
comers of the school playground. The stories teachers tell are a familiar part of the
culture of a school; they describe everyday life in classrooms. A teacher's lengthy
description, her use of jargon, and her tone of storytelling pique our own scholastic
memories. And perhaps because we all share some experiences of schooling, classrooms,
teachers, and lessons, we listen and respond to teachers’ stories as a form of
entertainment. The connections to our own mischief as young students and clumsy
children, or our struggles as little scholars, are vividly recreated in a teacher's story of
yesterday’s events. In telling a story, a teacher knows she can touch memories, painfirl and
joyfirl, in ways that remind her that it is good to share these stories.

Yet it is this familiarity between the teacher storyteller and the most available

13

audience (e. g., fiiends and family) that seems to disqualify a teacher’s stories as subject
matter for her own analysis of teaching and learning. Relatedly, the mistaken belief that a
teacher‘s work is bounded by her interactions with children, between 8 am. a nd 3 pm,
makes it diflicult to appreciate talk of teaching outside of the classroom as a vital part of
their work. It is "just teacher talk.”

Contrastly, in the context of teacher education reform, teachers’ talk about life in
classrooms is recognized as a critical component of meaningful, sustained learning about
practicez. As reformers, we ask teachers to engage in collective thinking and problem
solving that necessarily draws on stories portraying messy events and real questions from
their real classrooms. We ask teachers (along with teacher educators and researchers) to
participate in forums that are fundamentally different from individual- and product-
oriented “make-it-take-it" workshops. With aspirations of creating new and meaningful
forms of professional development, we ask teachers to change long standing patterns of
communication with colleagues. Many reformers and teacher educators suggest this
change may best be supported through conversation, dialogue, and storytelling.

Through their study of narrative and its connections to teachers' stories,
educational researchers have provoked a wave of possibilities for new forms of teacher
education. Nationwide, teachers, together with researchers and teacher educators, are

beginning to experience a depth of inquiry into teaching and learning afforded by authentic

 

2 See Changing Minds, Spring, 1996: Teachers Helping Teachers, for an examination of five teachers’
groups where conversation, problem-solving, and long term support help to create carefirl, critical
communities of learners.

14

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storytelling and conversation; an inquiry that pushes beyond the surface difficulties of
learning new techniques. Teachers are learning to take seriously their own stories as ways
of exploring and understanding the complexity of teaching and learning in schools and the
embeddedness of professional issues in their full, complicated, developing lives as late
20th century women and men.

On the whole, educational researchers have come late to honor storytelling as a
powerful form of knowledge representation and a context for learning. Jerome Brunet,
noted developmental and cognitive psychologist, has been instrumental in bringing the
study of narrative in other disciplines to the work of educational researchers and teachers
interested in understanding narratives and how they contribute to learning. He has
theorized that we order our experience in one of two separate and distinct ways:

There are two modes of cognitive functioning, two modes of thought, each

providing distinctive ways of ordering experience, of constructing reality.

[These are: the narrative mode and the paradigmatic mode] The two

(though complementary) are irreducible to one another. . .. Each of the

ways of knowing, moreover, has operating principles of its own and its

own criteria of well forrnedness. They difi‘er radically in their procedures
for verification (Bruner, 1986 p.11).

D. Jean Clandinin and Michael Connelly are noted leaders in the tradition of
research on teachers' stories (Carter, 1993). Their program of research on teachers’
personal practical knowledge (Clandinin and Connelly, 1988; Clandinin , Davies, Hogan,
& Kennard, 1993; Clandinin, 1986; Connelly & Clandinin, 1985; 1988) provides a deeper

understanding of the ways teachers know teaching experientially. They argue that learning

15

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to teach and sustaining oneself in the work involves striving for narrative unity. For an
individual teacher, theory and practice cohere with the “images, rituals, habits, cycles,
routines, and rhythms” (1985, p. 195) they come to know through lived experiences.

Reform-oriented teacher groups support teachers as learners and encourage
storytelling as a way to situate their learning in daily practice. When telling stories in
authentic conversations about their practice and their lives as teachers, the storyteller and
the listener together create occasions for learning. Together, they enter what Harre (1984)
describes as the Vygotsky space. In this space, storyteller and listener create a social
interaction in which language mediates their sharing of experience and understanding.
Once shared publicly, the interaction becomes part of the private cognition each
participant carries into subsequent public and private iterations of thought, language,
action, and reflection. Movement through the public/private spaces of interaction is a
central concept of social constructivist theories of learning (Vygotsky, 1978; 1981;
Wertsch, 1990).

As a form of teachers' professional development we are only beginning to explore
what happens through and because of teachers' talking together about practice (Clandinin,
1986; McConaghy, 1991; Cavazos, 1994; Goatley, 1994; Florio-Ruane and deTar, 1995;
Swidler, 1995; Pfeifl’er and F eatherstone, 1996). But keep in mind, telling stories is not
new to teachers; it has long been a part of the culture of teaching. What is new is valuing
of teacher narrative and efforts to prompt and support teachers' use of stories in ways that

are educative. Telling stories to learn to teach is a new kind of work. Harold Rosen

16

(1989) commented that, "the educational world doesn’t [yet] accept that telling tales of
teaching as richly and honestly as we know how is a totally valid means of teaching each
other” (p. 164).

The personal stakes are high when a teacher offers an honest account of the
messiness and uncertainty in many of the tasks for which she is held accountable. In a self
study of her learning to teach mathematics differently, Ruth Heaton (1994) wrote about
the frustration she felt when she made visible to other teachers her understanding of the
complexity of her changing practice. Instead of joining her to grapple with hard questions
and issues of pedagogy, Heaton met with unsolicited advice and innuendoes about her
ability to teach:

I tried to initiate a conversation about changing practice around what I
thought were several difficult and complex mathematical and pedagogical
issues that I saw as key to teaching mathematics for understanding. Much
to my surprise, no one wanted to talk about the problems I encountered.
Everyone wanted to offer me solutions. One by one, those who had
listened to me unveil my problems ofi'ered me suggestions for what I
should have done differently. My problems were viewed as simple, the
solutions were seen as obvious.

My fellow educators wanted to be supportive but we viewed my teaching
difi‘erently. ..What I was concerned about could not be fixed by suggesting
that I try this or do that. No one but me seemed to see the teaching or the
mathematics I was trying to help students learn as inherently difiicult. At
the time, I could not understand what was happening. I fought back
feelings of inadequacy and frustration. Part of me felt badly for not
knowing, thinking that I should have known, while another part of me had
spent a year learning to appreciate the value of not knowing, of never being
certain, in a practice that was improvised. Why couldn’t these people see
the complexity I could? I feared I appeared to others as incompetent for
having questions about practice, the same questions that I have been
praised for recognizing and others had pondered with me...(p. 368).

17

Heaton’s experience and her stance as a learner were dismissed by colleagues who
favored instead a shared commitment to readily naming and fixing problems of practice.
Heaton’s efforts to engage in intellectual examination of the complexities of her teaching
were thwarted by the strength of other teachers’ advice giving about want she should do
to act like a teacher.

Engaging in teacher conversations as an active and focused form of professional
development work, honoring uncertainty and questions of pedagogy as opportunities
rather than incompetencies, and taking steps to challenge the traditional assumptions about
what makes teaching difficult, require that teachers stand in new relationship to each
other. As I believe this study will highlight, these new and different relationships must
serve two purposes concurrently: 1) they must be relationships in which teachers can learn
to engage in new forms of dialogue about their work, learning that requires new skills, a
strong sense of confidence and courage in the face of long standing norms of non-invasive
collegiality; and 2) these relationships must becoming self-sustaining in order to support
the continual change and reflection called for in the reform of continued professional
development. Burbules (1993) has noted the reflexive character of the dialogical relation:

To the extent that [dialogue] helps draw participants into such relations,

and the communicative interactions they support, it can promote actual

development of these relations, to the point where they do become self-

sustaining...we develop our capacities for creating and maintaining such a

relation only by being in it, and so must work with, and within, at least

some of the relations we have available to us. Waiting for ideal conditions

in which to pursue or express these values means that we will be waiting a
terribly long time. This bootstrapped process is the essential problematic

18

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of learning in and through dialogue. We teach our partners, they teach us,
and we each teach ourselves in the context of sustaining and developing the
dialogical relations we actually have. We improve by imitating, practicing
and experimenting in the midst of real-time activities (p.49).
Reform-oriented teachers need knowledge of the kind of conversations that
currently dominate their interactions, images of the kind of conversations that are
possible when teachers work in dialogic relation with each other, and skills to

engage a kind of conversation that offers opportunities to examine their work and

learn from their own experience and the experience of their colleagues.

fl 5 Lgrngr ang Self as Teachgr

A third challenge to teachers’ professional development is the relationship of a
teachers’ personal/professional identity to her continual learning and development as an
educators. Slowly, with false starts and little to no support, teachers engaged in projects
of education reform are beginning to develop new identities as teachers that stand in stark
contrast to the commonly held image of the classroom teacher. Teachers who envision, for
their students and for themselves, communities of learners guided by social constructivist
views of teaching and learning also envision substantial changes in the culture of their
profession and their identities as educators.

Learning to teach means, in part, exploring the question, what does it mean to say

‘I am a teacher?’ Responding to this question means developing a self image—a

19

conscious sense of self—as a teacher in the classroom. It also involves developing a self-
image as a member of the profession, figuring out where one belongs in relation to a range
of colleagues and associates. As I think this study shows, coming to know oneself in
practice can only take place in relation to others, through the creating and sustaining of
critically collegial relationships. Such relational work in teaching can contribute to
sustaining one's professional development in ways that are meaningfully situated in local
contexts and personal experiences.

Learning to teach also means learning to reason through, articulate, and act on
one's view of teaching. This work is a process of figuring out where one stands on issues
of practice (e.g., What is the place of effort grades in assessing a child's learning? How
should curriculum be created and for whom?) It is also a process of figuring out one's
multiple roles both in and out of the classroom, interacting with children and adults in the
school community. In the many forms it may take, this is a kind of intellectual work in
teaching that contributes to one’s on-going development of a stance toward teaching and a
conscious engagement with one's practice.

These conjectures about learning to teach: developing a sense of selfas a teacher
and learning to reason, articulate, and act on one’s view of teaching, mark for me a
changed in perspective on professional development. As a classroom teacher I believed
that professional development was getting smarter about subject matter. Certainly it was
about learning new instructional strategies, about learning to design, develop, and enact

curricula, and about learning to measure student progress. I believed that ifI was

20

acquiring knowledge and skills in these areas, then I was developing as a teacher. I still
believe that these are important elements of professional development. But I have learned
from my work in this study that fundamental to this knowledge and skill development is
the psychological and social development of a teacher's identity—one’s view or stance
toward teaching and one's relationship with other teachers.

A third conjecture about learning to teach in the context of reform involves
developing strategies for managing the tension that can arise between the intellectual work
of reform-oriented teaching and the relational work of belonging to a culture of teaching.
In addition to learning more and different subject matter and fundamentally difl‘erent
approaches to pedagogy, teachers must also learn to recognize moves, muster resources,
and develop social and psychological tools for managing the predicaments that arise from
engaging in the critical examination of practice while participating in the current culture of
teaching. This kind of learning includes helping teachers to identify themselves as
intellectuals and to view their continued learning and development as an explicit part of
their work as teachers. It also includes helping teachers sustain an awareness that an
identity as a teacher intellectual is a dramatic shift in the prevailing images of teachers in
most schools. Moreover, they will need to work to establish the descriptor as a legitimate
view of teachers and teaching. A decade ago, Giroux (1988) argued that a way to
reconceive the nature of teacher work is to view teachers as transforrnative intellectuals.

He wrote:

21

The category of intellectual is helpful in a number of ways. First, it
provides a theoretical basis for examining teacher work as a form of
intellectual labor, as opposed to defining it is purely instrumental or
technical terms. Second, it clarifies the kinds of ideological and practical
conditions necessary for teachers to function as intellectuals. Third, it
helps to make clear the role teachers play in producing and legitimating
various political, economic and social interests through the pedagogies they
endorse and utilize (p. 125).

The concept of teacher intellectual has a powerful link to the vision held and

described in the reform documents. Teachers, living and working as intellectuals, are

teachers who fully embrace a stance and a commitment to the calls, the questions, and the

hard work of educational change; they are reform-oriented teachers.

Becoming A Reform-Oriented Teacher

There is a growing awareness among researchers, teacher educators, and
classroom teachers themselves that it is no longer acceptable to believe that professional
growth is gained from the disjointed, isolated activities, and packets of prescribed
information that are given to teachers to tell them what teaching is and how it should be
performed. Teachers know a lot about what they do. They know a lot about creating
environments and activities that help students learn. They also know that there is more to
be learned about teaching. Critical to their work as teachers is their direct involvement in

creating their own continuing education, individually and collectively, about what it means

22

to teach and to learn in classrooms. The challenge is to find ways to help teachers develop
the knowledge and skill needed to be more active participants in the on-going and
integrated design of their own professional development in the practice of teaching. The
challenge is to find ways to help teachers become reform-oriented professionals engaged

in the complex work of educational change.

T ch r flecti n or! Learnin f Pra ice

Researchers suggests that the work of classroom teachers is strongly influenced by
what they think; how they think; and when they think about their practice. Their work is
based on ”thoughtful and systematic (though often implicit) notions about students,
subject matter, teaching environments, and the teaching process itself“ (Y inger 1986).
Many reformers believe that the power of professional development in teaching is in
helping teachers to make these implicit beliefs explicit and to see the relationship between
their own beliefs about teaching and learning and the impact of those beliefs on their
interactions with students in the classroom (Calderhead, 1993; Larnpert & Ball, 1990;
Fullan & Hargreaves, 1992; Louden, 1991; Schon, 1991; Witherell & Noddings, 1991).

Becoming a reform-oriented teacher, as I have described here to include
knowledge of the culture of teaching, of teacher interactions, and of self as teacher,
necessarily calls on a teachers’ capacity to reflect on the particulars of all aspects of her

practice. The term reflection is often used in describing how teachers might interact with

23

their cognitions about teaching and learning. Donald Schon (1987) has examined
reflective capacities in the performance of professionals (e.g. architects, lawyers, and
artists) and he claims the perception that professionals conduct their work based on a
concept of technical rationality is not accurate. He explains:
Technical rationality holds that practitioners are instrumental problem solvers who
select technical means best suited to particular purposes. Rigorous professional
practitioners solve well-formed instrumental problems by applying theory and
technique derived from systematic, preferably scientific knowledge (p. 3).

Schon argues that real-world situations do not present themselves in such
systematic ways. Rather, they appear as “messy, indeterminate situations” (Schon, 1987,
p. 3) that require the practitioner to draw on various sources of knowledge and to
creatively use that knowledge to construct new understanding about a given situation.
This is an accurate description of the complex interactions that occur in every school
classroom. Teachers are constantly engaged in interpreting, analyzing and evaluating
multiple phenomena, while at the same time, they are carrying out a variety of tasks.

Often, when asked about their work, teachers cannot explain to someone else how
and why they perform as they do. Schon refers to this inability to verbally explain what is
revealed in intelligent action as “knowing-in-action.” The knowing is embedded in the
action and when the action is broken down for verbal description it is no longer an
accurate account. However, Schon explains that it is sometimes possible for practitioners

to reveal the tacit knowledge underlying their actions through observation and reflection

on those actions. Their accounts will vary depending on the purpose for their reflecting

24

and the language they have for verbalizing the description (Schon, 1987).

Another distinction, important to developing new lenses for professional learning
and development for teachers, is that between reflection-in-action and reflection-on-
action. Reflection-on-action involves thinking back on what has already occurred to make
sense of the influences that guided the action. This thinking occurs when a practitioner‘s
knowing-in-action fails; when some interruption has kept the practitioner from performing
in the automatic manner that was anticipated. At other times, it is possible to reflect on
one's knowing-in-action and to make adjustments to the action without interrupting the
task performance. Schon refers to this as reflection-in-action and describes the process as
a reflective conversation that practitioners have with the situation, deriving new meanings
and determining new steps (Schon, 1987).

Schon points out that, “Clearly, it is one thing to be able to reflect-in-action and
quite another to be able to reflect on our reflection-in-action so as to produce a good
verbal description of it; and it is still another thing to be able to reflect on the resulting
description.”

These concepts of reflection seem to map onto a teachers’ classroom practice in
straight-forward and helpful ways. It is helpful to think about a teacher talking through
her reasoning for changing instructions to the whole group or adapting an explanation for
a particular student. In reflective conversation with the situation in the classroom, a
teacher draws on her knowledge of the subject matter, the particular learner or learners

and the goals she has for the activity at hand to guide her --to know-in-action-- how she

25

wants the interactions to proceed. Layers of reflection: reflecting on our reflection-in-
action and reflecting on the resulting description can all help a teacher to construct and
reconstruct the sources of knowledge the teacher draws on in those messy, indeterminate
situations. What does the mapping look like for teachers’ practices outside of the
classroom? More specifically, what does reflection look like when a teacher is learning to
engage colleagues in critical conversations or raising diflicult questions about teaching and
learning, questions that rock the culture of sameness or threaten the safety of peer
relations?

When teachers ask questions about their work, investigate why they teach as they
do, and study the relationship of their interactions with students to their beliefs about
teaching and learning, they engage in a kind of professional development work that has
stronger potential to surround and support their actions in the classroom than many
traditional in-service interventions. In part this is because—in creating this interaction
between their own teaching and their own learning about teaching—teachers engage in
efforts to raise their own awareness of how they make sense of the multiple influences that
shape and bound their work.

Again, at the heart of this work are teachers' conversations and storytelling.
Teacher storytelling groups, collaborative research projects, and teacher study groups are
promising examples of professional development forums where teachers gather,
sometimes in company with university-based teacher educators and researchers, to learn

from articulating and interrogating their experience. In these forums, teacher talk is taken

26

 

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seriously; it is given space and time and respect as intellectual work. ‘Learning from
experience’ in this context is firndamentally different from the trial and error education in
many teachers' histories. It puts at the center of teachers’ learning the kind of intellectual
work I was beginning to sense in my early masters study experience, (See the Prologue),
with a crucial difference: teacher groups support learning in ways that are deeply
connected to life in teachers’ particular classrooms. Through teacher group work,
teachers are supported in making stronger links between the intellectual work they do in
and out of the classroom. And they find good company with likeminded colleagues who
share their aim of becoming reform-oriented teachers (Featherstone, Pfeiffer & Smith,

1993)

A Teagher and A Researcher Explore What’s Possible

For the past seven years, I have had the opportunity and privilege of working with
Lisa Pasek, a teacher committed to the unending challenge of learning to teach. In Lisa's
good company, I have explored some of what it takes for a teacher to support her
continued self-directed professional development; what helps and what hinders her
development as a practicing teacher in a period of intense educational reform.
Additionally, I have explored how my own learning as a researcher can both contribute to
and be served by a collaborating partnership.

In the spring, 1992, Lisa Pasek, a sixth grade teacher in a mid-size, Midwestern

27

school district invited me, a researcher with the National Center for Research on Teacher
Learning at Michigan State University, to help her document her mathematics teaching
with videotape during the coming year. Lisa and I met through the Investigating
Mathematics Teaching (IMT) group--a group of teachers from mid-Michigan and
university-based researchers who meet regularly to talk about the teachers’ efforts to
change the way they teach elementary and middle school mathematics. Lisa hoped the
tapes might inform her efforts to develop a discourse with her students in which they
explored multiple perspectives on mathematical problem-solving and looked to themselves
and to their peers as sources of support for their own learning. Lisa also hoped to use
videotapes of her teaching to talk with her faculty and administrators about her practice.

Lisa’s interests and concerns created an authentic context for me to explore some
of what it takes for a teacher to support her continued self-directed professional
development; what helps and what hinders her development as a practicing teacher in a
period of intense educational reform. Drawing on sociocultural theory (Vygotsky, 197 8;
M011, 1990; Wertsch, 1985) and ethnographic methods (Erickson, 1986; Hammersley, M.
and Atkinson, P. 1983; Erickson and Shultz, 1981) I pursued an investigation rooted in
the ongoing practice of a classroom teacher. The following question guided this research
project: What does a teacher learn from conversations around videotapes of her
teaching?

Additionally, I was interested in these questions: (2) What is the nature of the

discourse as a group of teachers and researchers respond to a teacher’s narrative around a

28

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35 7-2.1

videotape of her teaching? (3) What does a teacher learn about herself as a teacher by
reviewing videotapes of her practice in conversation with other educators? and (4) What is

the nature of our collaborative relationship in trying to support this work?

f ' u nt

My aim in this opening chapter has been to situate my work, my research interests
in general and this study in particular, in the current context of reform in education. I have
sketched a framework of three aspects of reform work in teacher professional
development, each of which is influenced by social constuctivist theories of learning. In
subsequent chapters, I will continue to explore this set of challenges to reform, drawing
specifically on the study of my work with Lisa Pasek, to articulate my own learning about
the challenge of becoming a reform-oriented teacher.

In Chapter Two, I introduce Lisa and our collaborative approach to this study. I
describe the ethnographic methods and sociolinguistic techniques that guided my
documentation and analysis of our work.

In three chapters that follow, I look closely at aspects of our work together. In
Chapter Three, Lisa shares her videotape with the IMT group and I examine the rights and
duties that surround her conversation with the group. In an analysis of Lisa’s reflections
on this experience, I learn about a shift of these rights and duties that supports the

emergence of a culture of critical colleagueship. In Chapter Four, Lisa and I spend time in

29

her classroom after school, re-viewing the videotape she shared with the IMT group and
segments of video fiom other mathematics classes. Our conversations, notes, and journals
document Lisa’s efforts to develop the conversational skills that will advance her sharing
videotape with other colleagues and her continual understanding of her mathematics
teaching with her students. In Chapter Five, I present a weaving of events that took place
in the spring our year together, a time during which Lisa explored a new inquiry situated
in her practice. This small investigation became a site for Lisa to make connections
between her experiences as a learner, a beginner teacher, and her envisioned identity as a
reform-oriented teacher. Together we learned about the impact of the reforms of school
instruction on a teacher’s personal/professional identity.

In Chapter Six, I draw on our experiences, our reflections and analyses, and the
theoretical constructs that have guided my study to discuss some of the learning that Lisa
was engaged in during this year of professional development work with the [MT group
811d with me. I describe the kinds of knowledge Lisa was constructing and using. I
sPeculate about what this study suggests might be needed for teachers to actively

Participate in substantive and sustained work in the current context of reform.

30

CHAPTER TWO

Lisa

I met Lisa in October, 1991, when she joined a teachers' group at the National
Center for Research on Teacher Learning (N CRTL) at Michigan State University. Lisa
and seven other elementary and middle school teachers agreed to participate in a project
organized as a masters level independent study called Investigating Mathematics Teaching
(IMT). From a research perspective, the aim of the project was to explore how practicing
teachers might use a set of materials that were being deve10ped for mathematics teacher
education.

What began as a course for credit and a pilot research study evolved into a
voluntary teachers' group that, seven years later, continues to meet regularly on the MSU
camms during the school year. In the IMT group, the teachers seek and provide social
and intellectual support for their efforts to change their mathematics teaching. While they
came to the group with different amounts of teaching experience (1 to 21 years), different
8Tade level responsibilities (first through seventh grades), and different opportunities and
constraints in their districts and communities, these teachers all share an interest in
developing a practice of mathematics teaching radically different fi'om their own

exPeliences as schoolchildren. They are looking for, giving, and getting help in making

their way.

31

I came to the first Thursday night meeting as a research assistant, interested in
experienced teachers' learning in the context of educational reform, and curious about how
new technologies (e.g., hypermedia, videotape) might support teachers' learning to teach
in new ways. For me, the project was a site for bringing together questions about
professional development that grew from my own intellectual hunger as a teacher, my
interest in the relationship between constructivist theories of learning and new
technologies, and my conviction about the importance of working with teachers in ways
integral to their lives in classrooms.

Lisa came that first evening at her academic advisor's suggestion that the IMT
project might be an interesting and helpfirl extension of her summer project: a study group
that read and discussed the NCTM Standards ( 1989; 1991). She was interested in finding
ways to stay connected to people and opportunities that would help her sustain a vision of
teaching she had only begun to grasp as she left her preservice program and entered the
field as a teacher.

In this first meeting and at most subsequent meetings of the fall term, 1991, we
spent part of our time together watching and discussing videotapes of Deborah Ball's third

gTade mathematics classroom3 . As the year progressed, the teachers in the group shifted

X

3 These videotapes were part of a collection of materials generated by Mathematics and Teaching Through
HYpermedia (M.A.T.H.). In the summer of 1989 The National Science Foundation funded the M.A.T.1-1.
Project permitting Deborah Ball, Magdalene Lampert, and colleagues to document the teaching and
1‘:inning in their classrooms. Over the course of the next academic year they videotaped many
mathematics lessons, as well as interviews with students, mathematicians, and mathematics educators.
saved and reproduced all student work including the math journals in which students wrote
evel'yming, homework and tests. A team of graduate students kept ficldnotes on the mathematical and
Pedagogical issues raised in each lesson, and reproduced the teaching journals. During the following two

32

their focus away from Deborah Ball, her students, and their problems of practice
represented on the tapes. They began to talk more about their own practices, their own
students, and their own questions. One of the ways my research colleagues and I
supported this shift was to spend time in the teachers' classrooms. For several teachers
this support included videotaping their math class and giving them the cassette to use as
they wished.

Getting to know Lisa in those early meetings, I was impressed by her confident
sense of selfas a learner. Still conscious of the feeling that my own professional learning
seemed to lie dormant and virtually untapped while I was a classroom teacher, I was
struck by this third year teacher’s active pursuit of colleagues who could help her. As she
introduced herself to the IMT group in the fall of 1991, Lisa tried to articulate her struggle
to develop a discourse-based classroom and how her perspective on teaching and learning
conflicted with that of her public school colleagues:

My name is Lisa Pasek and I was also in the teacher education program
here at MSU. My first year of teaching I was at a Montesorri school which
enabled me to really focus on math for understanding. It was really nice to
jump right in and get my feet wet and try everything I had come away with
from my undergraduate work. The next year I got a job teaching sixth
grade in a public school. And the veteran teachers there are saying, that
you need to give the right answer, period. I‘m thinking, “Oh, no, this is
horrible.” So, even though I live an hour and fifteen minutes away, I come
back here for support because even though there are teachers in Lake Port
that are changing, the process is slow and people don't understand that
you're not trying to [merely] change the activities, you're really trying to
change the whole way you‘re teaching and they don't understand that.
They think that it's just do an activity and then teach everything else. So,

\

Wits Ball and Larnpert worked with teams of graduate students to create videodiscs that would permit
We teachers outside of the college to explore some of these materials.

33

I've been working on developing discourse in my room and trying to get
the kids talking to each other about their mathematical ideas and not to me.

I‘ve been slapping myself in the face when I want to jump in all the time
(transcript 10-3-91).

Lisa's humor and animated descriptions, (e.g., “slapping myself in the face”)
became an expected feature of her talk in the group. The group learned to ready
themselves to listen to Lisa with an ear for her use of images and metaphors. Her
narratives would serve many firnctions, including lightening the burdens of struggle. Lisa
would frequently mix her comments about serious concerns with quips and comic relief.
Her introduction foreshadows this mix as she first conveys the urgency of her need for
collegial support and then lightens the description of her stnrggle to develop discourse
among her sixth graders.

As we took turns introducing ourselves that first Thursday night, each of the
teachers described her teaching position and something of her relationship to mathematics
as a subject matter. Several of the other teachers talked about fearing math or hating
math; Lisa talked about dealing with-~ideally, connecting with—her faculty colleagues.
She was still struggling to learn to teach math differently than she had experienced it as a
young student. She was still struggling to learn to create a mathematical discourse with
her sixth graders. But, from the start, Lisa made known to the IMT group her primary
need for support to “teach against the grain” (Cochran-Smith, 1991); that is, support as
She tried to teach math in a way quite different from and somewhat threatening to other

teachers at her elementary school.

34

Lisa's Story

A week after the first IMT meeting, I visited Lisa's three sixth grade mathematics
classes and interviewed her after school. On February 4, 1992, I videotaped her math
class for the first time. At the end of the school year, June 10, 1992, Lisa and I met on the
MSU campus for another long conversation about her teaching. Through these initial
one-on-one conversations, classroom visits, and the numerous Thursday IMT meetings, I
learned about Lisa's experience as a learner and as a beginning teacher. In what follows, I
have composed Lisa's Story, drawing on transcripts from our first year conversations
combined with her draft of a learning autobiography written for a masters class she
attended in Fall 1992. I merged parts of these texts and then gave the new text to Lisa for
further revision and editing. This account introduces the reader to Lisa as a learner, a

classroom teacher, and a member of the IMT group.

Learning about Oneself:
If I’m going to figure out where I’m heading,
I need to figure out where I’m coming from...

Lisa Pasek

While heading into teaching, and now, in the still early years of my career, a
(hitting motivation of mine has been a passionate determination to avoid ‘falling into a
RU T. ” The scariest part of this vague goal is that ruts are never well-marked so that you
"light easily avoid them, and actually, they seem to feel quite comfortable and secure

While you ’re in them. In fact, people often remark that they never even lmew they were Ln

35

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a rut until they got out of it. “Whew! ” they sigh. It also seems impossible to predict who
might be next. Sometimes I hear teachers who I think to be the most energetic and
creative teachers I know complain of feeling in a rut! That makes me wonder if one
person ’s rut is mother person ’s wonderful, refieshing revelation? And if that ’s true,
then maybe we need to admit that a rut comes from inside. And so, this is my driving
passion—or apprehension. But where does it come fiom and why does it haunt me so?

Usually when I think about the influences on my teaching, I think primarily of my

university experiences at Michigan State. These experiences have been unique, out of the
ordinary experiences. I have been blessed to have worked with some incredible people
and innovative programs. In the past few weeks, however, I ’ve been thinking that if these
university experiences stick out in my mind as such critical turning points, I must have

been turning away from something...or towards a new alternative? So, a look at who I
was before these critical events:

Morn ’s Little Angel

An only child for seven wonderfirl years, and then the older sister of three
brothers, I was a “second mom ” by the age of twelve. During that year, I received a
Special badge from my girl scout leader, a friend of my mother ’s. This sensitive scout
leader had recognized that my lack of badge earning was an eflect of filling in, as best I
could for a mom who had recently gone back to work. This badge was an appreciated
award for a dutrfitl daughter.

Schooled in a traditional Catholic school for eight years, my favorite class was
English; sentence after sentence, in my best handwriting, underlining the subject once,
Predicate twice. High school was equally cut and dry as I carefirlly did my best to
(”gauze and memorize. The most positive benefit from my school experiences was a
sense of belonging and of being supported; by my family, by my classmates of eight
years, and by the diversity of friends I enjoyed in high school.

The College OfBusiness Welcomes You!

I enrolled at MS U with every intention of pursuing a degree in Personnel
Management. I wanted to go into the training and placement of employees. I was taking
business classes, but there was nothing that I was taking, as far as I could see, that would
891 me to that goal. Unfortunately, my business requirements of Statistics and Calculus

36

lacked people. I was getting really frustrated and began playing around with the idea of
going into teaching. By winter term I was hearing the echoes of a high school
government teacher who had encouraged us, as seniors, to reconsider the teaching field
as a rewarding option. I thought that placing people—interviewing and placing people in
roles that are good for them-4s a lot like teaching, so I decided to switch to education
and it was like a tremendous weight had been lifted off me. I felt like I had truly found
my niche; I felt like I belonged there.

I began as a language arts major and that is my first love. I got about halfway
through and I had taken a couple of math methods courses. Through high school, I had
always struggled a little bit, but worked hard enough to get As and BS. 1 depended on the
teachers who would give you a second chance at the test and I worked really hard to
memorize and get through each test. When I got to State, the math classes there were
with foreign teaching assistants. I was failing math. I got my first zero point in Math
108 and it was just devastating. But I did have these math courses that would apply to
teaching and I wanted to go for language arts.

The Allure 0f Whole Language

The oldest of my younger brothers was diagnosed with a learning disability. 1
saw the tears and heartache caused by his having trouble with reading. In my sophomore
year, I did an honors project on whole language as a result of following up on a
reference to this alternative philosophy mentioned by one of my English professors. At
the same time, I was working in a first grade classroom with a mentor teacher, as part of
my teacher preparation program. My mentor was experimenting with components of
Whole language. We talked enthusiastically and openly about how her own teaching had
evolved as a result of working with researchers from MS U who had asked her only to talk
’0 them as she reflected on her teaching without any sort of evaluation or direct
intervention fiom them in her classroom. It was here that I became very interested in
leacher decision making. How do teachers make decisions about what they do? Upon
What do they base their decisions? How can talking about your own thinking, in turn,
Change it so radically?

During my senior year, I engaged in an independent stuay with an MS U professor
071d a local second grade teacher. It was here that I _ first felt the power of whole
language. I experienced the empowerment of 7-year-olds. The teacher had offered some

37

questions that I might ask the students about the books that they were choosing to read
for 45 minutes. Imagine my wonder when I asked a second grader why she chose a
particular book to read and the young miss responded, “Oh, it ’s by one of my favorite
authors! Here, let me read this part to you... ” The valuing of learners and of their

opinions and ideas made this classroom much more alive and rewarding that anything I
had ever experienced

"And why do you think that?"
A Redninking (J Math, A Rethinking of Thinking
As part of my teacher preparation program, I was involved in a research project

which required me to take a series of extra math courses, including one for which I had
already met the requirements. Needless to say, I was fiarious. Math was my least
favorite subject, and it was unfair, I thought, to introduce new requirements now that I
was already in the program. This series of classes was part of a study intervening in
teaching teachers to teach mathematics. Not to be melodramatic, but it changed the
course of my life. If they hadn ’t told me we were retaking the same course I ’d had the
year before, I never would have recognized it as the same course. The first time I had
taken math methods, we “did” patterns. We did activities, but it was always, “Do this
aCtivity or exercise long enough so that you can memorize the pattern” Then on the test,
you had to have the pattern memorized so you could extend it. When we took these
Classes over, I didn ’t even recognize the class until I went back through some of my old
"ates. This new coursework, to a large extent, completely retaught mathematics to me.
NOW, I could begin to see mathematics as sense-making. Operations had meaning and
reasons behind them, and I could discover these reasons for myself! The format of the
Class valued reasoning, communicating your own ideas, valuing diflerent ideas and
Strategies, making decisions based on mathematical sense, and building confidence in
your own thinking.

Perhaps just as crucial as this experience of my rethinking math was the
Opportunity to rethink my thinking. I was selected to be part of the “intensive study ”
e"wedded in this program. A small number of us, six or eight, were interviewed in depth
each term. The researchers would interview us at the beginning and at the end of each
term, We would fill out a survey, the exact same survey each time. They were watching
how our answers changed over time. They asked us to talk about our responses to

38

 

questions and to talk about our teaching as that came into play. The question, “And why
do you think that? ” to this day guides me in reflecting on my own thinking. Those
experiences really helped me to reflect on what I was getting out of those courses and
made me realize how I was changing. I remember when they first interviewed me, one of
the first questions was, “What are the parts of mathematics? ” The most I could tell her
was, “Well, there is adding, subtracting. ” I had no idea what she was talking about. I
said, “Algebra and Geometry; there is Trig and Calc and that's all I can tell you. ”

It wasn't until quite a few interviews later that I was starting to see how geometry
is related to numbers and I was starting to get a picture in my head about what
triathematics is about. Before, I just could see textbook covers and had no mental

picture. Being part of the research project helped me to get the most out of the course.

7711’s opportunity taught me about reflecting and about personally valuing my own
perspective; my way of looking at things. This was incredibly empowering for me as a
leaner. I had thought about how to empower kids, but feeling this empowerment for
noiself was difl‘erent. These experiences enabled me to begin to pull together my ideas

about, “This is what I want, for myself and for my students. ”
After that, with all these extra math credits, plus the ones I had gotten from

business, I ended up being closer to a math [minor] than I was a language arts [minor].
Ifllt that I was a living example that anyone can learn to think mathematically. So, I

thought that's what I should choose.

Making with Montessori
My first year of fill] time teaching, fresh out of college, was in a Montessori

*gchool directed by a professor in my teacher preparation program at MS U. This was a
Woizderful year in which I was encouraged and supported in my attempts to try out my
'a'ew ideas. The class size was about ten students to one teacher. It was a very workable
Situation. Because that school did not give out grades per se, it was the perfect
C2'lbptrrtunity to be able to talk with parents about what their children knew about

mathematics and what they didn't know, rather than having to narrow it into a single
(2 tier grade. I was given third and fourth grade. I taught multiplication andfractions,
Q11 sorts ofstufl that I really wanted to do. I had fiee rein there; I didn't have to worry

I 601“ someone saying, “What page are you on in the textbook? ” There was no textbook
It Was all teacher-created materials.

39

 

It was also my first opportunity to come up against people who would question or

challenge my ideas. This setting required me to continue to think hard about my
rationales in teaching. Having one of my professors there at the school, as support,
made it a natural transition fiom the university to “real life. ” During this time I was
introduced to Junior Great Books. This training provided me with a vision of where
thoughtful readers end up. This seemed to be a more sophisticated version of whole
language than exists at the primary levels, where students make decisions based on
evidence fiom the text and are empowered to feel that their opinions are valuable. This
literacy discourse would later help me think about similar sorts of conversations in my

mathematics classes.
The New Kid Gets Introduced to the “Real World”
In the fall of 1990, I began a "real job, " meaning job security, health benefits,
wad a more generous wage. It also meant coming face to face with “the system ” and
“the way we 've always done it. ” Here, the innovative ideas I thrived on in math and

mguage cats were viewed skeptically; as merely another swing in the proverbial
pettdulum. Theoretically, I was encouraged to use my professional judgement, but
realistically, I felt a great tension to conform and to “get those kids reaay ” for the

Smdardized tests. Being told “the kids need two dittos every night for practice, ”
seemed laughable, but it was a sincere expectation. Even as I attempted to stand my

gi‘omnd and argue that I disagreed the uncertainty often tugged at me, “Maybe I really
Cb): 't brow what I 'm doing. ”
I got married three weeks into the school year. This made my first year teaching

S i x1]; grade language arts to my homeroom students and mathematics to all three sixth
g7‘ade classes, to a large extent, a game of survival. But, as the year progressed I felt
Camdent that I was beginning to infuse my beliefs into my curriculum to move it toward
Witter I envisioned to be “my way of teaching. ” I felt like I did quite a good job my first
Jew, considering everything, and I felt that my teaching was truly reflecting goals I had
begun to form in college, while still pacrjying other stakeholders such as the other two
Six th grade teachers, my principal, and the personnel director who observed my class

(‘9 -
Ice.

40

 

Rebirth
During the summer after my first year in sixth grade, I returned to A/ISU to pursue

aMaster's degree in Curriculum and Teaching with an emphasis in mathematics. I
enrolled in a class that focused on the idea that learning is socially constructed I was
also participating in a six-person study group looking carefully at the Professional
Teaching Standards and at the Professional Curriculum Standards, published by the
National Council for Teachers of Mathematics. This combination brought me to one of
the ah-ha experiences that changes your life forever. Sitting and talking with other math
teachers about their classrooms, I was listening to one teacher explain how he “showed”
his students why this works and he “showed ” his students why that works and I sat there
feeling very uncomfortable with what he was saying. Slowly, a pit began to form in my
stomach as I thought about my “Innovative! Hands—on! Conceptual! Math class ” and
how I was manipulating every encounter with students' thinking about math! I realized I
was missing this huge piece, this huge component! I thought “I've been making it too
easy for them. ” Rather than give them a problem and have them work on it, I was saying
to nry students, “Here is the problem; do A, B, and C, and then tell me what you find
out. ” So, if they did A, B, and C, they'd all find out the same thing. I was showing them
how it worked not engaging them in discovery of it. 1 was explaining why patterns and
formulas worked not trusting them and valuing their ideas enough to let go and let them
02)) to figure it out; to construct for themselves as we construct meaning together. I had
been hanging on to my traditional ideas about control and direction, and stuffing them
into new wrappings. And nobody could have told me that... I had to hit it head on for

myselffor it to mean anything to me.

Learning in Good Company

As an oflshoot of that intimate group of six teachers, struggling heart and soul to
make sense of their ideas about what's important, I became part of a math study group; a
87"Oup of experienced teachers originally brought together as a research project that
would look at how teachers can use hypermedia to learn about their own practice. The
Group has evolved into a support group in which to vent, to brainstorm, to provide
e’ZC—‘ouragement. It has increased my sense of professionalism and has verified for me
tact any teacher willing to work hard at it can become incredibly insightful and smart
crbout what they do. The research project has evolved right along with the group. The

41

report title, “Learning in Good Company ” reflects our dual agendas of learning and
mutual support. The group provides honest, heartfelt compassion and inspiration, while
pushing us to ask hard sometimes uncomfortable questions.

My questions seem to center around my role in the classroom, and how my use of
discourse and inquiry helps students to gain power and direction in their own learning. I
have anecdotal records on my students in both language arts and math, and dialogue
journals I keep with my class. There are numerous other “pieces ” of my classroom that I
think can serve as windows to students' thinking.

Even the forms of assessment and opportunities for student feedback and
reflection provide valuable information as to how students are making sense and to what
extent they are “owning ” their own learning. For example, last year I was looking at
what kids wrote about what was helpful, what was not helpful. Several times I sat down
and went through their writing just making notes. Then I'd sit down a couple weeks later
and do it again to see if any other things come out. The time that I did this most recently
it hit me that a lot of things that they said are very helpful. They wrote about things that
they really liked-things that were different—not what we do routinely every day. A lot of
them wrote about the day we put together a three dimensional star. Reading this, I felt
fiustrated All this work I 'm putting into changing my teaching, I really believe in it, but
this is not a “make and take ” math class!

I tried to think about well, if this is bothering me what are some things that I
could do? I thought, remember when you were in sixth grade; what was fun and
important to you? I kept thinking, what are some ways that I can make a memory for
these kids because I was feeling frustrated that I wasn't doing the fun stuff that other
teachers are doing. Thinking back to my own grade school days, I didn't remember
sitting in science class, I remembered the field trips and the fun things. I kept asking
myself What am I going to do? I don 't want to be cutesy either! I don 't want to be
cutesy because then you spend all your time on that and don 't get to the meat of things.

The second time through their writing it hit me that they did realize that what we

had been doing every day was different, very different fiom what math was like for them
bqfore. When I went through their writing again, I saw that they listed these activities,
but then they also listed things like agreeing and disagreeing and discussing it and
explaining to other people. Even kids who were not the ones who were explaining at the
bow-d, wrote “I like the technique, “t-e-k-n-i-k-s! ” The lower ability kids mentioned they

42

 

liked the stars and they liked to explore calculators, but they also mentioned the
technique. And so, the first time I went through these comments I was surprised about all
of these cutesy things that I didn't give two thoughts to. The second time I went through,
though they really couldn't pinpoint the activity, I saw that they brew the format was
drflerent. I thought, that 's what they 're going to remember from sixth grade math. That
star is going to get crunched and it will probably never get home in one piece, but what
they'll remember is that this class is different and maybe it will affect them in the future.

The Roots of Desire
This desire I have for my students to be empowered and to have self-worth and
confidence, to feel like they contribute to the whole, seems to come from both what I
experienced (belonging) and from what I didn't experience (feeling valued as a
thoughtful learner). I suppose my ideal classroom is one where the lads have a chance to
think mathematically and have ownership of their ideas and feel empowered and in
control over deciding what makes sense and what doesn't. Even at the end of the school
year, I still had several kids who said “You never told us if we were right or wrong. "
And there were a few students who were really bothered For them, what makes
something valid should still be decided by the teacher because they think “we're not
smart enough to brow. " But most kids didn 't feel that way. I guess the ideal class would
be where everybody felt confident and trusted themselves to be able to make sense.
For myselfi right now, I think I 'm a really good math student because I think math

will make sense. That might be a blind faith, but I believe it should make sense and I
have the confidence that if it doesn't make sense I should be able to figure it out if I can
just backtrack and think about what I brow. That doesn't always happen, though. I have
a folder full of problems that I haven 't been able to connect with yet.

It would be nice to have kids come forward not so flown in fear that the answer they
write down is going to be the wrong one. Helping them shift their attitude toward seeing

problem solving as a process of successive approximations, checking, and proof would
help realize that ideal.

“I know now that I can 't do this alone. ”
There are many teachers who would sit here and think, “Why are you doing this? "
I (Dr: always running out the door at school saying, “Bye, I can 't talk today! I 've got my

43

 

class. " Other teachers will say, “You're sa'll taking that class? That is a long class! "
And I 'II explain “It 's a kind of study group, you brow, we get together and talk about our
teaching." They just say, “Oh. ”

Sometimes, my husband says, “A ren’t you done with that group yet? " I say, “No,
it is important for me to do this. " One of the things I have learned is the simple but
critical lesson: “I can 't do this alone. ”

A Teacher, A Researcher, And A Method Of Inquiry
In what follows I describe the methodological perspective and techniques that
guided this study. This description provides an overview of what Lisa and I wanted to

learn, why we wanted to pursue this inquiry and how we planned our work.

A of es ' us
Throughout my graduate studies, as I criss-crossed a territory of instructional
design, educational technology, consultation, and educational psychology, my web of
questions, born of my own experience in schools, has evolved. In what ways do teachers
16811! from their experience in the classroom? What do they learn? How is this knowledge
held and used in their work? How might they (and I) continue to grow as learning and
developing educators in the context of their own classrooms? How can technology help

“’ith this work?

44

 

When I began to plan for my doctoral dissertation, two goals were clear to me.
First, I wanted to pursue an inquiry rooted in the ongoing work of a classroom teacher.
While I hold a particular set of research questions about teacher learning and the use of
multimedia technology in support of professional development, I wanted the study to
emerge fi'om a teacher's queries about her practice. It was important to me that we find a
question that would firrther both the teacher's own learning about her practice and my
learning about how teachers learn from their experiences. In this sense, I knew that this
research project could be--should be-—a kind of intervention study, that engaging in the
study would have a constructive impact on the teacher's practice, as well as ofl‘er insight to
the field of educational research. Achieving this goal meant that I would probably need to
already know this teacher so that together we could frame an interesting research question
in the context of her practice.

I also wanted to design a study that involved the kind of work I plan to continue
doing as an educational researcher and a teacher educator. Specifically, I knew I wanted
to use the dissertation project as an opportunity to learn how to do a kind of educational
research, a kind of collaborative work that is called for in the literature that is neither easy
or obvious how to begin and sustain. I was aware that creating new roles for teachers and

researchers would be exciting and problematic. The study had to focus not just on the
Silbstantive topics of teacher learning; it had to also focus on learning more about the kind
0f interactional dynamics involved in working closely and mutually with teachersua topic I

didn't want to take as firlly understood.

45

 

My story, my hunger, and my questions eventually led me to the work that serves
as the basis for this dissertation about a teacher’s efi‘orts to engage in a new kind of
professional development strikingly different from more familiar forms of inservice

training.

Mgstering Resources

At the end of our final IMT meeting of our first year, I did not recognize in the
moment that Lisa's parting comments began the grounded inquiry for my research work.
As she was leaving the meeting, Lisa stopped to tell me that she had started thinking about
next school year and she was concerned by the warnings from other teachers in her
school: next year's sixth graders are a ‘Wd bunch.” Lisa said she was thinking that
videotaping her class and watching the tape would help her figure out how to deal with
this notorious group.

At the time of this brief conversation, I was pleased that Lisa wanted to pursue the
option of video documentation. In my mindset as a research assistant, her comments
suggested a commitment to the IMT research project and interesting possibilities for our
work at the NCRTL in the fall. I was excited about the opportunity to observe her class,
and I was curious about how videotaping might be helpful to her.

A month later, I came to recognize Lisa's comments and request for help with

Videotapes as an opportunity for my learning as a researcher. During June, 1992, with the

1131]) of lengthy conversations with my colleagues, I explored the multiple contexts and

46

 

issues embedded in the work of the IMT group. I was looking for connections and
questions in the service of my learning goals: to work with a classroom teacher in the
context of her ongoing practice and to learn about collaborative inquiry. In describing
some early interests, I remembered my parting conversation with Lisa and began to see her
prospective use of videotape as an authentic context for exploring the use of technologies

in support of professional development of experienced teachers.

Creating a Partnership

Over the summer, Lisa and I had a series of conversations in which we explored
the idea of working together during the school year. She was struggling with a question
about students who weren't key players in the mathematical discourse in class. In a class
where a premium is placed on talk—~—on the ability to express your ideas and the
confidence needed to offer ideas to peers—Lisa kept wondering, What do the silent ones
take from all this? How do the discussions influence their self-image as mathematicians?
The stage was set for a collaborative inquiry with mutual interests at its center.

Looking back, I understand that getting to know Lisa meant becoming a part of
the interconnected contexts that influence her sensemaking about teaching. It was
important for me to know her students, to have my own relationship with them in order to

hear Lisa's descriptions and be able to respond from my own knowledge of the child or
81’ Clip of children. I thought about my relationship with the students as being somewhere

between the in-depth personal connection Lisa has with them every school day and the

47

 

distant, polite manner of interaction many children have with adult professionals that move
in and out of their classroom. I wanted to be able to hear the children in ways helpful to
understanding Lisa's stories of events that would transpire when I wasn't there.

As I struggled to define and attend to my naturally fitting place on the “participant-
observer continuum” (Bogdan & Bilken, 1982) in Lisa’s classroom, I realized the same
was true in relation to her principal and faculty colleagues. When I listened to Lisa tell
stories in the IMT group I had a more connected way of listening because I had met her
principal and Melanie, the fifth grade teacher. I could create stronger images because I
was developing a relationship of my own, different from Lisa's, with these students, that
principal, those colleagues. As well, I was developing a feeling for Lisa's sense of her

relationships in this school community.

A Week of Videotajlng
Following my initial experiences with the children“, Lisa and I planned for our
initial focused conversation, a week of videotaping in her homeroom mathematics class,
and my part in helping her interview a small group of her students for Lisa's university
class project.
I videotaped the math class four days during the week of November 30‘”. I kept

my focus on recording the discourse among the students as they explored ways to

x

4111 November, 1992, I visited with the children in Lisa’s sixth-grade class. Together, Lisa and I
described our research project to them. Also, I accompanied the class on an all day field trip to the local

nature center.

48

represent and explain decimals. In talking with Lisa the week before there were at least
two concerns she was trying to keep in mind as she planned. She was ready to move on
fiom the topic of decimals, but was feeling uncertain about the students' understanding.
We spent a good deal of time after the Wednesday field trip trying to figure out what to
do next. Lisa was puzzled. She was thinking she wanted to move on from decimals; that
they had now worked with several models; that she felt that they had spent sufficient time
on it and many kids in the class seemd to have a handle on it. And yet, she still felt
unsettled. She was concerned about those who didn't seem confident in what they were
doing or did not have clear ways of explaining what they were doing. Lisa was hesitant.
It wasn't clear to her that she should move on. At the same time, it wasn’t clear to her

what she should do next. We generated a couple of options:

1) to continue with their discussion about number sentences equal to 1.019 (e. g., .500

+ .519 = 1.019) or

2) to do a comparison problem that gets at the concept that decimals are between 0

and 1 (e.g., 0.515 <, >, or = 0).

Lisa decided she wanted an assessment of what her students understood about
decimals. In addition to a mathematics assessment, she also wanted to pursue her broader

inquiry: Is this kind of teaching good for all students? What is the impact of this kind of

Classroom culture on the quiet ones?

49

3"

«A. l
v
‘2‘ I
W' .
l
0'...

Hit}

”W, ;
.1;

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l
in

v
9‘...

lump

M‘

‘4

“‘21:.

n i“

In planning the coming week, Lisa integrated these broader questions into the
students' continued work on decimals. She planned to have her students describe a math
class or a math routine from a year in the past—either the 5th, 4th, or 3rd grade. She
wanted them to recall and reflect on one of those years because they were then beginning
to do what she called “higher thinking” in mathematics. She planned a set of instructions
and questions to guide their autobiographical writing. They were to choose a math class
day from an earlier year and describe what the teacher did and what the students did. If
they couldn't remember a particular day, they were to describe the typical math leaming
routines in as much detail as possible. Also, each would describe himself or herself as a
math student back then: How would a classmate describe you? How would your teacher
describe you? Her intent was to ask a similar set of questions later in the week-—a parallel
set of questions about this year’s math class. When we talked about this on Wednesday,
Lisa explained that she wanted to have six target students whom she had identified for her
own project write about themselves as learners, but she was puzzling about how to do this
without pulling the six students out of the larger group and drawing unwanted attention to
them. I suggested that she have all the students do the writing as part of the school day.
She would get the writing from the six target students, but we would also get reflective
Writing fiom everyone else to permit looking for comparisons or patterns. Additionally,

everyone would feel part of the project with no singling out of the target students. Then

We hit on the idea of designing an interview with the target kids to get a deeper, richer

50

picture of their self images as math learners. We agreed that it would be helpful for me to
have these interview conversations with the six students. The students were coming to
know me and to see my presence as part of their year and they might be able to have safer
and perhaps more candid conversations with me than with their teacher directly.
Together, Lisa and I drafted a set of questions and scheduled these conversations to

follow my taping of their math class (see Figure 1).

  

' f ‘_ .Naveinber/Decemberlitfli = "

Initial interview Field trip to MLw'ng Holiday W4 ekend

 

 

 

 

 

 

 

 

 

 

 

24 with Lisa 25 nature center ‘
Videotaping in Videotaping in Videotaping in Videotaping in
Lisa‘s Math Lisa's Math Lisa‘s Math Lisa's Math
30 Class 1 Class 2 Class 3 C Ian 4
Viewing session
with Lisa after
7 l8 9 school 10 11
Viewing session IMT Meeting
with Lisa afier Lisa share her
14 school 15 '5 l7 videotape 18

 

 

 

Figure 1. Calendar of Early Events in the Project

Notes on the Week
I present here a set of brief field notes and an edited excerpt from my journal entry
for December 2, 1992. My aim is twofold: l) to provide an overview of the activities and
mathematical foci of the class during the week we gathered video records for Lisa to use,

and 2) to provide a sense of the kind of mathematical community Lisa was working to

51

foster, one that emphasizes student participation in shaping and constructing the
curriculum

Monday, November 30, 1992

Lisa opened the math class with a conversation in which she and I together
talked with the sixth graders about our ‘Video project” one more time. We
explained that I would be attending their math class all week and gave the
students an opportunity to ask questions of both of us. They had some
interesting questions about whether or not I was there to grade Mrs. Pasek
and when would they get to see the tapes. Lisa then moved the discussion
into the reflective writing activity we had discussed the week before. She
invited the students to “take a walk down memory lane” and to write about
a memory they have from one of their past math classes. Next, Lisa
directed the class back to the problem they began discussing last week,
before the Thanksgiving break: Make number sentences that equal 1.019,
but then she quickly changed direction. In introducing the class to Misty, a
new student who had arrived that morning, Lisa abandoned the math
problem and continued her inquiry into the children's perceptions of their
math class. She decided to use Misty's5 arrival as a natural opportunity for
the students to reflect collectively, for themselves and for her, on what their
math class is like and how they understand their participation in it.

Tuesday, December I, 1992

Picking up with yesterday's reflective writing activity, Lisa spent some time
listening to stories about math classes of the past which the students had
finished for homework. Reading aloud was voluntary. We heard fi'om an
even mix of boys and girls but, well into the sharing time, it was clear that
the stories we were hearing were all positive tales of experience. I noted in
my journal:

I wonder how hearing several students read success stories where they
viewed themselves as good math students and thought others (including
the teacher) viewed them as good in math might keep someone whose story
was not so successful from ever sharing their uncertainty and struggle in
math class? Did anyone write such a story?

After the stories, Lisa directed the class's attention to a claim that their
classmate, Mike, had posed to her before class. Playing around with his

\

5 All children’s names used are pseudonyms.

52

calculator, he tried to solve the problem 2.99 + ? = 3.000, without putting
a number in the thousandths place. “You can't do it!” announced Mike with
pride. What he kept failing to include in his announcement was that you
can't do it without using the thousandths place. Lisa made time and space
for Mike to share his exploration because she was excited about Mike's
independent investigation and she thought his thinking would provoke
discussion among his peers. Indeed, the students engaged in a lengthy
discussion about whether or not there could be one right answer to this
problem.

In the last part of the hour, Lisa asked the class if they had done all that
was interesting with the task of making number sentences equal to 1.019?
Two boys went to the board and generated a problem where both addends
were less than one, or as they explained, “no wholes”. Most of their
classmates seemed to know what they meant and agreed that no one had
yet generated such a problem. This led to a discussion about what happens
when you carry and you end up with a whole number. They thought it was
a difl‘erent and important idea.

Wednesday, December 2, 1992

Lisa and I had a brief conversation before the class started. She seemed
very excited about what she had seen in the videotape of Monday's
discussion." She was surprised by what she heard the students saying when
she revisited it. Specifically, she talked about Pedro's comments-crossing
out the 9s and making them IOs--it was now a bigger number—299--
>21010; it has more digits. At the time she thought that he was kidding;
how could he really think that? When she looked at the tape, it triggered a
response she wished she had made in conversation with him. She named
another example that suggested the same thing, that by going back and
looking again, she could hear differently or see more in what they were
saying which suggested other things she might have said back to them.

She was excited about watching the videotape. I asked her if she took
notes while she watched. My asking felt like a request and she squirmed
and said “Oh, well, no.” I heard myself say, “Well that's OK; I know we
are going to talk about it.” But actually, I do want her to take notes.
Thinking about it now, I need to specifically request that she keep notes as
she watches the tapes. In fact, I may email her to suggest just that. I do
think it is important that she take notes on this—that she record this, not

 

 

6 Lisa had watched the videotape of Monday’s mathematics class at home on her own.

53

only because of the “data collection” frenzy that I'm in but also because the
writing is a tool in her thinking and she can talk from that when we get
together. At the same time, I am constantly sensitive to how much I am
asking her to do. I need to trust a little more that it is going to require
some investment on her part and I need to push that and see how it goes.
She seems willing--motivated. I need to trust the interest she has
expressed in doing this work.

The students started to settle into the classroom and Lisa continued to talk
and describe what she was planning to do in class. She was going to let go
of the 1.019 problems and I acknowledged that fi'om her e-mail message
last night. I added that I liked the idea of the problem space she was going
to provide—where they could write additional problems and that I sensed
she was really ready to move on. She said yes, she wanted to do the 0 is <,
>, = .515—a problem she had given another class last week. This problem
had come up a couple of times as an option or next step and one I thought
would be really interesting. She had been interested in the conversation
with the first group she observed tackling this problem and so she was
curious about how this group might work. I readily told Lisa that I
thought is would be a good move. We had talked about such problem
forms earlier, agreeing that they might provide for a lot of rich discussion
that gets at their understanding of the relationship of decimals to 0 and 1.

Lisa started class by explaining how to use the large sheet of paper that
was hanging at the front of the room, that it was a place to write the
additional equations they had come up with = 1.019. She explained that
she wanted to get into something else but knew that there was always good
stuff that came later as kids continued to work with the math ideas and she
didn't want to loose any of that and they could use this as a place to record
their ideas and have classmates discuss them as they went along. It was a
nice way of acknowledging the work that they are doing and not calling a
premature stop to their thinking, but also pushing them forward and
redirecting where she wants the class to go. The kids seemed quite fine
with this and I even had the sense that they may have done this before or
something like it; they seemed familiar with it. One student raised her hand
and confirmed that they were to sign their name next to their equation and
Lisa said, “Yes, that is very important so that you know whose problem it
is and then you know who to go and talk to about the problem.”

With that established, she announced that she wanted to give them a new

problem and she set the context by explaining that a problem had come up
in a quiz from a class last year. She said that she was so interested in the

54

way last year's class had worked on the problem—the controversy that it
raised and the discussions that they had—and she was curious about what
this class might think about the problem and whether they too would have
a debate. So she wrote on the board <,>,= and explained that it was this
section of the test that had the problem:

0 .515

She said they needed to decide which symbol, <, >, or =, to put in the
blank space. At that point she asked them to first write in their own math
journal what they thought, what their argument would be for the answer
and then they would come together as a whole class and discuss it. After
about 5 minutes of very quiet writing time, the students began to talk to
each other. Mike and Susan, two bright and talkative leaders in the class,
were figuring it out for themselves, using a number line. Once they quickly
got a handle on it—and I would be interested in looking at the shorthand
they were working with (their language)—they then turned to explain it to
Shari who was just a half step behind them. She was working on her own
number line in her own notebook but needed more time and some
repeating. They also turned to Doug, the fourth person at the table, who
was pretty disconnected and didn't have anything on his paper; he was
looking all around the room at what else was going on. Mike was very
good about drawing him in and saying, “OK, now draw a number line.”
He was telling him exactly what to put on his paper. It struck me that
Doug was having a very diflicult time attending to the discussion that Mike
was trying to have with him.

It wasn't too long alter that when Lisa asked for volunteers to start the
discussion at the board and others to present some of their ideas. Someone
explained that .515 is something so it has to be greater that O which is
nothing. The student said it in a confirsed way and Lisa asked for someone
else to explain what he meant. A boy repeated it and tried to clarify it and
then Lisa asks for a model: “Is there anyone who used a model to show
what they are talking about?" At that point, Susan and Mike went to the
board and began to draw their number line which I had watched them draw
in the small group. Susan dramatically and emphatically explained to the
class what Mike is drawing...

55

I include this excerpt from my journal entry for December 2, 1992, in part because
the activity of this class became the focus Lisa's conversation when she first shared a
videotape of her classroom in a subsequent IMT group meeting. It is important to note
that the journal reflects a different kind of teacher-student and student-student interaction
than is typical in most elementary math lessons in American public schools. Still, there
were dramatic individual differences among the children in how apparently engaged they
were in the discourse opportunities that they pursued or let pass, and in the roles they
occupied-from math tutor, to graphic artist, to “explainer” to the class, to silent partner.

In the next section, I describe how Lisa and I explored questions about her use of
the videotapes to study the discourse in her mathematics class, her role with the students,

and her understanding of her own pedagogy. I connect our exploration to the

ethnographic theories and methods that guided our work.

 

I borrow directly from Max Van Manen (1990) the phrases: Investigating
Experience as We Live It, Gathering the Material of Lived Experience, and Reflecting on
the Materials of Lived Experience as a frame for talking about data collection and
analysis in this study. Van Manen's writing has helped me to think deeply about the way
the language we use to describe research methods is rooted in an experimental tradition--
with the lives of both subjects and research analysts separated from the focus of the

question. Vygotsky's (1986) teaching about the powerful relationship between thought

56

and language urges me to pursue new language for the way I think about my work.
Lakoff and Johnson (1980) teach me about the power of metaphor in shaping our
conceptual understanding. Was I "collecting" bits of information from Lisa or even with
Lisa? Struggling with this language is not just interesting; it seems necessary to continue
learning a practice that is fundamentally difl‘erent from traditional research on teaching.
The language I use is not just important for representing my ideas to others, it is
fundamental to the development of my own understanding.

It seems more fitting to describe what I did in conducting this study as gathering
materials of our lived experience. We generated and gathered together representations of
our conversations, our individual reflections, our interactions with each other and related
groups. And while still gathering, we reflected on these materials to make sense of our
experience and to connect it to our understandings of ideas as well as others'
understanding and representations.

Jean Clandinin and Michael Connelly have also contributed to my thinking about
aquiring another discourse for describing this work. For example, in their chapter in the
Handbook on Qualitative Research (Lincoln & Denzin, 1994), Personal Experience
Methods, they describe data as "field texts":

They are texts created by participants and researchers to represent aspects

of field experience. Some documents that eventually became field text may

have been created prior to the inquiry, or even during the inquiry but for a

different purpose. Such documents became field texts when they became

relevant to the inquiry...How we get from field to field texts is a critical

matter in personal experience methods. Central to the creation of field
texts is the relationship of researcher to participant.

57

Gathering the Materials of Lived Experience

Grounded in the stance that researching experience means at once living and
studying the questions of an inquiry, the primary materials of this study are the
conversations I had with Lisa. This work included conversations about first-hand
experiences (e.g., conversations about issues in our respective practices of teaching and
research; conversations stimulated by videotape representations of Lisa's classroom).
Other conversations were more reflective in nature (e. g., looking back at the experience of
watching tape or sharing it with others; revisiting conversations we each had with other
colleagues). In addition to conversation, our inquiry took the form of various written
materials: journals, notes, conceptual memos, and course and conference papers. A third
category of materials is videotapes: eleven videotapes of Lisa's classroom, three tapes of
our reflective conversations, and one tape of our talking about our work in a preservice
education seminar.

It does not seem feasible or productive to attempt a listing of the conversations I
have had with Lisa over the course of this project. The number is large but, more
importantly, it would reduce the strong sense in which our work can be characterized as
an ongoing conversation in the context of living the inquiry. Instead, I think it is
important to organize and reflect on the various settings in which Lisa and I talked
together and the kinds of conversations in which we were engaged across the year. Our

conversations took place in three general contexts: planned meetings, telephone

58

conversations, electronic mail conversations. The purposes of these conversations can be
distinguished as preparatory or investigative and reflective, although almost every
conversation involved each.

In addition to numerous conversations, Lisa and I had many opportunities to
observe each other in a range of professional settings. How we presented ourselves to
others in the presence of one another was a source of information about our relationship,
not only for the work of the relationship, but also our sensemaking about our collaborative
work. Hammersley and Atkinson (1983) caution ethnographers about the influence of the
researchers presence on participant's unsolicited accounts and importance of considering
the audience to which statements are offered. The reciprocity of this influence is
important as well. I found it helpful to attend to the various ways Lisa described her
practice and our work to others when I was with her. The occasions, for example, when
she explained to an MSU undergraduate in a class session we visited or to a mother
volunteering in her classroom, that we were working together to learn about the discourse
in her mathematics class, reassured me that we shared, at some level, the qualitative
research goal: to understand (Bogdan & Bilken, 1982). I was always wary that the goal
of judgement, a commonly held perception of research and a traditional purpose for
classroom observation, was influencing my interactions with Lisa. Therefore, I would
listen particularly closely to her descriptions and be as explicit with her as seemed
authentic about my worries. I often used the image of us each as learners: one a learner of

mathematics teaching, the other of qualitative research, to counter any concerns about my

59

judging or assessing her competence as a teacher. And this is where the reciprocity I
mentioned above is important.

I believe Lisa continued to learn about my understanding of our experience when I
spoke about it in more “public” settings. I had several opportunities to present our work
in progress at national and international conferences.7 For each presentation, Lisa and I
met to review and discuss the ideas and the data I would be sharing. In these preparatory
meetings, I would share my academic and personal thinking about the importance of the
ideas and the purposes of our collaborative work. During such a meeting, in preparation
for my presentation at the urban ethnography forum at the University of Pennsylvania, in
particular, Lisa commented that she was gaining a deeper understanding of the links
between my own history as a classroom teacher and the questions we were pursuing in the
study.

I observed, early on, that Lisa and I both avoided detailed conversations about our
collaborations in the context of the [MT meetings. Our perception, which we only
discovered we shared upon reflection, was that it may have violated the unspoken norms
within the group for sharing of the resources of the group. Over time, I gained an
understanding of Lisa's characterization of our relationship to other educators outside the
IMT group. On separate occasions, Lisa introduced me to her principal and a district

administrator, to fellow teachers at her school, and to colleagues in her masters program.

 

7 My earliest presentation was in a data analysis session at the annual meeting of the Urban Ethnography
Forum at the University of Pennsylvania, 1993. I also presented our early work at the meeting of the
International Study Association on Teacher Thinking in Goteberg, Sweden, 1993. Lisa and I presented
our work together at the annual meeting of the American Educational Research Association, Atlanta,
1994.

60

Only in the instance of meeting her administrators did she introduce me as a researcher. In
all other occasions, I was “a fiiend from MSU.” As an aside in a conversation the summer
following our year together, Lisa explained that she consciously avoids telling people that
I am a researcher or that what we are doing is a research study, because such vocabulary
carries “baggage” that I am “studying her” and distorts the purposes of our work as we
understand them.

It is clear to me that my work with Lisa in this study is a beginning example of the
kind of collaboration called for in the reforms of educational research and the work I to
which I aspire as a researcher. We both took seriously the complexity of a
participant/observer role—herein lies our collaboration—enabling us both to engage, for

distinct purposes, in researching lived experience (Van Manen, 1990).

Reflecting on the Materials of Lived Experience
The most difficult aspect of this work for me, both personally and professionally,
has been the messiness of it all. No matter how many accounts by other human science
researchers I read, from descriptions of their own studies to methodological guidelines,
the work has felt uncomfortable and uncertain to live it. Early in the study, I read
numerous narrative accounts of experience (e. g. Freedman, 1984; Rose, 1990; Grant,
1989; Paley, 1992; McConaghy, 1990). In addition to the core references that introduced

me to the theory and method of qualitative work, I sought out researchers conducting and

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reflecting on qualitative techniques (Lincoln and Denzin, 1994; Krieger, 1991; Clandinin
& Connelly, 1988 ;Polkinghorne, 1988', Van Manen, 1990).

A key device in my effort to study, understand, and represent my work has been
the book outline. My numerous attempts at outlining a book, or narrative account of my
year with Lisa, was the primary structure by which I framed my working assertions and
also revised them continually throughout the study. The movement from the outline to the
text to the materials and back to the outline again is a continual process, reflective of the
iterative nature of analysis in qualitative work (Bogdan & Biklen, 1982; Hammersley and
Atkinson, 1983). There comes a sense of change and maturity of the work through this
recursive process. It is interesting and perhaps helpful to think about this movement as
similar to the way we lived our experience: deeply immersed in the activity and then
stepping back or to the side, sometimes just briefly, sometimes for days, to assess and
make sense of “what the parts have in common” (Bateson, 1990, p. 15).

My iterative working from materials to outline to text and back again focused
largely on the use of audiotapes, transcripts, and journals to support or disconfirrn and
“triangulate” (Gordon, 1980) the inferences generated in my study of the experience.
Reflecting on this process made visible a triangulation of materials, as well as a use of
“methodological triangulation” (Erlandson, et a1. 1993). As an example of triangulation
of materials, in Chapter Three to follow, I draw heavily on the audiotape/transcript of

Lisa’s sharing of tape in an IMT meeting, the audiotape of our telephone conversation

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following the meeting, my field texts, and Lisa’s journal to pursue multiple reflections on
the experience and inform my research question. As an instance of methodological
triangulation, I point to the analysis presented in Chapter Five. This work shows my
continued study of audiotape documentation of MT meetings in which Lisa examined her
practice, together with her own documentation of her understanding in her journal, and my
participation in her classroom, triangulated with conversations with another IMT member
and follow up interviews with Lisa about my working assertions.

Additionally, Chapter Five presents analysis that approaches “theoretical
triangulation” (Erlandson et al., 1993). Because the data materials surrounding the IMT
meeting in which Lisa shared a videotape of her teaching are central to this study, they
have been reviewed multiple times, through distinctly different theoretical lenses. In an
early stage of my study, I examined the materials of the December 17“I IMT meeting in
terms of the relational issues influencing the interactions between and among Lisa and the
[MT members. The thematic framework that emerged from this analysis was informed by
feminist theory and conceptual work on the aspects of safety, trust, and care in teachers’
collegial relations (Belenky, Clinchy, Goldberger, & Tarule, 1993; Rogers, 1992;
Noddings, 1984; Coles, 1989; Clandinin et a], 1993; Giddens, 1990).

This same set of materials was studied from a sociolinguistic perspective, guided
by the question, what is happening in the conversation on December 17‘”? Drawing on
the work of (Gofl'man, 1959; 1967; Gumperz, 1982; Coultard, 1992; Tannen, 1989)I

analyzed the conversational rights and duties that directed the group’s interactions around

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Lisa’s videotape of practice. These analyses, triangulated with my analysis of Lisa’s
reflections, a study of the materials as a reflection-on-reflection-in-action (Schon, 1987;

1991) constitutes a convergence of ideas resulting in this thesis.

Inmetation as Conversation

I want to underscore the influence of several authentic occasions for reflection and
sensemaking on my learning of qualitiative research work. I will describe my experience
with and valuing of conversations about my inquiry with a range of conversational
partners. Just as Lisa and the IMT teachers have tried to articulate the "intellectual work"
in talking about their practices with colleagues, much of the interpretive work I did in this
study took place in conversation. About collaborative analysis, Van Manen writes:

Whether formal or informal, what one seeks in a conversational relation
with others is a common orientation to the notion or the phenomenon that
one is studying. Gadamer (1975) describes the method of a conversational
relation as “the art of testing” (p.330). And the art of testing consists in
the art of questioning—meaning “to lay open, to place in the open” the
subject matter of the conversation. And so the collaborative activity of
discussing and testing a research text should not be a situation wherein the
discussants of the text try to outwit the author or the other partners of the
discussion group by polemical debate or argumentative confrontation.
...the structure of the conversational relation much more resembles the
dialogic relation of what Socrates called the situation of “talking together
like friends.” Friends do not try to make the other weak; in contrast,
friends aim to bring out strength. Similarly, the participants of a human
science dialogue try to strengthen what is weak in a human science text.
They do this by trying to formulate the underlying themes or meanings that
inhere in the text or that still inhere in the phenomenon, thus allowing the
author to see the limits of his or her present vision and to transcend those
limits (of. McHugh, et al., 1974) (Van Manen, 1990).

For the purposes of illuminating my methodological approach to this study, I think
about a parallel to the way in which Lisa and I created a “conversational workspace”8 for
making sense of her experience in the classroom and in collegial settings where she was
learning to talk about her practice. Similarly, working with Dr. Christopher Clark as my
advisor created for me an additional “conversational workspace” in which to make sense
of my collaborations with Lisa, moving between the IMT group and our inquiry.

Chris and I met nearly every week during the work of this dissertation project.

Our collegial work, his guiding my learning of a new practice, created several important
learning experiences for me. First, it gave me another set of experiences in which I could
connect my ideas about Lisa's learning with my own. Van Manen (1990) writes that "we
gather other people's experiences because they allow us to become more experienced
ourselves...” (p. 62 ). Second, I learned a particularly valuable lesson in my
development as a collaborating researcher. I learned first hand that the analysis—the sense
making of one's independent study—cannot be done in isolation. I recognized in my own
experience that I was still carrying a image of "doing analysis work" that aligns more with
experimental traditions where the researcher singlehandedly applies a set of prescribed
strategies, deals with the data, and comes back to report the findings. I did spend many
hours alone with the materials of our work. But it was in my conversations with several
committee members and colleagues that I did a significant amount of the interpretive work

of this study. In conversation I raised questions, I tried out language, I found/fit

 

8 See Denyer and Pfeifl‘er (1996) for their development of this sociolinguist concept.

65

connections among ideas; I forced some connections that later—broke. In my explaining
and re-explaining, I made sense—and continue to make sense—of my collaborative work
with Lisa.

What Have I Learned? How Might I Show Others?

Throughout this project, I have grappled with a set of questions traditionally
connected to the completion of a research study. What are the results? Have you finished
your analysis? Are you writing yet? When will you be finished? The language and thus,
the standpoint of these questions is rooted in research that poses clean questions and
produces definitive answers. How do I answer these questions when my project was and
continues to be an evolving colleagueship?

If I return to my perspective on learning—always my strongest starting point——
then I need to alter the way I conceive of and articulate the closure aspects of my research
work. Much as we aim for teachers to hold open their questions of practice (e. g., What
does it take to facilitate the discourse in my classroom?), the aim of human science
research is, in part, to hold open our study of experience and phenomena. My research is
my learning—can it ever be finished? So how do I talk about where I am and who I am in
my work thus far? How do I share what I have learned in this one project that it may
contribute to others’ research? The first answer is I must continue learning to write about

my work.

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As Van Manen notes:

Writing fixes thought on paper. It extemalizes what in some sense is

internal; it distances us from our immediate lived involvements with the

things of our world. As we stare at the paper, and stare at what we have
written, our objectified thinking now stares back at us. Thus, writing
creates the reflective cognitive stand that generally characterizes the
theoretic attitude in the social sciences. The object of human science
research is essentially a linguistic project: to make some aspect of our lived
world, of our lived experience, reflectively understandable and intelligible

(Van Manen, 1990, p. 126).

Many scholars have shown by example and by word that "research is the work of
writing—writing is its very essence" (Barthes, 1986, p.316). For all the messiness and
uncertainty of learning from my inquiry and my struggle to articulate the methodology of
this research project, I have developed a deeper understanding that writing is the method.
It is in the writing that I think. It is in the writing that I come to understand. (Heilbrun,
1990; Bruner, 1963, 1986; Brande, 1934; Dillard, 1989).

But this text is not the only product of my work. The text is a representation of
the work. And the work is embodied by those who have lived the experience, reflected on
it and crafted a way of sharing it with others. The text then, is one representation of the
writer. In producing a text, writes Van Manen (1990):

...the writer produces himself or herself. As Sartre might say: the writer is

the product of his own product. Writing is a kind of self-making or

forming. To write is to measure the depth of things, as well as to come to

a sense of one's own depth (p. 126).

I am curious about the ways in which relatively new and tentative moves in

educational inquiry toward a relational pedagogy (Kreiger, 1991)—where the researcher is

67

a product of the research—will shape and reshape the way we think about written texts as
the best representation of who we are becoming through our work.

Relatedly, I want to close this chapter with a brief exploratory note about my long
term study of this project and, perhaps more importantly, my work as an educator since
this project. I believe that time and subsequent new work have informed my analyses and
revisions and have shaped my understanding in ways that could not have been anticipated
at the time I was designing the study as a doctoral dissertation project.

In the year following my completion of the draft of this thesis I took a firll-time
teaching position in a sixth grade classroom in an elementary school about 85 miles fiom
the university. The decision to pursue this position was in many ways agonizingly
difficult, a time of my greatest professional and personal uncertainty. Nearing completion
of the dissertation work and entering the period of transition that moves a doctoral student
from intensive study to new work and new status, usually as an assistant professor, I
found myself considering very seriously a return to “new work” with former status as an
elementary classroom teachers'. My decision was influenced by the work of my
dissertation project and more so, by my long term involvement with the IMT group. I was
not aware, early on, of the ways this decision would influence the revision work I chose to
engage concerning the analysis and interpretation of my dissertation project.

When I returned to revising the thesis, six months after beginning my “new”

elementary practice, I was struck by two changes that I think are important and

 

9 I am grateful to Janet Navarro for sharing with me the phrase, “returning to a place I‘ve never been
before” as a way to describe the experience of transfomring a teaching practice.

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unanticipated methodological outcomes of this work. First, there was a change in my
writing voice. I believe that I still write as a researcher, but now with a particular sense of
confidence, or more specifically, a sense of connection to practice that secured my
confidence in interpreting the study materials. Second, my understanding of my analyses
and interpretations has been strengthened by my actual return to a classroom position and
moreover, to the culture of teaching. I grapple, whole heartedly, with the questions: Is it
necessary to return in order to understand, the longstanding participant/observer dilemma
that pushes researchers? Must I be one to understand one? I still stand in agreement with
the anthropological notion that we can achieve deep understanding of another’s
experience (Clifford, 1988; Geertz, 1988) without enacting the same experience. Indeed,
we know we cannot have the same experience. Still, I am intrigued and excited by the
ways my recent experiences have enhanced my understanding of the work I did with Lisa
and my serve potentially to shape my subsequent research work as a direct
participant/observer in the culture of teaching. And so, my understanding of my work

with Lisa continues to grow.

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CHAPTER THREE

Learning New Norms For Making Practice Public

“So to use videotape in a way, in a trusting, sharing inquiry, is very difi'erent. ”
Lisa, 1-6-93

For many classroom teachers, responding to curricular and organizational reforms
is largely a decision about whether or how to comply with a new mandate handed down
from a distant part of the larger system— “the district” or “the state.” Sometimes,
responding means deciding whether or how to adhere to a new set of guidelines, new
instructional materials, new inservice programs, or new committee work. For Lisa Pasek,
responding to the reforms is personal.

In Chapter 2, Lisa shared with us highlights and pivotal events that have shaped
her view of learning and her view of her teaching. Lisa is in good company with a
growing “community” of teachers nationwide who view the call for change as a challenge
to craft for themselves professional identities and career paths that are labor intensive to
forge and exhausting to sustain. Once introduced to a vision of reform, the greatest
challenge may be for teachers to figure out ways to get from here to there, fi'om the
familiar world of teaching as they observed it as students, imagined it as teacher
candidates in college, and were socialized into it as eager, energentic novices.

Kenneth Brufl‘ee (1993) writes about his own experience with crafting a new sense

of identity as an assistant professor, struggling to understand the transition process

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students in his freshman English class must make in order to participate successfully in the
academic culture to which they arrive from a range of communities. He describes how
their difliculties acquiring the language, values, and ways of being “academic” can be
understood if framed as a process of acculturation.

Brufl‘ee describes his own participation in a group of fellow faculty members who
met to explore strategies for working with their students to show how the collaborative
conversation and joint work the group provided a transitive support community in which
they were able to change their perspectives and practices. Moreover, the group provided
a model of the kind of conversations they needed to foster among their students in order
to provide the transitional support nwded for them to become active, learning members of
the academic community. It is in the “boundary conversations”, Brufi‘ee suggests, that
students move from one knowledge community to another, acquiring the necessary
understanding and skill to authentically participate in the definitive ways of the new
community. Part of the power, I think, in Brufl’ee’s contribution to this study is the idea
that the transitional process is not just a matter of shifting one’s participation to a new
place and a new group. Rather, it is a transforrnative process that involves learning and it
is the work of a transitional community to work at the knowledge boundaries of the
both/all communities that converge in the process. In Brufl’ee’s words:

What we have to do, it appears, is to organize or join a temporary

transition or support group on the way to our goal, as we undergo the

trials of changing allegiance fi'om one community to another. The agenda

of this transition group is to provide an arena for conversation and to

sustain us while we learn the language, mores, and values of the community

we are trying to join (1993, p.20.)

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This transitional process of translation, this willingness to learn the
elements of new languages and gain new expertise, is the most important
skill in the crafi of interdependence. It is a willingness to become members
of communities we have not belonged to before, by engaging in
constructive conversation with others whose background and needs are
similar to our own but also different. Reacculturative
conversation...combines the power of mutual self-aid help groups with the
power of successfiilly collaborative intellectual work. It integrates the will
and the way. ...To be able to engage in constructive reacculturative
conversation, however, requires willingness to grant authority to peers,
courage to accept the authority granted to one by peers, and skill in the
craft of interdependence (1993, p.24).

Using a different set of constructs, linguist James Gee has also addresses the
notion of movement between communities and the enculturation process required for
participation. Gee (1989) draws a distinction between primary and secondary discourses,
where the first refers to the “oral mode” (p5) of enculturation that takes place generally
within a family structure and the second refers to “other discourses which crucially involve
social institutions beyond the family” (p5). Gee fiirther differentiates primary and
secondary discourses such that the first is acquired “by exposure to models and a process
of trial and error, without a process of formal teaching.” The second is acquired “by
having access to and practice with secondary institutions such as schools, workplaces,
stores, government offices, etc.” Gee uses these concepts to construct a framework for
understanding literacy development in children; he describes children’s acquisition of their
primary discourse in the home and their learning of a secondary discourse when they enter

school. He also likens the acquired discourse to an “identity kit” which “comes complete

72

with the appropriate costume and instructions on how to act and talk so as to take on a
particular role that others will recognize” (1989, p1).

Of particular relevance to my analysis of Lisa’s work in the [MT group is Gee’s
argument that learning a secondary discourse enriches and expands a person’s social
competence. Moreover, he points out, a secondary discourse enables one to reflect upon
and critique a discourse previously acquired. Denyer and Florio-Ruane (1995) draw on
Gee’s ideas to articulate the opportunities teacher education programs might create for
teacher candidates “to learn about alternative discourses for teaching or different ways of
realizing the teacher’s role and her wor ” (p. 540). These authors worry the problem of
balancing a candidate’s formal learning of teaching methods with acquisition and
internalization through models and guided practice. Similarly, educators concerned with
the professional development of reform-oriented teachers—that is, teachers oriented to the
alternative discourse of education reform—face the challenge of creating contexts in
which practicing teachers can critique their early acquisition of a teaching discourse while
acquiring and practicing a new one.

Together, the constructs offered by Bruffee and Gee with the application of some
by Denyer and Florio-Ruane create a helpful frame for situating Lisa’s efforts to learn to
use videotapes of her teaching in representing and examining her work. This chapter
centers on Lisa sharing her videotape with her colleagues in the IMT group. By looking
closely at her preparation for this event, the activities of the event, and Lisa’s reflection on

her experience, we have an opportunity to consider what was needed for one teacher to

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participate in a transitive support community committed to learning new ways of thinking
about, talking about, and doing the work of elementary mathematics teaching.

Lisa’s sensemaking of her sharing of videotape, the key event in our research
project illuminates ways she was reassured in her efforts to crafi a practice responsive to
the reforms. My analysis of Lisa’s analysis suggests ways of understanding why teachers
in pursuit of a new kind of practice and a new kind of intellectual engagement with
colleagues around their practices will need to create for themselves new norms of
interactions, interactions that hold potential for altering the culture of teaching that
currently shapes their work. Lisa’s experience in making her practice public through
videotape illuminates how creating these norms requires teachers to develop and use a
conscious knowledge of the existing culture. They must also develop and use images or
beginning experiences with an envision culture. They must stand both in and out of the
familiar culture of teaching, drawing on knowledge and skills acquired through their initial
socialization into the profession, in order to create and sustain new ways of being in
company with other teachers.

Lisa was interested in figuring out how to create and use a learning community of
colleagues to support her efforts in learning to teach mathematics, one that included close
examination of the activities in her work with students and carefirl, critical talk about the
reasoning behind that work. She was interested in learning how to use videotapes of her
own classroom teaching as a tool in conversations with other teachers so that she might

get smarter about how to create a mathematical discourse with children that was

74

meaningful and educative.

The account to follow describes Lisa’s efforts to alter her experience of
storytelling by adding video images and to explore how conversations with her colleagues
might help her improve her teaching. I begin with a description of the portion of the IMT
meeting in which Lisa shared her videotape, interrupted by a description of her preparation
for that discussion, and followed by an account of her reflections on the experience in the
weeks following the meeting.

The remainder of the chapter includes a descriptive analysis of Lisa’s reflections on
her experience and a sociolinguistic examination of the rights and duties at work in the
IMT discussion. Stepping back from the analysis of talk, I discuss the relational context
of trust that is needed for Lisa and other reform-oriented teachers to begin altering the
rights and duties of teacher interactions in ways that approximate the critical dialogue

described in reform literature.

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Sharing Her Own Videotape Of Teaching

When Lisa arrived at the conference room inside the College of Education, the
regular meeting place for the IMT group, several teachers were engaged in a conversation
about their students’ ideas about place value. It was December 17, 1992, and the last
meeting of the IMT group before the holiday break. Lisa unpacked her grocery bag fiill of
snack foods and added them to the buffet of holiday specialties in the center of the table.
Other group members moved in and out of side conversations about current happenings in
their classrooms. Then, almost abruptly, the group settled into a conversation with Sheryl,
a fourth grade teacher. She was asking several members at one end of the table, “So, [in
my class,] we’ve been doing lots of problems like that, two digit problems. My problem
is, where do I go after this? ...IfI think they understand [the concept of multiplication]
where do I go now? How do I transfer over to the algorithm? Do I do that?”

About fifteen minutes into the group’s exploration of the difficulty in helping
students connect what they know about place value from working with manipulatives (e. g.
what the tens mean; what the ones mean) to the algorithm for two-digit multiplication,
Lisa entered the conversation. She responded to Sheryl’s frustrations with a strong tone
of encouragement saying, “Well, I would say, keep with it.”

Sheryl asked, “Keep with it?”

Lisa continued, “Keep trying to connect it. I think—keep trying to connect [the

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concrete to the algorithm]. Because, well, I brought tape today and my sixth graders had
this discussion and nobody could explain—they were showing a multiplication problem—-
nobody could explain why you have to have a place holder in a two-digit multiplication
problem. We can look at it later, but sixth graders who are top notch students are saying,
‘Well, you just need a place holder.’ I ask, ‘Why?’ and they say, ‘You just do. Or you’re
going to get the wrong answers.’ They really—we never get to it.”

I watched closely as Lisa stepped into the discussion and set the stage for sharing a
videotape of her own teaching. In this brief exchange, she put on the table the idea that
she wanted to show a videotape of her classroom. She did so carefully, not taking the
floor from Sheryl nor changing the topic of discussion nor putting herself in a position to
show the videotape right then. Rather, she let it be known that she had a videotape of her
teaching with her and she suggested that watching it together might be helpfirl to the
group’s discussion.

Lisa had told me earlier that she wanted to “ease in” to sharing the tape. She
didn’t want it to be “Lisa Night.” She had explained that she didn’t want to show tape
first thing because she knew that people would come to the table with concerns and

questions and she didn’t want to take that time away from them.

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E i r ' f r Sh 'n

Lisa and I met in her classroom after school a couple of days before this meeting.
There we talked about her expectations for what she might gain from showing her
videotape to the [MT group. Lisa likened her image of sharing her videotape with the
IMT group to jamming with a group of excellent jazz musicians. Rather than merely
telling about her practice, she was looking to share, seeking affirmation, observations, and
questions she was sure would push her thinking. She said:

It’s maybe like a sax player or an instrumentalist that practices and

practices a certain piece that they really want to excel at or they really want

to be able to perform well. So they work really hard on that piece and they

perform it and they still want to work to keep it up. But then, they also

probably like to get together with a group of other musicians and jam...

So, part of it is, I want to kind of show—and jam. ...[T]he stories are fun

to tell and they are fun to listen to and I think the video would provide a
way to do that. I’m just really interested in what other people will notice.

We talked about how she was thinking about her selection of a fifteen minute
segment of videotape to show to the group. Lisa worked back and forth in her thinking
about how much to structure her sharing of tape around a question and how much to
explore a piece that seems to have “lots of rich stuff in it.” She thought aloud, “Maybe I
use the same criteria I use when I think of a mathematical task...I would want to have a
question, but one that is open ended enough that it would engage people on different
levels.”

Lisa considered firrther why, rather than posing a question, she was interested in

what others might notice. In Lisa’s words, “there is the value of having people look at

78

something you think you have a handle on and then a different perspective can kind of
blow it wide open for you, too.” Lisa continued this line of thinking, explaining that
getting different perspectives is “more of what I’m expecting from the group; their
questions may peel more layers. I don’t know if that would happen the first time; if
people will be timid; I kinda don’t think they will be.”

This same aftemoon, Lisa and I watched some videotape together, segments from
the third of the four math classes we had recorded a couple of weeks earlier. Lisa had
selected these segments by watching the tape on her own at home. As we watched, I
prompted Lisa to articulate her reasons for showing these clips to the group:

Maybe another [reason] I want to share this is because (pause) I can tell
stories at the group of what my math class is like and I can listen to other
pe0ple’s stories, but we could all be lying and just telling our perceptions
of what happened. AND there are no other models around that I can
compare to or get feedback about. There is no one around [here] that
would come to me and say, ‘that was an interesting question.’ Just
because of the set up of our system and just not having that kind of
support. So part of it is just wanting somebody to say, ‘that was a good
question.’ Or, ‘I’m interested in why you did that’, because there’s no
feedback like that [here]. With the stories, they respond to the stories. It’s
not really—they can’t ask me about things that I don’t tell them about.

She continued thinking aloud:

Part of it is—I want—a kind of coming out party. Where you say, ‘This is
what it really is. Whatever I told you, whatever my perceptions are of it,
you know, better than or worse than or more confused than’, everything
else has been my perceptions of what happens and I want to get (pause) I
want to have a feel for someone’s input about whether there is a lot of
student exchange or there is more teacher exchange than I thought. I want
to know where I fit in. I don’t know if that’s the right way to say it.
(pause) It is interesting because when we were watching a tape of
Deborah’s (Ball) and she cut ofl‘ a conversation that was going on between

79

some students, Kathy said, ‘Why did she cut it oh? I would have let it
go.’ And Jane said, sitting right next to her, ‘I would have cut it off a lot
earlier.’

It was a beauty of a moment because there were two teachers that are
professing the same beliefs and the same ideas about how kids’ learn and
they took very different stands on how that discourse should have been
manipulated. And so I’d like to—I suppose it would be the same thing
with my example of discourse. There might be pe0ple who would say, ‘Oh
you’re—like in their heads they might say, ‘Oh you’re talking way too
much’ and somebody else would say, ‘you’re not directing the kids
enough.’ Just depending on what they are used to. It’s not really finding

out if I’m right or wrong, but just kind of getting a feel for who did I agree
with more.

As our conversation continued, Lisa and I talked about this notion of assessing
where she fit in--who she agreed with—and she explained that knowing how the [MT
group works, that even if she showed them a tape that looked like very traditional
teaching (e.g., “doing 20 problems out of the back of the book”), she expected the group
members would ask her questions about her purposes for doing so, trying to
understanding her thinking about her teaching. This understanding of the IMT group
assured Lisa that sharing her tape was, as she said, “not threatening...I predict that
whatever happens it will be helpful.”

Lisa’s sense that it would be helpful seems connected to her descriptions of her
experience in the group during it’s first year together. In interviews during her first year
of participation in the IMT group, Lisa used analogies to describe the support she found in
the group.

[T]he intensity of the IMT group and the sense of purpose and renewal I

felt made me liken my participation to the spiritual experience of attending
church. On Thursday, I make the drive to the university to talk and listen,

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to push and be pushed, and to gain strength in the power of the group. It is
this planned and predictable source of affirmation that enabled me to return
to my own school and continue pushing [myself] to teach mathematics in
new ways. Had I not had this source of support, I worry that I would have
become a “lost sheep” (April, 1992).

I was involved in a year long math in-service training sponsored by my
school district. This training was conducted concurrently with my
participation in the IMT group. This district in-service was an introductory
kind of investigation into difi‘erent ways to teach math. Perhaps, like a
recreational raquetball league, these people were satisfied to get together
and just hit the ball around for awhile. During IMT meetings, however, I
could tell I was in a different league. These people were serious players,
fascinated with the foundations of the game they were playing. The
members of the IMT group seemed committed to looking beneath the
surface and working hard to analyze alternative ways of teaching and
learning mathematics (August, 1992).

In Lisa’s words, she saw the IMT group as “a predictable source of aflinnation,...a
source of support” for sustaining herself in the challenge of teaching in new ways. Lisa
looked to these “committed” and “serious players” in the game of reform for the analytical
help she needed to understand the reform of mathematics teaching and to use her
understandings to transform her practice. She trusted these colleagues to help her find her
way.

As our planning meeting was winding down, I asked Lisa how she was
thinking about setting up the clip for the IMT group, “so that you get something
out of it?”

Well, I know I’m going to get something out of it. That’s not even an

issue, I don’t think. At this point, there are—kind of—difl’erent levels.

Part of the reason I want to share is to jam—part of it is to share what I’m

doing. And part of me wants them to say, ‘Yeah, you’re OK.’ That would
reaffirm for me that this is part of what other people are thinking of as—

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the vision.

Then there’s the level that this was something neat that happened in my
classroom and here’s the story about it. And then there’s the possibility—
almost guaranteed—that they will ask me questions and make me think
about it in a different way. So already, there are four things, four levels,
that don’t even include having me have a particular question answered.

Showing and Talking about Prgctice

 

Lisa’s predictions and thoughts in planning to show her videotape are critical to
the analysis that follows. Of particular interest is her thinking about how people will
engage and her four levels of purpose for making her practice public. But first, I continue
my description of what happened during the IMT meeting on December 17, 1992.

Noting Lisa’s move to “ease in”, I returned my attention to the discussion at the
IMT table. Connecting to Lisa’s point that her sixth graders didn’t seem to understand the
convention for two digit multiplication, Carole, a third grade teacher, was describing her
students’ struggle to understand the meaning of zero in a multi-digit addition problem.
She said:

“See with my third graders--I had Jacob saying to me the other day, ‘Let’s just get
rid of this zero. The zero is worth nothing, so when you are adding 245 + 755, you can
just drop the 0 and put down the 1.”’

Carole continued to explain that this was the same little boy who, a few weeks

earlier, had grappled with the meaning of zero in 6 X 0 = 0. According to Carole, he was

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the first in the class to see that zero means nothing in 6 X 0 = 0. The connection Carole
was making now, with the help of other IMT members, was that Jacob was trying to use
his understanding that zero means nothing in a new mathematical context. Carole was
puzzling about how to help him sort out what may seem like conflicting ideas: in one case
zero means nothing (6 X 0), but in the addition problem it does mean something (245 +
755 = 1000, not 991).

The group’s conversation was interrupted briefly when Kathy, a second grade
teacher, arrived and took a seat at the end of the table. Helen redirected the conversation
back to Sheryl’s algorithm problem, asking her, “So how are you thinking about next
steps? The discussion grew more lively as the members continued to investigate the way
we teach kids the multiplication algorithm and how little “real sense” it makes to do what
we do in multiplying two-digit numbers. Carole commented that the way Sheryl was

arguing (see Figure 2) to present it to the kids, to break it apart, actually made more sense

than the convention:
A. 324 B. 24
a! all
192 32 (8x4)
+160 (8120)
192
The conventional algorithm for Sheryl’s propowd alternative algorithm
multiplying a two-digit number for multiplying a two-digit number

Figure 2. Two approaches to multiplying two-digit numbers discussed in IMT meeting

83

Helen was helping Sheryl to see how what she was trying to teach them conflicts
with the prior knowledge they already bring about carrying--even though they don’t know
why they carry. Sustaining the investigation, Helen turned to Lisa and asked, “how do
they [your students] do it, Lisa?”

Lisa laughed, “That wouldn’t help!”

“What?”

“They have a tool”, added Lisa.

In the moment I did not catch what Lisa was doing. Slowly, I began to see that
she was taking Helen’s question as an opening. Adding her own humor and drama, she
was creating another entry into the conversation that was connected to her videotape.

Lisa smirked and said, “They use stars. It’s on the videotape. This multiplication
thing actually came up when we were working on adding and subtracting decimals.”

Having captured the group’s attention, Lisa introduced the videotape. She
described how her students had been generating number sentences equal to 1.019
(e.g., .744 + .275 = 1.019). Then, she started the videotape. Suddenly she became
confiised, almost panicked. She thought she had the wrong videotape. She stopped the
video player. She looked to me for clarification. I didn’t react because it looked to me
like she had the tape she had decided on at the end of our prep meeting. But something
did feel confused.

The problem was Lisa had described for the group the math class that proceeded

the class she was about to show them and she had gotten momentarily flustered. I was of

84

no help other than to react so slowly that she figured it out, regrouped, and explained the
correct context for the segment:

The context instead—that (number sentences = 1.019) was the previous

day. I was getting a feeling that there were kids that were thinking that

decimals were less than zero. No one had said that they were less than

zero, but I was wondering if they thought that. So the next day I told them

that last year’s students took a quiz. And on this quiz there was a problem

that asked them to compare zero (0) and 515 thousandths (.515) and to

show which is greater than or less than and to have an argument for it. I

told them I wanted to know what they thought about this problem. So,
that ’s where this started. And the star issue is in here.

The group waited quietly as Lisa worked through her mix up. As the videotape
began to play again, Carole commented, “Oh, nice!” as she watched one sixth grade
student say to her classmates, ‘thile he is drawing this, I will explain.” The IMT group
settled into quiet viewing.

There was some difiiculty with the audio on the tape and I was keenly aware that
having been there and having reviewed this segment several times I was able to fill in
where sound was weak. Both Helen and Kathy were good about asking for clarification
on what they were missing.

Helen asks, “Wait a minute, I don’t get it.”

“I don’t either”, said Kathy.

Lisa stopped the video player and explained, “He was saying that zero is a whole
number and so think about the place value of zero as the place value of one whole. But a

decimal has a place value of tenths, hundredths, thousandths, and smaller. What he was

85

saying is, ‘if the decimals are here—(0.) zero point whatever number—then zero is still
larger than all decimals.”’

Helen repeated the student’s idea, “So zero is bigger (than .515) because it’s a
whole number.”

Lisa nodded ‘yes’ and started the video player again. There was a long stretch of
silent viewing as the sixth graders’ discussion moved away from the comparison of 0 and
.515 to one student talking with Lisa about how they were taught in fifth grade to use
stars as place holders in computing two digit multiplications problems. Lisa probed the
students for their use of this “placeholder” and why they needed one to work on the
problem. In the midst of Lisa’s probing, Tammy, a sixth grade girl, made a comment that
linked the discussion of place holders to the problem of comparing 0 and .515:

Pasek: So why are you concerned about not being in the ones
place, or --?

Student: ‘cause you could take 200--what--280- or 218...you add
on another zero.

Pasek: I am just wondering what that placeholder is for.
Tammy?

Tammy: Um, Another way that you can show if 0 is greater
than .515 is urn, put 0 and put .515 and then you can
add 0s as place holders and then you say, there’s 0
here and 5 there, so this must be greater, ‘cause
there’s already 5 there. That’s 0 and that’s 1, that’s 5
and that’s 0.

Pasek: Did you do div--subtraction, or?

Student: No.

86

Student: No.--just compare

Student: comp-

Student: compare ‘em.

Student: Like if the 5 is bigger than the 0, then that’s larger and if
the 1 is bigger than the 0, that’s larger and if the 5 is
bigger than the O--then, then the whole problem is bigger
than the other problem.

Student: I agree.

Lisa stopped the videotape and went to the write board to show the [MT group
what Tammy had written on the board:

000
.515

She explained how Tammy compared the numbers in each column to show that 5
and l and 5 are each more than 0 so, .515 must be more.

Marian, a seventh grade teacher, asked, ‘What if it’s .505?” Lisa responded that
she had asked that question of Tammy next. It wasn’t clear what Tammy’s response had
been. Instead, Lisa emphasized to the [MT members that everyone in the class seemed to
understand what Tammy was talking about, but this like other ideas ofi‘ered by Tammy
frequently seemed to come out of nowhere.

Without firrther investigation, the group returned to watching the tape which
included two more students making interesting moves in the discussion. One sixth grade

girl went to the board and drew a representation (see Figure 3.) of the base ten block, a

87

wooden block that the students frequently use in worldng out solutions, and she used her
drawing, shading in the squares to show what .515 looks like and to argue that it is greater

thanO.

 

s.‘ E
Figure 3. Base ten block shaded to show .515

Kathy, a second grade teacher, asked, “Do they understand that [drawing] Lisa?
That seems so strange to me.”

\Vrthout stopping the tape, Lisa replied, “Oh, I use it a lot.”

“Oh, do you?”

This exchange of question and answer between Kathy and Lisa struck me as odd,
unnatural somehow. I was reminded by their talk that we were engaged in a novel kind of
dialogue and everyone seemed to be moving carefirlly into this new territory. It was as if
Kathy and Lisa, who had a year long history of talking together about their teaching, were
now conscious and careful in their remarks, as if they were new conversational partners.

The tape continued to play through the last episode Lisa wanted the group to see.
In an efi‘ort to convince his classmates that .515. was more than 0, one sixth grade boy

wrote on the board:

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l-.515=.485
1-0=1

“So”, the student argued, “zero is one whole from being equal to l and .515. is
only .485 away.”

Lisa stopped the tape and IMT members began to comment on this last episode.
One IMT teacher wondering about how what she saw on the tape was connected the kind
of instruction the students have had in previous years. In response, Lisa told how she
thought the students understand that fractions are part of a whole. But, when working
with decimals the way we write them creates conceptual confusion. Lisa said, “It’s like a
count down 5, 4, 3 ,2, l, 0 and coming down the number line you get to 0.2.

Another IMT member wondered aloud about one student’s comment, very near
the end of the class discussion. Lisa explained that “it’s two minutes past lunchtime at this
point. I don’t know if he really understood that. . .the timing was bad for having a lot of
time to go through it.”

And so for the next forty minutes the IMT members continued to ask Lisa
questions about the students, about the activities in this unit on decimals, and about a
particular strategy that might be helpful. They asked a lot of questions. Indeed, the
question/response rhythm of talk around Lisa’s videotape drew my attention to the
patterns of conversational involvement in how Lisa was using the videotape and how it

was helpful.

89

At one point, there was a lull in the group’s discussion and Kathy made a comment
that shifted the pattern of talk. She said to Lisa, “Well, I really liked watching your tape,
Lisa. I feel much better.”

Helen said, “Well, it made me feel both better and worse because it was really neat
to watch. But I realize how hard the ideas are”.

Kathy added, “I feel like I could come into your classroom and learn math.”

Lisa thanked Kathy and returned quickly to talking about the complexity of
understanding her students’ ideas, telling another story of a time when her students made
visible their understanding of place value. The students’ explanations reflected algorithm-
based teaching rather than conceptual understanding. Lisa made clear once more the
connection she had seen between Sheryl’s original questions about the multiplication
algorithm and her own teaching. She said:

Thank you, [Kathy]. Even though it’s frustrating, it is exciting to have--
even when you see how much they’re confused about... One day we were
having a discussion...we’re talking whole number subtraction (3000 - 2000
= ?) and I kept saying, ‘Why are you getting those 95? (3000 - 2000
changed to 299910 - 2000 = ?) Where are the 95 coming from?’ They said,
‘We are stealing them.’ They explained that the same teacher who taught
them to use stars told them they are stealing, not borrowing in subtraction,
because you don’t give it back. I said, ‘What are you stealing from the 3?’
They said, ‘a 1.’ I asked, ‘1 what?’ They said, ‘a l and you have 2 left.’
Then someone circled 299 and said, ‘All you really need to worry about is
the 299.’ ‘But is that 299?’, I asked. ‘Yes. 299 and a 10.’ He is a sixth
grader... That is why I would suggest [with your fourth graders] keep
going with connecting the algorithm with the concrete because if you go
from the concrete to the algorithm they’ll never...they won’t connect it
back and if you don’t teach them the algorithm they’re going to learn it
somewhere and they might never know why.

90

Lisa’s comments seemed to bring the group full circle and shortly thereafter the
discussion shifted to a new topic, marking the close of Lisa’s sharing and the group’s

focus on her practice.

Lg ’g Egur Coniggtures about Showing Videotape

Before showing her tape to the [MT group, Lisa had outlined four ways that
showing her videotape would be helpful to her: 1) jamming; 2) reaflirming her vision of
this kind of mathematics teaching; 3) the fun of showing and telling about happenings in
her classroom; 4) questions fi'om the group that would push her thinking. I want to note
at this point that in her preparation for showing her video Lisa refers to her having a
question to answer. In one instance she talks about having a question “open-ended
enough that it would engage people on difl‘erent levels.” Another time, she summarizes
her four levels of potential benefit by saying, “. . .four levels that don’t even include me
having a particular question answered.” This note is important to the analysis that
follows. Lisa’s “four levels” held for her the potential to create a “kind of coming out

party.” I will use these four levels now to look closely at Lisa’s sensemaking of this

experience.

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Making Practice Public
“A Kind Of Coming Out Party”

Describing her sharing of tape as a debut, Lisa was talking about making a move
that she knew was unfamiliar, perhaps viewed as radical in the traditions of teachers’
interactions (Little, 1990). She wanted to make her actual practice public; she wanted to
show the others her teaching in a way that her stories could not. Lisa’s phrase, ‘a kind of
coming out party’ reflects the drama embedded in revealing to her peers a vivid, multi-
dimensional representation of her classroom. Lisa had imagined sharing videotape in the
group as a way of saying, “This is what it really is—whatever I told you—whatever my
perceptions are of it...I want to know where I fit in.” In part, she had described a desire
and an expectation that the IMT group would affirm that she was enacting the vision of
teaching they shared as the Investigating Mathematics Teaching group. She wanted to
know if what she was doing daily aligned with the other teachers’ efl‘orts to create a
discourse among children through which they represent their thinking to one another,
explore conjectures, and argue evidence for their solutions to problems. She was using
the videotape to say to the group, “This is who I am as a teacher in my classroom, in
action.”

While she approached this debut with enthusiasm, Lisa wanted to avoid having her
debut jeopardize her good standing as a member of this group. Her concern was
grounded in her perception that they were a “likeminded” group of teachers (Little, 1990).

What if this debut exposed her as too difl’erent from the others? Lisa understood the risk

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of critique, judgement, and advice-giving that might come with showing her practice on
videotape (“There might be people who would say... ‘Oh, you’re talking way too much’
and somebody else would say, ‘You’re not directing the kids enough.’). She understood
that in showing a videotape she might have less control over what others attended to than
when she told them a story of her teaching (“With the stories, they respond to the
stories...they can’t ask me about things that I don’t tell them about”). She understood
there might be differing perspectives among group members. Lisa used her understanding
of the group to shape and guide her approach to talking about her videotape.

Lisa seemed, too, to have a strong grasp of the way these risks were also
opportunities. She seemed to have weighed the risks in making her practice public against
her desire for affirmation and decided that public disclosure was likely to be worthwhile
(“I predict that whatever happens it will be helpful”). She knew that how she shared her
videotape with the [MT group mattered for the kind of conversation it might stimulate and
the message her sharing could convey to these colleagues. She planned and acted with a
protective stance toward the group members’ relationships and the ways of interacting
already in place. Lisa did not want to appear to her colleagues to be taking more than her
due of the resources they shared in the time, attention, and support of the group. This
cautious, almost timid, approach to attending to an individual teaching practice coupled
with her female propensity to know and learn through connections with others (Gilligan,
1982; Belenky et al., 1986) gives reason to Lisa’s “casing in” to her sharing of videotape

and to her flaming the situation loosely such that she would see what they might see. Her

93

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She dic
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valuing of the group’s history, her concern for sustaining it’s work, and her aim in
preserving it as a resource for everyone seemed to shape Lisa’s expectation that whatever
happened, she would gain from the experience. She was seeking affirmation and that in
itself was worth this pursuit.

Lisa considered that her pursuit of affirmation via a public example of her work
might provoke an unusual kind of exchange among teachers (“two teachers that are
professing the same beliefs...and they took very different stands...”) and such possibility
was exciting to Lisa. Beyond jamming, showing, and seeking affirmation, Lisa expected
to be asked questions that would “push her thinking.” She had experienced this pushing
in previous IMT meetings, particularly in the fall of 1992 (Pfeiffer and F eatherstone,
1996), and it seemed predictable that the group members would ask her to describe further
what they saw on her videotape.

Lisa expected to gain all this, “even without a question to be answered.” Her
expectations were met—with high marks. She had set the session as a jamming session,
not telling the group exactly ‘how to play’ the conversation. She had been affirmed that
she did “fit in” among teachers who are working actively to make significant changes in
their mathematics teaching. In addition, she came away from sharing her videotape with a
sense of success: “I felt good”, she reported. Feeling affirmed that she was on her way to
creating a different kind of math class, she found the experience enjoyable and rewarding.
She spoke, for instance, of her fascination with the different perspectives members held in

interpreting Tammy’s move in the discussion of 0 and .515. She now saw Tammy’s

94

move as significant for the way it pulled together the students’ talk about the relationship
of 0 and 1, and 0 as a placeholder.

I first learned about Lisa’s satisfaction with the experience in an extended
telephone conversation. My understanding of her experience developed through our
numerous conversations in the months that followed. Lisa’s journal writing also provided
me with insights about her sensemaking, her analysis of what this form of public inquiry

involves.

Reflgtions on Sharing Videotape

I telephoned Lisa in the evening on January 6, 1993. The holidays and the
semester break had interrupted our routine of meeting and talking about this work. We
talked briefly about our holiday travels and the fact that she was now back in school.

I had telephoned Lisa the night before to arrange this conversation, asking then if
she had written about her sharing videotape in the meeting. When she said she had only
sketched a few notes, I urged her to write in her journal in preparation for our extended
conversation. The following evening, when I asked Lisa to begin describing what it was
like to share her video with the group, she talked from her journal entry about her
response to Kathy’s comment:

“I ’m so glad you shared that. It makes me feel so much better. ” Kathy’s

very first comment caught me ofl guardum y first (paranoid?) reaction was-
”what? this is so awful, you don’t have to feel so fly! about what you do? " But

95

 

considering the source and the context I immediately knew that t_h_is was why I
had shown the tape. In fact, what Kathy expressed is actually what I had hoped
would happen, and actually did happen for rue—being reassured of a shared
vision—of acknowledgement that my struggles are good, worthwhile struggles, not
futile, time-wasting pointless discussions.
(Lisa ’s journal, January, 5, 1993, underlining in original)
As Lisa spoke about her realization that Kathy had provided her the
afirmation she was seeking, she realized, too, that by showing her videotape, she
had provide the same for Kathy. She said:
What she was really saying was—what I had wanted to get out of it myself
was having other people see it to see if—am I sharing their vision? That’s
what I wanted to get out of it. So, she actually got the same thing out of it.
Seeing somebody else’s teaching, ‘Oh, wow, I am on track.’ So it was kind
of—I don’t know—we shared that.
And also, the acknowledgement that spending this much time struggling

with this question, affirmed that this is a good worthwhile struggle and
you’re not wasting your time with pointless discussion.

Lisa said that since returning after the holidays she felt a strong tension in her
school. It seemed to her that teachers were “doing double takes” when they stopped by her
room, looking at the board and asking questions about what was going on in her
classroom. She said she was keenly aware of justifying, at least to herself, what she is
doing in her teaching. It reminded her “of the contrast between sharing with people you
trust in an IMT group and justifying to others-being on the defensive--or others being
defensive themselves.”

When I asked Lisa to talk more about her experience in the IMT meeting, what

seemed like the best part about sharing her videotape, she focused on her interest in what

96

in
to it
lift a
m’0 w.
helped

”in lid

others attended to in the segment. She commented:

There was no way to predict what others would pull out. Tammy, for

example; the conversation about Tammy’s comparison of 0 and .515. I

have a heading in my journal now called, Tammy: Diplomat rather than

Daydreamer. It is pushing me to listen harder to her in class.

I asked Lisa if the experience of sharing tape in the [MT group “cost” her
anything. She was quick to respond, “N o, it did not.” She said that it ‘Vvas not a
fabricated situation—to collect research data—it felt like a natural progression” from
where the IMT group had been. She likened it to playing baseball, saying, “OK, I’ll go to
bat first and I guess I got to base.” She explained that she knew this because she felt good
about it: “It felt safe.”

Lisa was telling me that three of her four expectations had been met in this “trial”
use of her videotapes. She had already described her sense of afinnation, the firn of
sharing the tape, and her fascination with seeing what others see. She was also telling me
that she had a sense of having moved the group into new territory in a way that felt like a
natural next step—and it felt safe. As we continued, Lisa began to talk about the
limitations of the group’s conversation. She grappled with language to describe her desire
to return to the group with more videotape so that she might be pushed or “dig deeper.”
Her analysis of what went well and what was missing is important to this study in at least
two ways. First, Lisa’s marking off her first sharing experience from possible future work
helped us explore what more beyond safe, aflirmative sharing is needed for her to use her

own videotapes in learning to teach mathematics. Through our conversations, she

97

identified two changes that would help shape the conversations around her videotape to be
deeper, more investigative. Second, understanding why Lisa’s reflections made sense in
light of the current culture of teaching, offers other teachers, researchers, and teacher
educators insights into how we might begin to alter familiar ways of interacting that
actually block the transformational work envisioned by reformers.

I turn now to my analysis of Lisa’s analysis of her experience. I will describe more
specifically the two changes Lisa identified as important for her continued use of

videotapes in discussions of her practice.

A Qggsg'gg 9f My Own
Lisa continued to reflect on her experience of sharing videotape in the IMT group
and she commented that it would be interesting to go back to the same videotape and have

a question of her own:

I was thinking that this first time was, and I think we had talked about this
the last time we talked, that this time felt kind of like a trial—I want to see
how this goes. And so there was a lot of value I think, it was just kind of
at the base level, the general, ‘What do you think? Is this what you think
too?’ And so, I think it served definitely that purpose. It felt on level with
what people were talking about. And probably—I was thinking about—it
would be interesting to go back to the same tape and have a question. Get
at the same thing. Look at the same thing and dig deeper, or um, kind of
open up to be pushed a little bit about, well, ‘Why did you ask that?’ Or
some of those questions that kind of take a little bit of easing into.

It had been Lisa’s expectation that the group would have questions that would

push her thinking. But that hadn’t really happened. Together, we concluded that without

98

a question, a wondering of her own, the conversation seemed to stay at a certain level.
She wanted to “dig deeper, or kind of open up to be pushed a little bit some of those
questions that kind of take a little bit of easing into.” We began to explore, struggling for
language, why she must pose a question and moreover, why she must be the one to raise
the question in order to engage the kind of conversation she wants. We said:
Lisa: I liked having a piece with a lot of potential. Um, and I think a
lot about you know, I don’t know exactly what questions I
would have, but I think it would, I think I would need to have
some sort of wondering to ask them about it, to bring up myself
in order to get um, maybe at a, I don’t know whether to term it
deeper or higher,....
Lauren: I know what you mean though.

Lisa: Going past and going up to pushing, or working down to
pushing ideas.

Lauren: I think it could happen even in that same clip. I think one of the
things I learned is that does have to come from you then. I
don’t think we did that. I think there was a lot of thinking and
responding, but I do think it sort of stayed at a different level.

Lisa: For that clip, I don’t know what the question would be. I don’t
know if it was another tape, if we’d have to see it again, if we’d
have to see a piece of new tape, one to get a general feel and

hash out the surface, and then see it again and get at a question
or

In this part of our conversation, we see Lisa’s thinking shifi fiom sharing videotape
in exploratory ways to more purposeful investigations. Relatedly, and critical to our
understanding of this new work, I think, we see Lisa taking responsibility for this shift.

She assigned herself a more active stance toward shaping the conversation to fit her needs.

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Shared Experience with Sharing Videotape

In addition to needing to have her own questions, Lisa identified another

way to improve the conversation around her videotape. As we talked, these two

criteria became woven together as a complex response to what makes using her

own videotapes of teaching a potentially educative experience. We said:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

And 1 think, I think having other pe0ple share too, would help.
Yeah, I think so too.

Because then it wouldn’t be um, you know, it wouldn’t be so
one sided. They would all have a stake in wanting to push and
you know, the first time it’s nice and reaffirming to come away
from it, “Oh, that was nice, I’m glad they did that.” And the
next time, I would think everyone would want more.

Yes.
The first time is kind of like a show-and-tell.

Yes.

You know, like, see, that’s what I did, this is what ‘I brought.
And people wonder all about it and ask questions. Oh, that
was really nice. But then, you know, it’s different if you keep
coming back and you want to dig at it.

So you think presenting it would look at little differently the
next time you did it?

Yeah, I think so. It’s almost like, I want to go back, you know,
if I could go back into that meeting again, okay now, what do
you really think? It’s like, I mean, and I wish I had a question
to ask of, you know, what do you really think about this? Um,

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or, but it’s hard with that tape because I can’t think of a
particular question that fits there.

It seems clear in this part of our conversation that Lisa held in mind a distinction

between a first time sharing and a next time opportunity. She seemed to value the first

opportunity to show and tell as an occasion to be affirmed in her vision of reformed

mathematics teaching. But it seemed, too, that affirmation would not be enough the next

time. She believed that everyone would want to move beyond a nice, warm and firzzy

visit to her classroom. In order to create more, the others members of the group would

need to have more of a stake in the conversation, more of a stake in wanting to push the

conversation. What Lisa seemed to mean by this becomes clearer in her next comments.

She reiterated her need to have a question of her own, adding that it may need to be a

video segment that she doesn’t like. And she interlocked this questioning, this

problematizing of her practice, with a call for others to share videotapes of their teaching.

Lauren:

Lisa:

Lauren:

Lisa:

Lauren:

Right, and I think that’s where I was thinking earlier, there has
to be a genuine question. And you’ll find them, you may not
find them in all clips.

And it may also be a part of a clip that I don’t particularly like.
That’s what I’m thinking, is where it would come in.

A part of a tape--
That I don’t like. That I feel is awkward or not handled well. I
mean, in order, there has to be a real dilemma or a real you

know, genuine wondering.

A real problem of practice.

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Lisa: I can’t just go and poke my finger in my cheek and say, ‘I really
did like this part, what do you think?’ And if it flows well and it
seems like the kids are really thinking, it seems like it was okay.
And it’s not going to be a very meaty analysis. I mean, it
would be a springboard, but as far as digging in deep, and that’s
why I think it would be important for other people to share,
because I think after people would share it, they’d feel more at
ease to know just from their own perceptions of what they
would be comfortable with. How much they could-—and then it
would be like--I don’t know-J just think there would be more
of a reciprocal kind of feeling. I’ll push you, but next time you
push me. I think that’s what people would want.

Making Practice Public and Problematic and Shared

Lisa worked hard to articulate what it means to use her practice publicly, in a way
that would be meaningfirl and helpful to her. She figured out that in order to have the
digging, pushing kind of conversation that makes her think hard about her teaching, she
needs to identify a question around which the group will look at the videotape with her. It
was good and worthwhile to see what the others might see. At the same time, this
approach to the conversation constrained how the teachers talked together. The group
did not delve into a more complex level of talk.

In order to engage the group around a genuine question, Lisa realized she would
need to be willing to show her practice as problematic, “something that is awkward or not
handled well.” This need to make her practice public and problematic is linked tightly to
Lisa’s second criterion: others need to share in the experience of being vulnerable to other

teachers’ observations of their practices.

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Lisa’s concerns reflect her socialization into teaching that taught her a teacher’s
competence is measured largely by her performances of smooth, clear, “successfirl”
lessons. To disclose to other teachers the rough, messy, uncertain events in her practice
can be uncomfortable. This difficult public “scruntiny” (Little, 1990) of the messiness of
her teaching is necessary to “open up” to the pushing and digging and investigating that
she seeks. She believed it would make a difference if others had a shared sense from first
hand experience what it feels, sounds, and looks like to present their practices in this
public way. Then they would know “from their own perceptions of what they would be
comfortable with...” This would ready the group to up the ante and to push everyone’s
thinking. There would be a “reciprocal kind of feeling” about pushing each other.

As the first sharing of tape went, it was helpful to Lisa, but she wanted to gain the
benefit of pushing further into an investigation of teaching and learning. Lisa trusted the
IMT teachers, but she was seeing that, as a group, they would need to learn to stand on
that trust, to use their shared resource of predictable support and good will, to “dig in” to
their practices.

Lisa’s experience and her understanding of the group convinced her that to benefit
fiom using videotapes to stimulate conversations with her colleagues two changes needed
to occur in the group’s conversations around the videotapes: 1) the teacher showing the
tape needs to have a question/problem around which she wants the group to focus a
collective investigation and, 2) the other teachers/viewers need to experience making their

teaching practices public with a videotape of their work. These changes in the way the

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members interact with each other are changes in the social dynamics that shape the roles
and relationships held by individuals and guide the work of the group as a collective. The
dynamics of the IMT group, or of any group, argues sociologist, Erving Goffman (1963),
are governed by rules of behavior that direct members’ interactions within a “social
occasion” (p. 18). A next step in understanding the changes Lisa identified is to examine
them in terms of the rules of behavior that directed her first experience in sharing tape and

to explore how altering these rules might result in the kind of interaction she seeks.

Boundaries On Conversation, Boundaries On Learning About Teaching
Much of Lisa’s talk about sharing her videotape in an IMT meeting--her

preparatory talk and her reflective talk--focused on structuring, defining, the experience in
a particular way; even an open-ended, wait and see, approach is a structure. The structure
or boundaries that kept the [MT group’s conversation around Lisa’s videotape “safe” and
at a “base level” were the result of choices Lisa made and adhered to in the meeting. She
chose to “ease in” to the conversation, where the activities of the meeting did not deviate
much fi'om other group meetings. She chose what she thought was a “safe piece of
teaching”-without real problems she might be uncomfortable exposing. These moves on
Lisa’s part contributed to the boundaries that surrounded the group’s talk around her
video. We can think of these boundaries as the rules of behavior that directed the group’s
conversation. Though not explictly discussed by its members, the group’s discourse

around Lisa’s sharing of videotape was rule-govemed.

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What are these rules and where did they come from? Rules or norms, as Goffman
defines them, “are the kind of guides for action which are supported by social sanctions,
negative ones providing penalties for infraction, positive ones providing rewards for
exemplary compliance” (p.75). In the IMT group, the teachers draw on the social norms
of the predominant teaching culture to guide their interactions during a meeting. These
norms of collegiality, as teachers know them, direct the way they act or don’t act; what
they say or don’t say in response to another teacher’s practice.

In general, Goffman describes the relation between norms and interactions in this
way:

It can be argued that norms or rules impinge on the individual in two

different ways: as an obligation that requires him to do (or refrain from

doing) something in regards to others, and as an expectation that lead him

to anticipate righteously that something will be done (or specifically not
done) by them in regard to him (p.96).

As I described earlier, the prevailing culture of teaching reinforces norms of
politeness. Generally, teachers’ interactions follow a fine dance of attention and
helpfirlness that aims to support a friendly atmosphere (Johnson, 1990). But the dance as
it is constructed, for good and for bad, sustains a sense of privacy and individualism
around teachers’ own practices (Little, 1990; Hargreaves, 1993.) Through their early
socialization in the culture of teaching, teachers acquire and refine supportive, but “hands-
off” norms that gain them successfiil membership in a faculty. They become skilled in

knowing how to help without being pushy (Lorrie, 1975). When teachers do talk about

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their work, most are quite facile in talking about teaching without revealing the struggles
and uncertainties inherent in the practice. And collectively, they master ways of
exchanging information on teaching without linking it to an assessment of a teacher’s
actual practice (Newberry, 1977). As Feiman-Nemser and Floden (1986) report, teachers’
conversations address “politics, gripes, home life, and the personalities and family
background of individual students, rather than curriculum, instructional content, or
teaching methods” (p.509).

These “expectations” and “obligations” (Goffrnan, 1963), which preserve a culture
of non-interference, constituted the boundaries that delimited what Lisa experienced as a
first time, “base” level use of videotape in talking about her teaching. In order to move
beyond, to reset the boundaries, the expectations and obligations or rights and duties
would need to change. That is, what a participant is required to do or refrain fiom doing,
and what a participant can righteously expect will be done or not done must be altered in a
way such that the group can collectively investigate the particulars of a teacher’s practice.
In Lisa’s words, this change meant, “Open up to be pushed.” What she explored in her
reflections on the December IMT meeting was the creation of new norms that would
support making her practice public toward educative ends. To better understand the
relationship between Lisa’s call for a question for herself and shared experienced for the
others, and the changing of norms in the group’s conversation, it is important to first
understand the rights and duties that were at work when Lisa shared her videotape the

first time.

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The Egg hts and Duties in the IMT Conversation appund Videotape

The full seventy-five rrrinute conversation, fiom Lisa’s introduction of the
videotape until the group moved on to a topic distinct from Lisa’s video segment, has four
main components: introduction, viewing/discussing, discussion following viewing, and
transition to a new discussion. The discussion following the viewing of tape can be
marked ofl’ into six segments. (see Figure 4.) By count, there were 170 conversational
turns in this forty nrinute discussion, during which 56 questions were asked. The
question/response pattern of the group’s talk showed a strong pattern of one—to—one L
(Lisa) and M (IMT member) exchanges. This pattern became particularly interesting to
me when I saw that all but one (turn #168 of 170) of the 56 questions are questions asked

of Lisa by another group member.

Introductim Viewing/Discussing Videotape Discussion following videotape Transition
of Videaape 1 2 3 4 5 6 to next diswssion

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4. Three segments of the discussion following group’s viewing of Lisa's videotape.

In what follows, I look closely at segments two, four, and six from the discussion
that continued after the group viewed Lisa’s videotape. I selected these three segments

for what they illustrate about the patterns of talk in the IMT group and how members of

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the group, particularly Lisa, adhered to and, in one case, attempted to deviate from the
norms that governed their talk. The first example shows a clear pattern of questions and
answers. The second illustrates a break in the pattern of questions and answers, while the
group adheres to a set rights and duties for interacting with Lisa about her practice. The
third segment includes a possible shift in the rights and duties, but no uptake from Lisa.
My analysis of each segment includes an outline of the rights and duties that governed the
discourse among the IMT members. Together, these three examples illuminate the

boundaries that kept the group’s conversation at “a base level.”

Smart Twp: A Pattern pf Questions and Answers

In this first example, the second segment of the discussion, Lisa led the group in
defining the situation (Gofl’rnan, 1959) as a conversation about her students’
understanding of zero in a multi-digit multiplication problem. She did this by introducing
the tape in connection to the ongoing discussion of Sheryl’s problem of practice. She did
not We the situation as “bringing a videotape to the group for their help in grappling
with a particular issue”; remember, she was “interested in what other people might
notice.” In this way, Lisa “positioned” (Davies and Harre, 1991) herself and, in turn, was
positioned by the others to be a respondant. We can see in the discussion how she was
positioned by others to be a respondant, an informant, and even an expert about this
particular sixth grade classroom.

In this segment, IMT members asked Lisa questions about her curriculum

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and her pedagogy and she responded with detailed descriptions of what she is

doing in her classroom, how it compared to the previous year, and what she knew

about the problems in her students’ thinking:

Sheryl:

Lisa:

Carole:

Lisa:

What have you done with decimals up to this point? Lots of...

We’ve done a lot of representing decimals and thinking...the
way I went about it this year like we never talked about. . .tenths
as this is .1 this is a tenth. We talked about: You have 3 candy
bars and divide it among ten people. Then they talk about ways
to show that and we went into it through fractions. Then we
talked about how would you represent this with decimals. Then
they did it on the calculator they found they could do the
same problem on the calculator and get .3 so we talked about
that it means the same thing as something divide it into ten parts
and each part is a tenth. It was really hard because the little unit
cubes that second and third and fourth [grades] use as one...I
still have kids saying. . .when they’re using their model with the
base ten blocks...they have one whole, they’ve got tenths, and
then they’ve got ones. ‘What is that?’ ‘This is the ones.’ I
said, ‘Show me one whole again.’ They would say, ‘This is one
whole.’ ‘And this is a tenth of it and this is one.’ I say, ‘Why
do you call it a one?’ And they say, ‘It takes one hundred of
them to make a whole.’ ‘So what do you call it if it takes one
hundred of them to make a whole?’ ‘One!’ But it’s...This is
the first class that’s ever done that.

That’s when manipulatives came in.

Yeah. So they’ve got one whole, tenths, and ones. A lot of...it’s
been really interesting. Last year’s group, we did decimals and
fractions all together and they had all this background and
decimals were like...I don’t know if it was that they understood
it so much better because they were a much stronger group.
Skills wise. I don’t know if they understood it that much more
or if I just approached it differently so I just assumed more. I
never dug into problems like this. . .so maybe they did have these
misconceptions but I didn’t dig them out. But I...like I asked
them to write about what they knew about decimals before 6th
grade and they knew it involved a “point” and they drew

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Lisa:

Kathy :
Helen:

Lisa:

Marion:

Helen:

Lisa:

Helen:

Lisa:

Lauren:

pictures and they’d show 3.37 and they’d draw an arrow and
say see like this. Last year’s class when I asked them to write
about what they thought 6th grade would be about they said
we’ll learn more about decimals and fractions. This year’s
group when I asked them to write about what they thought 6th
grade math would be about said... ‘I think I’ll get better at my
multiplication tables.’ So... ‘cause I’m really bad at them.’

I would like to grab anyone that was one of the NTCM-—that
has their names on any of those books and have them come to
my school and tell my principal-

-Drill, drill, drill.
Did you ever do anything with negative exponents?

We didn’t touch it at all. I showed them 1 divided by 10 of the
first power and 1 divided by 10 of the second power and you
know so you looked at that pattern. And that was...in fact it
was a long time afier we had talked about tenths, hundredths,
and thousandths. So we kind of went back to that and picked it
up and showed the pattern cause I didn’t want to spend a long
time going into..then it would be ten thousandths, then it would
be a hundred thousandths, but I wanted them to see that it
would continue and that they already knew the pattern. So it
wasn’t anything like that. It was just lO,9,8,7,6,5,4,3,2,l,0...and
then it’s...l can see where...

Have you had them do that...have them take a number line and
a bunch of numbers and have them put it on the number line?

What happened?

There are a few kids in every class but still...if it was .5 or .87
but if it was 1.7 they accurately put it one whole and 7 tenths.

--space between two and one.

Yeah. Once they have a whole number in front of it like 2.2
then it’s fine; then they have a whole number to grab onto.

It’s like Jose’s idea that zero is a whole.

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Marion: 0.515 is ...... [inaudible]
Helen: So they’re completely clear that 2.24 is more than 2?
Lauren: but .24 would be less than--

Lisa: Well out of 30 kids maybe 2 or 3--I’d have to look. I don’t
know if anyone in my class did that. I know--

In this segment, the rights of the IMT members to ask, to comment, and to infer
about Lisa’s practice provide the structure to the conversation. There is a pattern of IMT
members asking questions and Lisa responding, adding information, and clarifying. Lisa’s
responses firlfill the corresponding duties that enable the group to sustain their dialogue.
Table 1 shows an outline of those rights and duties at work in this segment.

The IMT members’ rights and Lisa’s duties worked together to reinforce Lisa’s
role as expert informant about her classroom. Across the seventeen conversational tums
in this segment, the IMT members ask Lisa five questions:

- What have you done with decimals up to this point?

- Did you ever do anything with negative exponents?

- Have you had them do thatnhave them take a number line and a
bunch of numbers and have them put it on the number line?

- What happened?

- So they’re completely clear that 2.24 is more than 2?

Each time, Lisa responded with additional information, details, quotes of students’
explanations, and her own color commentary about the struggle to help students develop

conceptual understandings about decimals. Though Lisa had not framed a problem or a

question it seems the members were working on an assumption that Lisa was struggling

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with how to teach decimals. However, the group’s questioning seemed to be only a
general poking about, general questions about the kinds of work they had done and
whether or not she had addressed a topic.

Lisa IMT members

 

 

Right: to wait for group to determine next Duty: to make clear what they want to talk

focus about with a question or
observation
Duty: to respond, offering additional Right: to ask about Lisa’s curriculum,
information progress, accomplishment this year
Right: to offer commentary, opinion on Duty: to listen and respond to her
topic triggered by questions commentary
Duty: to respond with description and Right: to ask about pedagogical strategies
assessment for use or not use of Lisa has used

strategy and how it relates to topic

Duty: to correct or qualify members’ Right: to propose summation or inference
summary or inference from Lisa’s description

 

 

Table l. Reciprocal Rights and Duties for Segment Two of the Group's Discussion

By holding the right to “see what other pe0ple might notice”, Lisa assigned the
group members the corresponding duty to make clear what they wanted to talk about. By
holding the right to ask questions of Lisa, the group members assign Lisa the duty to
respond. But, additionally, by Lisa holding the right to wait and the duty to respond, the

group members are left unsure about what Lisa might want or be willing to investigate or

112

how to probe ideas with Lisa-~that is, how hard to push.

The rights and duties at work in this segment suggest that Lisa’s right to wait and see
bound everyone’s participation. The traditional norms for talking about her teaching
blocked her fi'om also holding a right to frame specific problem or question about her
work. As the conversation was defined and governed she was not in a position to ask the
IMT members questions that might inform her practice. Moreover, she was not
positioned, by the familiar rights and duties, to ask questions of herself publicly. Claiming
such a right would go against the norms that direct teachers to present themselves as
competent, smooth performing practitioners. To ask questions of herself would focus the
discussion in a particular way and Lisa wanted to see what others might see. Again, Lisa
positioned herself in ways reflective of the existing norms of privacy and sameness among
teachers.

Were Lisa to assign to herself the right to ask questions of the other members she
would have then assigned the group members a corresponding duty to respond with
opinions, examples, additional probing questions that seem to create the kind of
conversation that Lisa describes as pushing her thinking. It seems probable that this shift
in asking and responding would have altered the conversational pattern. There may have
been a greater likelihood that the pattern of questions and responses, directed by Lisa to
members, would not have been sustained. And instead, the IMT members may have been
positioned by Lisa as informants about teaching and learning, situated in Lisa’s practice,

but perhaps also drawing on their own practices and other references. It is likely the

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group members would still have asked questions, but they may have also offered probing
inquiries that reached beyond the information Lisa could provide because she was the

teacher, probing inquiries that pushed Lisa’s thinking and the collective thinking of the

group.

out F ur° A Break in the P ttern of ions n A ers
I now examine a second example of how the rights and duties of the group’s
conversation bound Lisa’s opportunties for deep, educative talk about her teaching. This
example is the fourth segment of the discussion, about fifteen minutes into the group’s talk
around Lisa’s videotape. There was a lull in the conversation and Kathy shifted the focus
to what it was like for her to watch Lisa’s teaching on videotape:
Kathy: I really liked watching your video. It made me feel better. [laughter]

Helen: It made me feel both better and worse because it was really neat to
watch but I realize how hard the ideas are.

Kathy: It made me feel like I could come into your classroom and learn math.

Lisa: Thank you. Even though it’s fiustrating and exciting to have them
...even when you see how much they’re confused about. One day we
were having a discussion about-Jose was saying that people were
taking 3000 and subtracting something--there was discussion about
how you borrow. Jamie went up and put up a whole number problem
3000 - 2000 or whatever, it didn’t matter, some situation that you
would have to borrow. She crossed off, everyone is saying crossed ofl’,
it’s 10; crossed off, and it’s 9; crossed ofi; this is 9; crossed ofl‘, this is
2.

Carole: I understand.

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Lisa: Everyone agreed that ....and that’s how it had to be and Jose said... I
was saying, ‘15 that the same number?’ Jose went up and said, ‘No,
that’s a larger number’ and he wrote 29910 and 3000. ‘See, this is a
five digit number and this is a four digit number.’

Lauren: How ‘bout you put it up on the board. I think then we imagine the
dramatics there. What they did.

Lisa: ...For dramatics he went and wrote them right on top of each
other...29910. He said, ‘It’s obvious.’

Kathy: So he put the one on top...
Lauren: What did you do?

Lisa: This is—we’re talking whole number subtraction and I kept saying,
‘Why are you getting those 9’s. Where are the 9’s coming from?’ They
said, ‘You are stealing.’ It’s called stealing. I said, ‘Then what are you
stealing?’ They said, You’re stealing from the three.’ I said, ‘What are
you stealing from the 3?’ They said, ‘A 1.’ Lisa asked, ‘1 what?’ Kids
said, ‘A 1 and you have 2 left.’ Then someone circled the 299 and said,
‘All you really need to worry about is the 299.’ ‘But is that 299?’

‘Yes. 299 and a 10.’ He’s a 6th grader...

Steve: That’s like the star...

Lisa: He said, ‘Mr. Miller said you can just circle the 299.’ That’s why I
would suggest keep going with connecting with the algorithm with the
concrete. Because if you go from the concrete to the algorithm they’ll
never they wouldn’t connect it back and if you don’t teach them the
algorithm they’re going to learn it some where and they might never
know why.

In this segment of the conversation, the group broke the pattern of questions and

answers. Kathy altered the pattern of the group’s talk when she made a reflective

comment about what it is like to watch Lisa’s teaching, acting in her duty to respond to

Lisa’s sharing of videotape, but not with a question to Lisa. As an observer, I noted that

115

Kathy is particularly sensitive to the importance of acknowledging that Lisa has offered
her practice for others to observe, comment on, and ask questions about. Kathy had
shared a brief clip of her own math class with the IMT group one time at the end of their
first year together. Also, she had shown videotapes of her own teaching in other
professional contexts.

When Kathy commented that she liked watching Lisa’s videotape, Helen followed
with a comment that had potential for shifting the conversational rights and duties. Helen
said, “It made me feel both better and worse because it was really neat to watch but I
realize how hard the ideas are.” Helen’s comment can be viewed as an invitation or
opening for Lisa to frame an issue, a question, an observation of her own learning to
teach Lisa acknowledged Helen’s affirmation of the struggle but she maintained the
boundary line on her “opening up to be pushed.” She told another classroom story,
sustaining her duties as a respondant in the conversation and an informant on her

classroom:

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Lisa IMT members

 

 

Right: to hear what the members think Duty: to respond to Lisa’s videotape and to

about what they see on her tape and the event of watching it together
what they think about watching in a
meeting

Right: to tell additional story, to use Duty: to respond to Lisa’s direction for the
comments to direct the conversation, by reponding to her
conversation story

Duty: to give a clear descriptive account of Right: to direct Lisa on ways to make her

the event she is telling about description clearer.

Duty: to respond to the connections Right: to make connections between her
members make between her descriptions, previous discussions,
descriptions, previous discussions, the video, and their own practices

the video, and their own practices

 

 

Table 2. Reciprocal Rights and Duties for Segment Four of the Group's Discussion.

Had Lisa claimed a right to ask questions of herself, she might have used Helen’s
supportive acknowledgement of how hard the ideas are to problematize the group’s
conversation and to explore more deeply what she and others understand about the
students’ thinking. She may have moved toward posing a question about how she or
others might work with or act on this thinking in class. This example suggests that it is
Lisa, the teacher whose practice is the site for situating the group’s conversation, who
holds the key to changing the norms—the rights and duties—that guide the conversational

work of situating an investigation of teaching and learning in one’s practice.

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n ix' P si le hift in he Con e ational ° hts and Du ics

Looking at the last part of the group’s conversation, I think we can see another
step toward creating Lisa’s right to frame an issue situated in her teaching and to engage
the group in an investigation that is stimulating and potentially educative in their
respective practices. Just before the group transitioned to a new topic, Helen modeled for
Lisa a question that would summarize the discussion the group had been having over the
past hour. She seemed to be suggesting something that could be explored as an inquiry, a
question stimulated by the videotape and the group’s discussion:

Helen: So one question could be...whether you could help them to a
way of thinking like—where, when the fifth grade teacher
proposes all of these things like stars and——they would ask him
why. Is that a natural thing? Can you?

Lisa: What are you saying?

Helen: I’m saying whether you could actually create a need in the kids
to understand why the next algorithm that they’re presented
with—when Sheryl’s kids go into 5th grade—is it possible that
they could ask a Mr. Michaels, when he tells them to put a star
in or whatever, ‘Why?!’

Sheryl: That would be the ideal. Unless you have—Nancy Baker’s
niece is doing some tutoring in my class and she is so frustrated.
She said, ‘I’m so fiustrated with a physics class and I keep
asking the teacher, ‘Why?’ And he keeps telling her
that...’you’re too much like your Aunt Nancy. Don’t ask why,
just do it.’ She doesn’t understand any of it. She said, ‘I can’t
believe he said that.’ She’s a senior in high school and is
getting a D in physics. Normally an A student and he told her
she’s too much like her aunt. ‘Don’t ask why. Just do it.’

As I studied this conversation, this segment stood out because of Helen’s opening

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remark: “So one question could be...” Situated in the larger context of the IMT group
and the group’s shared committment to understanding this kind of mathematics teaching
and to figuring out how to create such a practice, I infer several messages from Helen’s
comment. She was saying to Lisa, ‘one question you and we can ask...’ She was also
saying, ‘one question that this videotape makes me think about is....’ Further she was
saying, ‘this videotape is teaching us something about the complexity of this classroom
and how that complexity influences Lisa’s decisions and her actions as the teacher.’ Any
of these connections to Helen’s question is also connected to the group’s vision of this

kind of teaching. In terms of rights and duties, this segment has just two pair:

 

 

Lisa IMT members
Duty: to listen to members propose a Right: to propose a conjecture, question,
conjecture, question, summary, or summary, or inference related to
inference related to Lisa’s Lisa’s practice
practice
Right: to probe members’ comments for Duty: to elaborate on a proposed
understanding conjecture, summary, inference

 

 

Table 3. Reciprocal Rights and Duties for Segment Six of the Group's Discussion.

I think this exchange gives us a glimpse of the possible. In these few moments, we
see Lisa hold briefly a right to ask a question of a group member. And we see Helen
respond with a corresponding duty to elaborate on what she is thinking. Helen’s
hesitating, her partial statements, indicate her own struggle to work through for herself

what she is thinking.

119

Further, we see a group member, Sheryl, enact a right to elaborate, to respond to
Helen’s proposed question. In this way the question Helen posed was not heard by the
group as a question for Lisa, as informant, but rather, an inquiry for all the group
members to consider. Using this exchange as a working example, I can conceive of an
additional set of rights and duties that would begin to shift the conversational pattern and

engage the group member in a collective inquiry situated in Lisa’s practice:

 

 

Lisa IMT Member
Right: to ask Duty: to respond
Duty: to respond Right: to ask
Right: to respond Duty: to listen
Duty: to listen Right: to respond

 

Table 4. Possrble Rights and Duties for Lisa and the IMT members

These rights and duties are comprised of three actions, asking, listening,
responding. They hold a kind of symmetry that I think approximates what Lisa was
describing when she said, “I just think there would be more of a reciprocal kind of feeling.
I’ll push you, but next time you push me. I think that’s what people would want.” When
Lisa and the others hold a right to ask questions, the corresponding duty to respond is
also shared by all members and it carries potential for the group to collectively work their

way into a “digging” inquiry.

120

 

Sharing The Relational Work Of Creating New Norms

Stepping back from the language of conversational rights and duties, we can use
these examples from the group’s discussion to understand more deeply Lisa’s analysis of
what is needed for her and her IMT colleagues to use videotapes of one another’s teaching
in educative ways.

Lisa’s two new requirements for using videotape have strong ties to the relational
work of the group. Lisa trusted her colleagues in the IMT group. By fi'aming her viewing
session to see what they nright see, Lisa was trusting the IMT members to be afirrning, to
support her work, to attend to her and her practice in ways fitting with their past
experiences. But given her additional goal to stimulate a conversation that would push her
thinking, Lisa saw the need to frame a viewing session with a question of her own, more
specifically, a problem she wanted to investigate. From her first experience, Lisa
conjectured that if she posed a question of her practice in public the IMT members would
be more likely to join her in inquiry. Shifting the conversational involvement in this way,
shown in the analysis above as shifting the conversational rights and duties, may also
require developing the trust relations of the group in new ways. For Lisa to pose a
question about her practice she must trust her IMT colleagues to support her disclosure of
uncertainty about her own work, to listen deeply, withholding judgement and advice, and

to respond honestly about what they see, wonder, and understand.

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Builging and Stpnping on thg Trust of Qolleagpes

The connections between this deeptrust and new forms of conversation as a tool in
teacher learning is becoming more frequently addressed in the literature on teachers’
collegial relations. As educators, we know that trust is critically important to all learning
and development. Across all life experiences, we know the centrality of trust to growth in
fiiendship, in business, in parenting--in all sustained human relationships. From our own
personal experience we know the dangers and costs to life’s quality when trust is lost.

In theories of learning and development, trust is a construct most directly
addressed in developmental psychology. Erik Erikson (1968) described the struggle to
achieve trust over mistrust as the first critical crisis we must resolve as healthy developing
humans. In order to achieve further development we must achieve a sense of trust with
those on whom we are dependent and with whom we want to continue interacting.
Erikson also taught us that inherent in the ongoing work of identity development we will
have to negotiate and resolve crises of trust over and over in the course of a lifetime.

Perhaps trust is showing up as a topic in educational literature because there is a
kind of identity crisis, in the collective, as teachers and researchers struggle to develop
new identities adaptive to current educational reforms. Teachers are learning to be
researchers in classrooms. Researchers are learning to be students of teachers. Both are
learning to be colleagues capable of dealing with contradictions and uncertainties when we
explore and modify who we are and what we do. Reformers are asking teachers to

reconceptualize what it means to identify themselves as teachers and how they describe

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the nature of their work. In turn, researchers who are interested in working with teachers
as partners in inquiry are also struggling with their identities as colleagues who study
teacher learning with teachers. Lieberman and colleagues (1988) write that “trust and

rapport...are the foundation for building collegiality in a school.”

Trust and Dialogue

It makes sense that trust plays an important role in our efforts to learn and enact
the principles of collaboration. The collaboration sought by teachers and researchers is
centered on open, critical dialogue. In describing the dialogical relation, Burbules (1993)
quotes Patricia White’s (1990) observations on the role of trust in education:

Trust has a belief component (as many emotions do): the belief that you

can rely on someone or something where there is an element of risk. But

trust also involves a feeling, a commitment, that underlies and strengthens
the belief that one can depend on another’s goodwill (p.37).

Drawing on White’s account, Burbules highlights several aspects of trust in
dialogical relations. One is the notion that conscious effort is made by the participants in a
relation to create a context in which both participants feel safe to offer up their beliefs, and
the experiences or feelings that accompany them, even if they may provoke disagreement.
A second aspect of developing trust is the importance demonstrating trust, initiating our
own personal disclosures, before we ask others to trust us. According to White, over
time, the significance of the dialogical relation should engage the participants such that

conscious attention to establishing trust can move to the background, only to be nurtured

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alli

11C

in

and maintained occasionally. White cautions that the more attention that needs to be

given to establishing and maintaining trust, the more problematic and uncertain the relation

is. Additionally, Burbules highlights the especially pertinent risks at stake in dialogue:
We trust our partners to keep certain things that we say in confidence; we
trust our partners to withhold judgement upon some of our comments, at
least initially; yet we also trust them to tell us honestly what they think and
feel about a topic, even if it disagrees with us. In many ways the
firndamental risk in dialogue, especially perhaps in educational contexts, is
the risk of extending ourselves outward conversationally, endeavoring to
express as well as we can a point of view, belief, feeling, or experience in
the expectation that our partner will respond thoughtfirlly and
sympathetically, but not knowing if they will. The dialogical relation needs

to be developed over time so that we can establish and sustain this
confidence in the reliability of our partners, and they in us (p.38).

A commonality across these researchers’ definitions and descriptions of trust is the
notion that trust is grounded in a basic reliance on someone or something where there is a
felt sense of risk. We know about trust in the interpersonal interactions we have with
others and understanding it is often assumed because it seems so basic, so simple. But, is
it? Is trust so simple to understand when we are trying to significantly alter long-standing
roles and relationships between the university and the school, between researchers and

teachers? between teachers and colleagues?

Relational Work In Dialogue And Reforming The Culture Of Teaching

Why does the relational work seem so visible in Lisa’s moves and in her
descriptions of her experience? Why are relational issues bubbling up in so much of the

work on educational reform? (See for example, Witherell and Noddings, 1991; Lensmire,

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1992; Little, 1993; Hargreaves, 1994.) What is happening in our classrooms and our staff
rooms and our university project rooms that prompts us to appreciate the importance of
human relationships in learning?

Teachers and researchers engaged in efforts to reform teaching, guided by social
constructivist views of learning, are necessarily drawn to examine the complexities of
learners’ interpersonal dynamics and the ways these dynamics help or hinder participants’
learning. In classrooms, teachers struggle to understand students’ peer relationships and
figure out what it takes to develop learning communities in which children interact with
each other as resources and guides for subject matter inquiries. In his study of children’s
relations in a third grade writers' workshop, for example, Lensmire (1991) describes the
influence of the peer culture on the "classroom's official work of producing and sharing
texts. " In professional development work, researchers and teacher educators grapple with
ways to create and sustain collaborations with and among teachers (Little and
McLaughlin, 1993; Mtherell and Noddings, 1991; Lieberman, 1993; Hargreaves, 1994).
Among numerous possibilities for powerful outcomes of collaborative work is the
continual development of a teacher's sense that her learning is supported, in critical but
trusted ways, by her peers.

Current irmovations in professional development work press for teachers to
situate their continued learning in their own practices, to talk openly and in detail about
their beliefs, decisions, and actions as teachers (Little, 1993; Lord, 1994). Reformers

press for teachers to make their practices public. This call is based on principles of

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learning that emphasize the importance of making explicit one's understanding and one’s
uncertainties about the practice of teaching and drawing on the richness of multiple
perspectives of others as a resource for continued learning. Much of the writing about this
call seems to imply that altering expectations, structures, and activities will result in
teachers knowing how to create and sustain the intellectual engagement aimed for by the
innovations. My work with the IMT group, and with Lisa in particular, has shown me,
however, that teachers need vivid images, a range of models, and practical understandings
of what deep, trusted, critical support looks like and, perhaps most importantly, what their
role nright be in creating it.

Trusting collegial relations can be the connector (see Figure 5) between the
existing culture of teaching and the new culture envisioned in the reform documents. As
teachers trust in the images of what's possible, they have the opportunity to use what they
understand about the existing culture of teaching to develop conversational skills that will
transform their conversations from shields of privacy to critical examinations of practice.
As teachers trust their own conversational capacity to engage in critical conversations,
they begin to act according to new norms and to craft for themselves new roles within the
culture of teaching. As teachers trust each other as dialogic partners, where judgement is
withheld and professional honesty is emphasized, they begin to interact according to the

envisioned description of reform-oriented practitioners (Little, 1993; Lord, 1994).

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AWARENESS or EXISTING CULTURE CONVERSATIONAL SKILLS

Trust in images of the possible

 

   
 

Trust in others
Trust in self

NEW CULTURE or TEACHING

Figure 5. Connections between trust and a new culture of teaching.

Learning About The Culture Of Teaching

Lisa’s experience and her sensemaking about it help to identify aspects of the
learning that surrounded her attempt at a conversation that was situated and analytical.
Throughout her work, I think we see Lisa possessing and using a tacit knowledge she has
constructed about the culture of teaching. It is tacit knowledge in that she does not talk
about rights and duties or beliefs or customary ways of interactions. She does not analyze
what is needed in terms of cultural norms, participants’ roles, or trust relations. Rather,
her words and her actions suggest She intuitively understands what serves as an

appropriate approach to presenting her practice to a group of peers, how to present

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herself, and how to take and keep the conversational floor, all with concern for preserving
the cohesiveness of the group and her good standing as a member.

Lisa was able to launch her efforts at using this new form of sharing her teaching
by drawing on an old form; Lisa used her knowledge of and experience with telling stories
of her teaching or talking about her practices to design her first sharing of a videotape of
her teaching. The way she chose to show her tape, with consideration of the other
members of the group, the meeting agenda, and the general open-ended approach to the
discussion reflect the existing culture of teaching and the way practices get shared.

Lisa’s behavior also illuminates how she is learning about of a different culture of
teaching. She described what worked and what didn’t work in the IMT meeting in ways
that suggest she was comparing the experience with images of what is possible. From her
early participation with the IMT group she had gained a beginning sense of what can
happen in a teachers’ conversation that looks critically at teaching and learning and how it
can be helpful to her in making changes. She had experienced conversations in the IMT
group that were radically different from any teachers’ conversation she had had in a school
setting. She was developing relationships with these teachers that were different from
relationships she knew with other faculty members. She came to the December meeting
with images of the possible inquiry that sharing a slice of her practice could ofi‘er. She
came with a sense for what that conversation would look like, sound like, feel like when
they as a group created it. Using this awareness, Lisa analyzed her experience of sharing

her videotape for the adaptations needed to achieve the educative conversation she

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31'!

kid

like

desires. These images of the possible drove Lisa’s interest in this exploratory work and
guided her actions and reactions so that she might intentionally create what she had
spontaneously experienced in previous interactions. It seems difficult to argue that Lisa
could have analyzed and interpreted the experience as she did if she did not already
possess this awareness of what’s possible.

The call for teachers to become attentive, to become analytical, critical students of
their work is a call for an intellectual engagement of the kind traditionally conducted by
educational researchers. A first step is for teachers to gain a conscious awareness that
their work has cultural definition and direction. Awareness that there is a culture of
teaching that directs teachers’ ways of interacting and awareness of what is possible when
guided by different norms is only part of the work in transforming professional talk among
teachers. Lisa’s work also illuminates the need for skills to create and participate in the
intellectual work of critical conversations.

The IMT group and the event of sharing videotape created a context in which Lisa
and her colleagues worked on understanding and developing skills needed for a different
kind of conversation. The IMT group provided a transitive support community (Bruffee,
1993) for Lisa and potentially for others to construct the knowledge and to develop the
skills needed to talk with teachers from a different cultural base. Lisa’s sharing of
videotape was situated in a group that was working hard to move itself, as a collective,
away from the traditional culture of teaching. The IMT teachers identified themselves as a

group set apart from their respective home faculties and they saw themselves as different.

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of
PM
me!

exp

And indeed, they were engaging in new workuconversations, storytelling, studying
videos, reading, writing—that they were not finding in their home faculty meetings. In the
IMT meetings the teachers gave lengthy descriptions of what happened in their
classrooms. They talked about what was hard, what was troubling, what wasn’t working.
They were developing and sustaining relationships they didn’t have elsewhere, learning
how important a sense of trust is for talking with another teacher (F eatherstone, Pfeifl‘er,
Smith, 1993; Featherstone, et al, 1993). But it is not the case that these teachers walked
out of the traditional teaching culture, cleanly leaving it behind for another. Made visible
in Lisa’s foray into using her videotapes is, I believe, the fitfirl emergence of a new culture
and the struggle of individuals who must negotiate their identities and their interactions
within it.

Next, in Chapter 4, we will see Lisa situate her skill development for educative
conversations about her practice, using videotapes of her teaching to prompt
conversations with me. In important ways, Lisa’s decision to wait before sharing tape
again provided her with time and space and potential opportunities to learn about the kind
of teacher conversation she seeks. As her partner in this inquiry, I helped her create a
practice context for this work. I served as a kind of “portable IMT group” that could
meet with her after school to work on this. I brought with me the history, shared

experience, and visions of what intellectual work in a teachers’ group could be.

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CHAPTER FOUR
Learning A New Kind Of Conversation About Teaching
“ ...it never would have crossed my mind to consider what we do in the IMT

group [ to be] curriculum development, but when you think about what we
do, in every sense of the word it is curriculum. "

Lisa, 1-19—93

Teachers talking together about their teaching practices presents a paradox.
Teachers are good conversationalists about the daily activity of classrooms, yet deep,
educative conversations about teaching are rare, difficult, and risky. Research on teacher's
conversations (Little and McLaughlin, 1993; Johnson, 1990; McLaughlin and Yee, 1988;
Goodlad, 1984; Lieberman and Miller, 1978) suggest that teachers limit their talk about
teaching to generalized comments, reports, and descriptions of successful lessons and the
swapping of creative ideas for instruction.

Still uncommon are teachers' detailed discussions of problems in the classroom.
Still rare are teachers‘ sharing of their beliefs and their theories of teaching and learning in
ways that support their development as practitioners. Using one's own teaching
experience to create educative conversations calls on personal skills not taught and
professional norms of interaction not supported in traditional school culture (Little, 1993;
Lieberman, 1988).

In a chapter entitled, Education as Conversation, Kenneth Bruffee writes a

compelling description of the relationship of conversation to learning and the construction

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of knowledge. In his simplest terms, “Good talk begets good thought” (Bruffee, 1993,
p.114). He argues the position that ‘Rve can think because we can talk with one another.”
Drawing on Vygotsky’s demonstration that thought is social conversation internalized,
Bruffee writes:

Ifthe talk within the knowledge communities we are members of is narrow,

superficial, biased, or limited to cliches, our thinking is almost certain to be

so, too. Many of the social forms and conventions of conversation, most

of the grammatical, syntactical, and rhetorical structures of conversation,

and the range, flexibility, impetus, and goals of conversation are the

sources of the forms, conventions, structures, impetus, range, flexibility,

issues, and goals of thought (Bruffee, 1993, p.114).

With an aim to engage teachers in situated and detailed conversations that employ
forms, conventions, and structures of close scrutiny of actual practices and a goal of
similarly critical thought in action, educators are challenged to create opportunities and
contexts for teachers to observe, model, and practice such conversations.

In this chapter, I look closely at a set of conversations I had with Lisa during
January and February of our year together for what they illuminate about a teacher’s
learning of a new kind of conversation about teaching. These opportunities came in the
aftermath of Lisa’s sharing a videotape of her teaching in an IMT group meeting and her
decision to wait before sharing tape again, until other teachers in the IMT group had done
so. Contributing to her decision to wait before showing tape again, Lisa wanted to think
more about what question--or, as she called it, “video dilemma”--she would take back to

the group when she did share tape again. How might she engage the group in a “deeper”

analysis?

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In January, 1993 Lisa and I met for two 3-hour meetings. We met in her
classroom at the end of the school day and we brought the videotapes from December,
our notes, our journals, and our current thinking about using videotapes and about recent
events that were influencing our ideas. These meetings illuminate Lisa’s efforts to try out
ways of framing a teacher’s conversation as an analytic, critical close look at her practice.
In the conversations, we used instances from her own recent teaching as the site for
investigating what she and others understand, believe, ponder, and do to create a reformed
mathematics teaching practice.

Through Lisa’s experiences in an alternative undergraduate program and
opportunties through her continued connections at the university, she was already
committed to the use of conversations about teaching as a valuable tool in learning to
teach. But knowing that they are important and becoming knowledgeable and skilled in
how to create and sustain them are separate achievements. In the three vignettes to
follow, we see Lisa shape our conversational workspace to work on various aspects of
dialogic participation specific to an exploration of teaching: (1) practicing the skills of
articulating what she wonders about in her daily practice, (2) framing questions about the
fit between belief and action in her pedagogical moves, and (3) negotiating for herself new

meaning for language she must use in talking with other educators.

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Conversational Workspace 1: Learning To Articulate Questions About Practice

Lisa started the videotape and let it play as we settled into what we expected
would be a long conversation. We ignored the audio and glanced at the action as we
talked about other things. Here and there a visual image on the screen triggered a
comment or question. I saw Mandy, for example, and asked how she was adjusting as a
new student in the school. Lisa reported that Mandy was doing well, but that she was
worried about another new student, a boy, who seemed really sad the last couple of days.
As images of her students passed across the screen, Lisa vented her frustration with trying
to help another student who seems to be forever complaining and putting herself down.
She joked about a hidden advantage in working with videotape, that it’s fun to be able to
stop the action or look again; and sometimes, it is just fun to fast forward over it all!

Lisa fast forwarded to the segment she had Shared in the December IMT group
meeting and said that she wanted us to watch the same clip. It had been almost a month
since I had been out to visit Lisa at her school and longer since I had seen the students.
AS I watched, I could feel my own connections to individual students and to the
personality of the class as a group reawakening.

The tape continued to play and Lisa and I continued to talk as if it was providing
background music to our conversation. With an eye on the monitor and both of us still
opening notebooks and finding pens, Lisa provided me with an update on what was

currently happening in the classroom. Lisa described her efforts to again “get them

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cooking in decimals” afier the holiday break and her intent to move into the multiplication
of decimals by first revisiting the multiplication of whole numbers. She talked about how
it felt like slow going and that one challenge was introducing and practicing new
vocabulary necessary for having these discussions. Her assessment was that the
discussions don’t feel very adventuresome: “They just feel dead.”

“Oh, here we go.” Lisa raised the volume on the audio and we turned our
attention to the video. We watched and we continued to talk, now recounting the IMT
meeting when Lisa showed this clip of her classroom. The videotape continued to play and
Lisa reflected again on the Opening conversation with Sheryl in the IMT group. I was
aware that we were watching the tape but it was not clear how it was functioning in our
conversation. We certainly were not studying it. As we continued to our conversation, as
if we were also occasionally attending to a old television rerun, the voice of Jamie, a
leader in the classroom, drew Lisa’s attention to the monitor and she laughed,
“Sometimes, I hear Jamie’s voice and I think it is me.”

We both became engaged with the activity depicted on the screen and we watched
more attentively as Susan prompted her classmates, “It’s likeu’member when we were
doing the which is greater, .51 or .511 and they were --er--it wasn’t that--it was like some
number with a zero on the end and they took the zero away and they said it was still the
same thing.”

Lisa stopped the tape and she said to me:

It’s sometimes interesting when they refer back to other discussions. And
I’m always wondering what they’re going to say. Like, what their

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recollection of the previous discussion... Like, are they going to say
somebody’s argument, or are they going to—like when she said, ‘One had
two numbers and one had zero on the end and they took off the zero and it
was still the same.’ Who’s ‘they’? Who [is she] thinking of? Class in
general? Or, does she remember somebody doing that and somebody
proving it? What do they take away from that discussion? Because, I
think about the kids like, at the end of the year, they still say, like, when
they give me advice for what I should do next year, they say, ‘well, you
know, I really think you should give the kids the answers because we really
never knew what the right answer was.’ So I’m always wondering when
kids feel comfortable that they know if it’s right or not. Like, do they ever,
I’m always anxious to hear, do they ever say, ‘when we decided that they
were the same.’ Or I’m afraid to hear, ‘Well, Mrs. Pasek told us’. If I
seem to be in agreement that they’re the same, do some kids interpret that
as, ‘okay, it must be right, because Mrs. Pasek is agreeing or she seems to
be agreeing.’ Or, I guess it’s, you know the mathematical--who decides
mathematical validity? And it comes out, it could come out when they talk
about previous discussions, but I am never quite sure.

I commented to Lisa that it seemed the students in this class do a lot of the
referencing she has observed. Here, they referred to a previous class session. And at
other times I had heard them refer to other school years and other teachers.

Lisa agreed that the students do draw on other sources. She added that at least
weekly, someone will say in class, “Well, my mom showed me this”, or “I remember this
from before.” She noted that this was good because it showed they were taking the
“initative to seek out other sources.” Lisa then told of a boy in her class who had asked
his mom about the problem 8 x 5/8 = 5:

Lisa: He had asked his mom, I asked them, we were talking about
whole numbers times decimals and I was having them put up
problems that they thought were interesting that we could
discuss, and see if they made sense. And one of the problems
was eight times five eighths equals five. And it was kind of at

the end of the hour and I asked them if they would--we talked a
little bit about it and I asked them if they would Show a

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representation of it. And that same boy had asked his mom--it
was funny, because the way he worded it was so cute-~he said,
‘I asked my mom how she would make sense of eight times five
eighths equals five.’ Just the way, ‘how She would make sense
of it.’ Not, ‘how she would answer it’, you know. Because
they had to draw a picture, maybe that helped. ‘How she
would make sense of that.’
Lauren: Picking up your language.

Lisa: Yes. And probably that was different than if I had asked them
to solve it.

Lisa began the videotape again, marking the end of this segment of our dialogue
and redirecting us back to the classroom record to see what else we might see. Lisa’s use
of the videotape in this dialgoue resembled her use of it in the [MT meeting in December.
We seemed to be exploring the tape to see what might be provocative, interesting to
comment on, or puzzling to investigate. However, our interaction differed fi'om the IMT
meeting in an important way. In our viewing session here, Lisa stopped the videotape to
raise with me something she was wondering about. In this way, our work seemed to align
with Erikson and Shultz’s (1981) approach to videotape viewing sessions. I think what
we were engaged in builds on Erickson’s and Shultz’s analysis protocol in that the images
served to contextualize a new conversation about teaching; what we talked about was not
directly observable in the video record.

Our dialogue about the struggle to understand the children’s use of language for
what it might tell us of their sense for mathematical validity lasted four minutes. But in

this brief exchange, Lisa used her videotape to situate our conversation in a way that

137

seemed productive to her and seemed to assist her in articulating a line of thinking she had
been considering over time. In one conversational turn, Lisa used six difl’erent phrases
that repeatedly conveyed that what she was describing is part of her in-action wondering
about what her students mean when they say “they”:

It ’s sometimes interesting when

And I ’m always wondering

So I ’m always wondering when

I ’m always anxious to hear,

0r I’m afraid to hear,

.. but I am never quite sure.

(transcript 1-12-93)

Lisa seemed to be acting on her desire to revisit the videotape for questions she
might pose to the group that would push her thinking beyond a show-n-tell. In our
telephone conversation on January 6, Lisa had said, “...it would be interesting to go back
to the same tape and have a question. Get at the same thing. Look at the same thing and
dig deeper, or um, kind of open up to be pushed a little bit about...” In deciding to watch
the same segment of videotape when we get together, Lisa seemed to move strategically
toward her goal, “mustering resources” (F eatherstone & Smith 1996) that would help her
return to the group and use videotape in a more analytic way.

Indeed, she seems to be tailoring a resource she already had-~our collaborative
study--to learn how to identify and articulate her uncertainty about this discourse-based
approach to teaching. Lisa knew I was familar with her classroom and her teaching and

this particular videotaped class. Perhaps this sense of familiarity, a viewing feature she

138

referred to in her reflections on sharing tape with the group, encouraged our use of the
tape as more of a stimulus for dialogue about teaching than as a show-n-tell example of
her practice. But I also think her new awareness about her needing to raise a question or
frame an issue was shaping our work in this viewing session.

In the [MT meeting in December, Lisa had shown the tape and waited for the
group to respond. Here, she stopped the tape and pointed to a specific instance of
classroom activity and then used that instance to engage me in dialogue about the
challenge of understanding her students’ thinking by studying what they say in class. She
questioned what she can interpret from their comments. In other words, she moved again,
strategically» to create a dialogue that would be productive, educative for her. By posing
the questions, for example, “Who is ‘they”’? and “Who decides mathematical validity?”
Lisa was working actively to engage a reciprocal set of rights and duties within which we
both could wonder about and investigate a vision of reformed mathematics teaching,
situated in her practice.

In his chapter on the rules of the dialogue game, Burbules (1993) draws on
Habermas’ (1984) theory of communication to show how dialogue is situated in a
relational context, that it is grounded “in conversational processes of persuasion and
intersubjective explorations” (p.75). Habermas identifies “strategic” forms of
communication and “communications oriented toward understanding.” Strategic forms of
communication, like the example above, concern purpose and ways of gettinguin a speech

act--what one needs or desires. Communications oriented toward understanding are

139

linked to a commitment to validity claims of comprehensiblity, truth, sincerity, and
rightness.

In addition to its strategic features, Lisa’s choosing to re-view with me the same
segment of videotape she showed to the NT group reflects communication oriented to
understanding. She used the videotape as a tool to help her communicate her thinking
about a complex aspect of her teaching. That is, Lisa used the videotape to point out an
example of student talk and then used that example to begin working with her uncertainty
in understanding that talk. By trying to help me understand what she saw on the tape as
an example of students building their authority with their peers, Lisa worked on getting
clearer for herself what that looks like and how to talk about it. So her work was two-
fold: Lisa was explaining to me the students’ thinking and she seemed interested in my
thoughts. Moreover, she seemed to be practicing her articulation of a complex aspect of
her work that she has mostly wondered about privately. She moved her thinking into a
public space (Harre, 1984). Revisiting Duckworth’s description of the power of verbal
explanation, Lisa was deeply engaged in sensemaking. Our conversational workspace was
supporting the social “public” context in which she could construct meaning.

I think it is important to reiterate that the videotape served as a stimulus for our
conversation; the substance of what Lisa and I talked about was only prompted by the
example she saw in the video. The videoclip image helped Lisa articulate how she thinks
about trying to facilitate students’ taking an active role in deciding the worth of ideas an

conjectures posited by their classmates.

140

for t
this

clas

the

her:

It is one of Lisa’s aims that the students will come to see one another as resources
for their own learning. In the Professional Standards for Teaching Mathematics (1991),
this aim is stated as a standard which shapes a new and different role for students in the

classroom:

 

STANDARD 3: STUDENTS’ ROLE EV DISCOURSE

The teacher of mathematics should promote classroom discourse in
which students—

0 listen to, respond to, and question the teachers and one another;

0 use a variety of tools to reason, make connections, solve problems,
and communicate;

a initiate problems and questions;
0 osmium examples and counter examples to investigate a conjecture;

0 try to convince themselves and one another of the validity of
particular representations, solutions, conjectures, and answers;

 

 

o rely on mathematical evidence and argument to determine validity.

 

Figure 6. Visions of the students’ role in discourse.

(From National Council of Teachers of Mathematics, 1991, p. 45)

Susan’s comment, (“Remember when they took off the zero...” ) is an example of
the student talk Lisa listens for in wondering about who or what counts as an authority to

her students in a mathematical discussion. Using what Tannen (1989) calls constructed

141

dialogue, Lisa talked through with me what her students say, what she listens for (e. g.

‘Vvhen we decided...”), and what she fears hearing (‘yvhen Mrs. Pasek told us...”).
Prompted by the example on the tape Lisa made explicit the complexity of

helping turn students away from the teacher and books as their only authorities in

the math discussions and of encouraging students’ ideas, conjectures, and

arguments as resources for one anothers’ understanding. Through her talk, she

gave meaning to a standard she knows as a key principle in the reformed view of

mathematics learning in school. Looking again at Lisa’s words illuminates how

she was working on—practicing—how to link her understanding of a particular

instance in her classroom to a standard that she knows to be central to the reform

oriented practice she is creating.
“...I 'm wondering who is “they

...I am always wondering when kids feel comfortable that they know if it
is right or not...

...I guess it ’s the mathematical-m decides mathematical validity? ”
In this talk, we see Lisa move from a description of her experience to a rough
version of the question to a formulation of the big idea, as she has read it in the reform

literature (NCTM, 1989; 1991). She began literally, wondering what the children mean

when they use the reference “they.” She then explained what she means when she says

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she is ‘Vvondering.” And in the last turn, she linked her wondering to language she has
read and heard used by reform-oriented educators. She constructed meaning for a
statement included in the Standards vision of mathematics teaching (try to convince
themselves and one another of the validity of particular representations, solutions,
conjectures, and answers) and this meaning was situated in her own classroom
experience. When Lisa said, “I guess it’s the mathematical-win; decides mathematical
validity?” she linked this aspect of teaching for understanding to what happens in her own
classroom, what it looks like for children to take responsibility for determining

mathematical validity.

Conversational Workspace 2: Learning To Be One’s Own Knowledgeable Other
Lisa’s vision for her classroom includes having her students feel valued as thinkers,
“where [they] have a chance to think mathematically and have ownership of their ideas and
feel empowered and in control over deciding what makes sense and what doesn’t.”
(interview with Lisa, August, 1992). Understanding her role in fostering this ownership
and empowerment in her students and knowing how to enact it is not easy.
The National Council of Teachers of Mathematics describes the teacher’s role in

discourse as follows:

143

 

 

STANDARD 2: TEACHER ’S ROLE IN DISC OURSE
The teacher of math ematics should orchestrate discourse by -

o posing questions and tasks that elicit, engage, and challenge each
students ’ thinking;

a listen carefully to students ’ ideas;
0 asking students to clarify and justify their ideas orally and in writing;

a deciding what to pursue in depth from amng the ideas that students
bring up during a discussion;

0 deciding when and how to attach mathematical notation and language
to students ’ ideas;

0 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;

a monitoring students’ participation in dicussions and deciding when and
how to en courage students to participate.

 

Figure 7. Visions of the teachers‘ role in discourse.

(From National Council of Teachers of Mathematics, 1991, p. 35)

Deborah Ball, (1996) a participant in the writing of the NCTM Standards,

writes about the undetermined nature of the guides and the challenge they pose to

teachers to situate the vision in their own practices and to articulate for themselves

the meaning these standards have in the particulars of their classroom.

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In Ball’s words:

[I]t is not just that the reforms represent dramatic changes in belief and
ideology that makes the changes evisioned complicated to attain. The
reforms are also undetermined guides for the minute-to-minute, day-to-day
work of practice... Even when supported with detail and image, these
visions cannot show teachers what they should do with particular students,
around particular topics, in a specific school community. The ideas of the
reforms--the portraits of the possible, images of the firture--are resources
for practice not prescriptions. Nor will we ever reach a state in which
those prescriptions can be authored (p.4).

Lisa was attempting in our work together to draw on the videotaped images as a
resource for her practice. We finished reviewing the fifteen-minute video segment Lisa
had shared with the IMT group. I suggested we continue by watching the next day’s math
class. Watching the videotape, Lisa observed herself writing on the board a conjecture
offered by Allen, one of her sixth grade students. She said to me:

Lisa: ...Another thing that I noticed is that um, a lot of times, in

Deborah Ball’s classroom, she would write up conjectures or
write up problems that people were giving examples of. And it
seemed to just flow right in and I don’t know if it’s me, I guess
I’d have to look at different examples of it, but I always feel

like, even to just do that, it takes the ball away, to an extent.

Lauren: To do what? To take their conjecture and put it up on a piece
of paper, on the board?

Lisa: For me to say, okay, your example is this, and for me to write
it.

Lauren: To restate it. Yeah.
Lisa: I just kind of feel like... But I’ve seen it, other people do it.
Deborah is writing up problems and it doesn’t seem to afi’ect, so

I don’t know if it’s just my perception or I feel like I’m getting
too into it.

145

Lauren: You’re talking about when you restate the idea or even just
putting it on the board for them.

Lisa: Yeah.

Lauren: That’s sort of interesting to me given that Ijust taught that class
this morning and how much I caught myself being aware of that
and restating pe0ple’s ideas and trying really hard to literally
restate what they were saying for the group. I guess I think
about that as facilitating and orchestrating. Um, but I can see
the question of how much is that infringing upon their
ownership, of it being their idea and they already made the
statement, so why are you dancing on my statement... But at
the same time, I guess I find myself doing it, or seeing Deborah
doing it as a way of um, sustaining the thought. Keeping it
from being lost or somebody having only heard half of it. I
don’t know. I guess I don’t think about it as being too
infiinging but I can see where that’s a question.

Lisa was articulating her concern about the message she is sending to her students
when she restates their ideas. ' She had observed other teachers document students’
contributions in class. Specifically, she had watched videotapes where Deborah Ball
writes a student’s conjecture (e.g. Any number below zero plus that same number above
zero equals zero.)10 and posts it in the room where students can refer to it, comment on it,
and offer evidence to support or refirte it.

For Lisa, observing herself making the same sort of move raised an issue that
hadn’t come up in her observations of others. She noted that when she restates or writes

out a student’s idea, it doesn’t feel as smooth as it looks for others. She offered qualifiers

 

1° See Ball (1990) for a description of her third graders’ work with this conjecture and “the dilemmas of
her role, of authority for knowledge, and of the clarifying/confirsing tensions inherent in group
discussions...” (p.19).

146

for her uncomfortableness (“I don’t know if it is me...maybe it’s my perception), but her
concern was that she might be jeopardizing her student’s ownership of ideas—“taking the
ball away”—and this is a feature of her classroom that she values deeply.

Lisa’s concern was also an investigation of the fit between her actions and her
purposes. We worked together to lay out the multiple cuts she might take on this
dilemma. Lisa tried‘on another example, not viewed on the tape, but prompted by it. She
said:

Lisa: Like, today there were some problems and I come in and jump
in and say, okay, let’s write that one up on the board and I
wrote it up on the board and I kind of felt like or maybe it’s just
me being leery of that feeling of whenever I’m up on the board
I’m going to start talking too much, I’m going to start taking
over. Or maybe it doesn’t happen, it’s just my perception.
Because like, in one class, they were having trouble getting
started with some problems. So I kind of led the class through
like, ‘try this one, what do you think it would be? Try this one.
What do you think it would be?’ Two times three tenths, two
times three hundredths, and I kind of gave them a model and I
felt like it was very directed. I think that was what they needed
to get them to handle the strategy for looking for patterns.

Lauren: Which reminds me, as we’ve said before, sometimes it’s
appropriate to be directive. So, sometimes it’s calling that right
shot.

Like the first example in this chapter, Lisa was creating for herself a dialogue that

would support her practice with fi'aming and articulating a dilemma stituated in her

practice. The videotape played an important role in representing her practice, stimulating

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her thinking and drawing me in as a dialogic partner. Once again, she seemed to be
approximating a different set of rights and duties (See Table 4 on page 120) than had
shaped and bounded her conversation in the December IMT meeting.

This second example is helpful in another way. It serves as a context for looking
closely at analysis skills Lisa was acquiring through her dialogue with me around her
videotape. Lisa began by analyzing her actions in the classroom for the possible messages
they send to her students and how these messages may affect the roles she is trying to
craft for them and for herself. By talking through her observation, Lisa shifted the focus
of her analysis away from what her writing on the board might convey to her students and
she began to question her insertions, her restatings, her possible stepping on student’s talk.
She recognized and articulated how being at the board to document a student’s ideas, also
physically positioned her to talk to the whole class--a classic image of the teacher
“teaching” and in Lisa’s words, “taking over the discussion.” This shift in the focus of her
talk seems to represent the kind of “digging” in that Lisa seeks.

As we talked, Lisa repeated her qualifier, “perhaps this is just my perception.” I
see this moment now as a missed opportunity. It may have been fortuitious for either of
us to suggest that we study the tape—segmenting it, reviewing it—to assess the extent to
which she is talking at the board, to investigate her speaking turns for their duration and
their content (Erickson & Shultz, 1981). To do so, would have firrther supported her
analysis and helped her connect images and language to her understanding of the standards

she enacts.

I48

However, from another angle, having missed this opportunity, Lisa continued
casting a wide net in exploring her practice. She drew on another story of another
instance that fit with her query about physical moves and their messages. Her perception
of this second instance was that she had been directive, a debated, bad word for many
teachers struggling to embody the standard for children’s active leadership in classroom
discourse. Lisa offered a rationale for her move, but she added that she feels uncertain
about its impact and its cost to her goals. In this next segment of our dialogue we see Lisa
continue to analyze her use of directed dialogue, and the reasoning behind her decisions to
make such a move. She said to me:

Lisa: Maybe, ...Because it always feels very easy to get into. You
just kind of fall back into it.

Lauren: Fall back into it as in old traditional ways? Fall back into what?

Lisa: Fall back into, I’ll say this, you say this back. I’ll say this ..... Or
even um, hmmm, or sometimes when I’m, and maybe I use it
too when kids are stuck in, because today the kids, we had a
half hour switch and it was hard to get going and sometimes if I
feel like the kids are sort of sleeping, I’ll ask a question and they
all should be able to answer, and I’ll say, ‘Say it if you know it’,
and encourage them to chant, or whatever.

Lauren: At least you don’t make them stand up next to their desk.

Lisa: Yeah. ‘Four times seven, say it if you know it.’ It kind of
serves a purpose too, to get the blood pumping. I am actually
um, working a little bit on times tables using the meter tape,
because we’re getting into fractions and they’re going to be
finding common denominators and thinking about how to split
these fractions into same size pieces. There’s a lot of kids that
don’t know their times tables. So that’s like, my meager
attempt.

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Lauren:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

To drill?
Yeah. ...count by sixes and sevens.
Great. I think that’s a neat idea.

I don’t know, it’s interesting to catch myself going, six and
seven is.... And I made it this far.

Now wait. I want to ask you a question. This is an interesting
topic here, you’re feeling like that’s--are you--that’s what you
were feeling when that was going on, or are you looking at that
now saying, ‘Oh gosh, I wish I wasn’t doing that’?

I think, I don’t remember what I did after this, but I seemed to
remember feeling like, because I kind of jumped right on when
he said, ‘Zero minus one. And I figured that probably meant...
But I kind of jumped on that, when I said, ‘Is this what you
meant’?

And you wished you hadn’t done that?

Well, I think I remember feeling like I kind of jumped in.
Where, if he had just explained a little bit more, or having him
explain and then having other kids question it if was still not
making sense. Kind of trusting other kids would flush out if it
was still not making sense. Instead of thinking that I have to be
the one to jump on him and say, ‘What do you mean by that?
Are you sure that’s how the number line should go’? I mean...
Because that would be easy to do and I’m wary of that. I guess
any time I start talking a lot with chalk in my hand... I’m leery
of falling back into... I guess if you had, like, if you looked at,
if teachers did some kind of um, research that looked for
behaviors or tones of voice that triggered falling back into old
modes. That having chalk in your hand, or standing up in front
of the class. There would be certain behaviors that might
trigger it.

Trigger “it”?

Trigger it.

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Lauren: “It” is falling back into old ways?

Lisa: You would sense that behavior as saying, ‘That’s right, I want
to do that’, and then go back and But, I guess, I know that
that’s one behavior that can trigger that. So I’m always leery of
it. Even if I deliberately choose to have them chant. ‘Say it if
you know it’, kind of thing. It’s something that I’m really leery
of because I know once I get that chalk in my hand, if I just let
loose, I could be writing on that board and just have the
discussion all by myself.

In this dialogue, Lisa grappled with a couple of things. First, it was her aim to turn
the classroom discussion over to the students and to facilitate their interactions, by
listening carefiilly, asking questions, and inserting ideas and alternative fi'ames, as well as
additional information. She explored here, ‘What does that look like in action? Is that
what I am doing? Or, is something else happening as a result of my moves?’ Second,
Lisa made explicit her struggles with deciding when to step in, and when to step out and
let the students “flush out” the meaning.

As we continued to watch and to talk about these issues, Lisa extended her
investigation further yet. While still grounded in uncertainty, in her struggle to align her
beliefs and her actions, she observed a “good fit” :

Another thing I was thinking: how hard it is to make up things as you go.

Just then (in the tape), deciding that I wanted them to write and trying to

figure out what I wanted them to write about. As I was watching it I’m

thinking, ‘Oh, good move Pasek, pulling it back to the original problem and
having them go back and... good move.’

And I was thinking about--we had an assembly today and the guest speaker
had been giving presentations all day long; that’s her job, giving
presentations to all these different schools. I was watching her during our
session and thinking wow, she’s really got it together. It just flows really

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well. She knows just the right analogies to use. She’s really got her act
together. Later, when my kids were in music, I stopped down by the gym
and I heard her telling the same jokes. Then, when my kids were at recess,
I was down there again and I heard her presenting to another group. She
was going through the same play by play, the same sequences, the same
jokes, the same strategy; no matter what age level or group was in there.
She did an excellent job. She didn’t look rehearsed. It looked very
spontaneous. Now, watching me on this tape struggling in the moment:
“Write--about--how-this--connects”; I’m really struggling to make it up
right there and making it seem like you know what you want them to do.

Lisa was grappling with constrasting images of herself as teacher. A residual
image from Lisa’s apprenticeship of observation (Lortie, 1975) is that of a teacher whose

“really got her act together.”

Conversational Workspace 3: Learning New Meaning For Familiar Language

Our second meeting in January was different from the first in that we got together
again to watch tape, set it all up, but never actually did so. Instead, we picked up our
conversation where we ended it the week before, and our memory of the recorded images
seemed to serve as a stimulus for our talk about the videotapes, what was on them, how
Lisa was drawing on them in daily situations, without literally reviewing them.

Our meeting on January 19th began with Lisa telling me about the masters course
in which she was enrolled at the university. The course was pushing her to examine her
practice and her role as a curriculum developer. As Lisa explained it, it seemed to her the

focus of the course was more on teachers becoming curriculum developers--for other

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teachers-rather than thinking about themselves as classroom teachers who do curriculum
development as a part of their ongoing work.

It was clear that Lisa was troubled by the perspective she was encountering in the
instructor, in the text, and in some of the other enrolled teachers. Having attended one
class session, she was raising questions about how her work with the [MT group, her
conversations with me, and her study of videotapes of her classroom were a kind of
curriculum development, but what she meant by that was, in her view, different from what
her course instructor was advocating. Between our meetings on January 12 and January
19, Lisa had noted her concerns in her journal:

-Frustration with curriculum class! ! How to make sense of how this

project can fit into the constraints of this more traditional form of

research on curriculum. How does this project help me to think about
curriculum as a more wholistic endeavor...

Implementing a curriculum. . .Reflecting in and out—How might this

project have an impact on my role as “teacher-leader ”.7 -other than

prompting others to consider the benefits of rethinking -thinking more
deeply about their own practice.

*My role in my district...

*How does this project/HWY” membership help me become...

a curriculum developer of some kind???
*Teacher
- objectives taught in an alternative way
-belief systems
-math-not a dish it up and pass it out to others

(Lisa ’s journal, January, I 993)

In our conversation, Lisa worked to articulate her understanding of her role in

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curriculum development guided by her belief that currieulim is an emergent process,
created with her students in response to their interests, needs, and chosen paths of inquiry:

Lisa: At this point-~I guess, because it is based so much on a belief
system, it almost cheapens it to call it a curriculum. To say
that this is a curriculum that I developed, it almost cheapens it
to sounding as if it were something I could package for you and
hand out to you, to look over “my curriculum.” That’s the
traditional [view]: ‘Well, if you have a curriculum, let’s see it.
Let’s see how you teach decimals; let’s see your worksheets;
let’s see your scope and sequence.’ Curriculum is often a word
that kind of--it always seems to be some thing that is dished up
and passed out. So, the work that I do with the IMT group
doesn’t seem like curriculum work because people have to--
come in and cook with us. (pause)

If you would ask me to describe what I do with the [MT group,
I would have never, ever gotten to the point where I said, “We
develop curriculum.” I would have never said, “We develop
curriculum.” Because groups that develop curriculum get
release time or stipends to go to a meeting and work on
something that is a package deal that they can Xerox and send
out. And so, I would have never thought of the [MT group as
creating curriculum because-(pause)

Well, it is what we do, but it is not that kind of what we do.
Just right now, I’m thinking I guess we do create curriculum,
but it’s still not the kind we can dish up and pass out. It is still
different. I still wouldn’t feel comfortable telling anyone else
outside the group that we develop curriculum, because they
would envision us sitting around making up questions, books,
and tests to pass out as “math this way” kind of thing...it’s the
baggage I don’t want to deal with--(pause)

It is consuming for me to think about. I am surprised I guess,
that it never would have crossed my mind to consider what we
do in the IMT group...[is] curriculum development, but when
you think about what we do, in every sense of the word it is
curriculum.

154

This transcript of Lisa’s extended turn, marked off into four segments by
pauses in her speech, makes visible Lisa’s active engagement with the meaning she
gives to the concepts curriculum and curriculum development and how these
concepts fit in her vision of teaching. Again, drawing on constructed dialogue
(Tannen, 1989), she worked through what some generalized ‘they’ might say
about curriculum (e.g. ‘Well, if you have a curriculum, let’s see it. Let’s see how
you teach decimals; let’s see your worksheets; let’s see your scope and sequence.’)

As she tried on these other perspectives, she bumped up against a rub
between the concept she holds in her head for the traditional use of these terms--
how they are being used in her university course--and what she does as a reform-
oriented teacher and as a member of the [MT group. In this excerpt of talk, we
can see Lisa change her mind, that is, change the meaning she gives to these terms
and the work they represent. She seemed to reconstruct her meaning for these
terms, shifting from curriculum as a product to curriculum as a process, a term she
could use to talk about what, in part, the IMT group does on Thursday evenings.

Lisa seemed to struggle with the contradictory assumptions beneath
various uses of the terms. She explained how the view of curriculum development
reflected in the course survey she took was ‘Very traditional” because it began
with the assumption that curriculum was created for teachers. In contrast, Lisa
was working with an assumption that teachers should necessarily create their

curriculum in response to guidelines and standards and the particular needs of a

155

group of students. She was grappling with the notion that someone outside of the
classroom could do what she viewed as an inside part of her teaching.

The confirsion Lisa confronted around these terms, their concepts, and
their direct relation to her work are not surprising and her frustration can be
readily understood. She had been reading and referencing texts that used
curriculum to mean a dynamic, developmental process that actively involved the
teacher, the students, and the material to be learned. Now, her new course was
prompting her to examine closely her use of the language of curriculum
development and the meaning it has in her work.

In the first chapter of their book, Teachers as Curriculum Planners: narratives of
experience, Connelly and Clandinin (1988) list nine difl‘erent definitions of curriculums
taken from “reasonably well-known writings in the field.” The authors make the point that
the range of definitions on curriculum stems from the range of foci pe0ple use to describe
the classroom and its processes. They encourage the reader of their book to link
“curriculum” with a picture in mind in which persons, things, and processes are in
interaction. They emphasize that this is quite a difl’erent thing from having “a textbook
flash to mind or a teacher lecturing flash to mind or an evaluator measuring intended
learning outcomes flash to min ” (p.7). It is important to note that this book was a
primary text for the course Lisa took the previous semester, in the fall of 1992.

In the Curriculum and Evaluation Standards for School Mathematics, the

companion document to the Teaching Standards, published by the National Council of

156

Teachers of Mathematics, curriculum is defined this way:
Curriculum. A curriculum is an operational plan for instruction that
details what mathematics students need to know, how students are to
achieve the identified curriculuar goals, what teachers are to do to help
students develop their mathematical knowledge, and the context in which
learning and teaching occur. In this document, the term descirbes what

many would label as the “intended curriculum” or the “plan for a
curriculum.”

Reconstructing her meaning of curriculum in this moment did not resolve
all Lisa’s concern. But, doing so did seem to draw out more of the complexity in
her thinking about this problem with the language. She seemed to be trying to
embrace a wider flame of reference (Elbow, 1986) for this language of curriculum.
She continued to hold onto what she saw as two views, working out for herself the
fit between what others say and what she would or wouldn’t say. And then there’s
“baggage.” It is the baggage that comes with the language that Lisa said was
consuming and something she didn’t want to deal with it. It is the baggage, I
would argue, she is dealing with in our dialogue and in doing so, constructing for
herself a deeper understanding of her work. Tannen writes:

Both the meanings of individual words (indeed, as frame semantics and the

philosophy of Heidegger and Wittgenstein have made clear, words can

have meaning precisely because of their associations with familiar contexts)
and the combinations into which we can put them are given to us by

previous speakers, traces of whose voices and contexts cling inevitably to
them (p. 100).

Again, we are reminded of the notion that the communities in which we

participate, shape and direct the meanings we construct. And I think we see in

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Lisa work the struggle to move between communities and to construct new

meaning.

nts Conv rsation Aroun e’ Vid "

This third conversational workspace is set apart flom the other two in this chapter.
Lisa and I engaged in a larger conversation that includes this dialogue with the same
understanding flom the week before that we were meeting to watch videotape of her
teaching. Indeed, we never actually used the videotapes. I think this discrepant event
affords us now a couple of interesting insights. Lisa flamed our conversation so that we
were talking about her practice, drawing on her recent experience in a university course
and images we share about her practice. The videotape, in its case, on the table, seemed
to serve as a symbolic representation of her practice, of which, we were both familiar with
its images and its relation to her membership in the IMT group. She was again, tailoring a
resource she already had—our collaborative project—to learning how to identify and
articulate her wondering about this approach to teaching.

Conscious of my commitment to following Lisa’s lead, to supporting her taking
ownership of the videotapes and the direction of our talk around them (the initiating goals
of my study), I was ready to join Lisa in this tailoring. I wanted to support her initiative in
flaming our work and I responded accordingly by offering my observations, questions, and
conjectures. In the midst of this interesting exploration, I felt pulled to link our

conversation to the “original” flaming that including the tape as a tool. I think this last

158

part of our dialogue, holds an interesting illumination of our conversational work and our
growing perspective on “mining videotapes” (Denyer and Pfeitfer, 1996) as a tool for
exploring one’s teaching:

Lauren: It suggests to me that “curriculum” might be a lense that you
take to watching the videotapes. Where in these tapes would I
say, ‘I call that currciulum development or I am working with
the curriculum or there is an example of my definition of
curriculum development as I have been trying to think about
it...?’

Lisa: Yes, yes. The whole idea of having a question, those objectives
forming those questions, the placing of questions, the laying out
of nuggets for kids to think about; all the decision making, you
could make a real argument for this kind of teaching being a

continual process of curriculum development--the videotape is
evidence of curriculum development-in-action.

Lisa was struggling to fit her sense of the “traditional view” of curriculum as an
object and her experience with curriculum as a process. She was making new connections
between her view of curriculum as a continual process that is co-constructed with her
students and the work she does in the [MT group. Together, we were constructing a
understanding of the way videotapes of her teaching might be used as a tool in her

practice, as a site for studying her “curriculum-in-action.”

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Learning About Teachers' Conversations

Lisa was using and developing the skills she needed for a kind of conversation that
reached beyond the surface elements of reporting, describing, and noticing. She was
learning to articulate an aspect of her classroom (understanding her student’s reference to
“they” as an indication of conceptual ownership) that piques her curiosity, something for
which there is not a clear, concrete answer. “With the video record and our
“conversational workspace”, a context that included our shared history with the IMT and
our shared interest in mathematics teaching, Lisa was able to explore, try out, practice,
and work through a way of talking about this curiosity. Her purpose for engaging in this
conversation was not an expressed interest in learning to have a different kind of
conversation about teaching. Her goal rather was to watch her videotape and talk with me
about it, originally in agreement to help me explore the question, What does a teacher
learn flom conversations around videotapes of her teaching? While she may have learned
something about her students’ reference to “they”, the analysis of her repeated articulation
of her curiosity suggests she was also working on the articulation and framing of a
question she could potentially take back to the IMT group and use to create another
conversation around her videotape that results in deeper inquiry or “digging.” While she
may have gotten a little clearer on managing the dilemmas that surround her role in the
classroom, she was also examining the fit between her beliefs and her actions, a skill that I

would argue contributes to her enculturation in a secondary discourse of reform-oriented

160

teaching. And finally, while seeking support for her feelings of flustration when talking
with peers who hold a difl‘erent perspective than she, Lisa was constmcting new meaning
for her concept of curriculum. I believe we were engaged in a “boundary conversation”
(Brufl‘ee, 1993) that approximates the transitional support needed for transformative

learning.

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CHAPTER FIVE

Learning About Oneselfln Learning To Teach
" Trust in yourself that you have solid reason for your actions, trust in yourself that
whatever happens, you ’1] figure it out—or at least try to. Trust in those around you., that
they ’11 help and support you in whatever way they am...

...if there were no audience with which to share and collaborate, all my work, alone in a
vacuum, would seem unimportant and not nearly worth the effort! "

Lisa, 54-93
In a newsletter addressed to the students, parents, and stafl’ of Central Park East
Secondary School in Harlem, New York, Deborah Meier describes what it means to be

‘yvell-educated”:

...getting in the habit of developing theories that can be articulated clearly
and then checked out in a thoughtful way. Of course, people who come up
with good theories are people who are knowledgeable. You can’t have a
theory about baseball if you don’t know the game. Good theorists are
close observers who are always in the process of wondering why, putting
things together and taking them apart! The things they put together and
take apart differ: some of us theorize more about people, others more
about cars. Some about history, others about numbers.

But one thing all good learners need theories about is their own way of

learning. Schooling ends early in our life, but learning goes on and on and
on. So being a theorist about oneselfas a learner is critical (1995, p.155).

Recognizing that the collaborative engagement they seek for their learners parallels
the collaborative engagement they seek for themselves with colleagues is one way in
which teachers begin to think of themselves as learners (see for example, F eatherstone et

al., 1993). This transformation in their professional identity as teachers can be threatening

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and fearful; it can also be liberating and empowering. The process of professional
development is tightly bound up with one’s personal development. Of all the identities we
have tried to place on teachers: teacher as technician, as manager, as caretaker, as
facilitator, the ones that may matter most to the fimdamental changes we seek will be
crafted by teachers themselves, individually and personally. Like learning about the
culture of teaching and learning about teachers' conversations, the transformation of a
teacher's identity so as to reflect an orientation toward reform, also requires the support
offered by transitive support communities of trusting relations and boundary conversations
(Brufl’ee, 1993).

Lisa saw the mismatch between her teacher preparation program and her early
experience in the field as her professional development problem; it was her responsibility
to flame the work, to muster the resources, and to take an active stance toward “avoiding
the rut.” The rut represents the kind of teacher identity she wants to avoid.

It is Lisa's effort to avoid the rut that places her professional development in
tension. Were she to not struggle to develop against the grain, were she to socialize
instead into the existing culture of teaching, becoming more like the teachers for which she
has so many models, were she to acquire the ways of being a teacher that continue to
define the community she seeks to belong to, there would be no tension. But, because she
seeks to develop as a reform-oriented teacher and because this goal is at odds with the
norms of interaction among most teachers, the rut she fears is visible to her. Moreover, it

pushes her to work actively to avoid it.

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In this chapter, we return to Lisa’s mathematics classroom, now in the spring of
1993. Across a series of experiences, Lisa drew on her membership in the IMT group for
support in exploring what she thought she understood and to help her pursue an inquiry
situated in the particulars of her classroom, her students, and their curriculum, that year.
The strength and the influence of Lisa’s boundary conversations with the [MT members is
visible in her efforts to identify, pursue, and tailor resources that would help her
investigate a problem of practice that she was theorizing about in direct relation to the
sixth graders in her classroom. This problem of practice was also linked to her own
experience as a learner. Through this investigation, Lisa tested the progress of her
transition into a professional culture of inquiry and her skills for engaging in the
intellectual work of her practice. She opened her questions and her private theorizing to
others who supported her own learning. She contributed actively to the collective work of
her boundary group. Lisa’s theorizing about herself as a “teacher intellectual” is key in
this story. Through a web of events and Lisa’s reflections on them, Lisa demonstrated to
herself that she is becoming the thoughtful, reflective, analytical practitioner she had
envisioned. Through her sensemaking of this self-directed inquiry, she resolved—at least
for the time being—her longstanding “fear of the rut.” She convinced herself that she
does have the commitment and the capacity to continuing to grow and change as a teacher

learner.

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The Grouping Experiment

Inventory! Thumbs up; Thumbs down. Look around and see who needs
encouragement today. At this time, I would like you to clear away your
music folder and your spelling sheet. I would like you to take out one
more clean sheet of paper.

On May 4, 1993, I watched as clusters of children's heads bobbed in and out of their
desks. All the while they were locating their supplies, they were also maintaining early
morning conversations with their classmates. For all the noise and commotion, there was
an atmosphere of a calmness, familiarity, and cohesion in the classroom.

Please raise your hand and look at me so I know you 're ready. We
have some special team time today.

There was a brief interruption flom a neighboring teacher and then Lisa walked to the

flont of the room and continued:

Thank you. Please put your hands down. Yesterday, we took an
interesting survey about how people act during small group
discussion and how people act during whole group discussion.
And what seemed to be most interesting is how people FEEL the
other people act. How do you think other people treat you when
you're sharing an idea? Do you think other people listen? Do you
think people in your small group listen? "

Lisa's manner and her words became slow and deliberate as she moved forward
toward the student's tables to share her thinking and her proposal.
And I was really surprised by the ideas that a lot of people felt that
your small groups didn't seem to listen as well as the large group.
I was thinking about that and I was wondering if we might use

videotape of our own math classes to investigate that—to
investigate the idea of how we work together.

I65

Now, it is an interesting and very unusual thing to be able to look
at something that you did a few months ago in your math class.
I 've talked before about how I used the videotape with other
teachers? -to look at how a lesson had gone? Another way you
could use a videotape—we've talked about how sports players could
use videotape to see how a game went, to see how that swing is or
how that pitch is so they can improve their own playing and that 's
kind of how I used it.

There was a very long pause. The students didn't react to each other. They
seemed to listen to her in a serious way. Lisa became quite animated and began to move
in and among the flont three tables as she talked to the group. Her voice became louder
and she began to speak rapidly:

Another way would be like the referees use it to say, ‘well, we

thought he was safe, but was he really We?’ Or, “we thought it

was afoul ball, but was it really afoul ball?’ They can use videos

to replay and you see that on sports all the time, now that we have

the videos to do that. Well, I was thinking that your small groups

went very well, but now I'm wondering, Hummm, maybe we should

look at that again to see is that really happening or is something
different happening. And so the video gives us a nice place to

replay what happened

Lisa spent a long time preparing the kids to watch the videotape. She continued to
refer to her own experience in sharing tape, describing for them how she was nervous to
show her tape to the teachers’ group. The students watched her even more intently as she
talked about worrying that the only thing someone would see when they watched the tape
was students misbehaving and they would think she was a bad teacher. She asks the class
to predict what did happen when she shared tape in her teachers' group. Students

responded:

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Susan: They listened

Belinda: The opposite of what you expected to happen.
Sam: They gave you good advice.

Lisa agreed: Right. Because 1 [wow these teachers and I really

trust them, I really didn't think they would rip me apart. I know

that they support me and they like me and I know they woulcbr't

want to hurt my feelings but, still, there was that feeling of what if-

-that nervousness. Beth was right. They were supportive. They

saw the same piece we are going to see today. Now what do you

think are some things we need to remember... ?

I stood ready to video-record the students as they watch themselves on videotape
during a math class in the first week of December. The work that we were doing in the
classroom on this day represented for both Lisa and me an exploration that takes seriously
the idea of revisiting one’s experience, drawing on multiple representations of that
experience, soliciting other perspectives and talking about your sense making with the
goal of clarifying, deepening or changing your understanding. The events which led up to
this morning’s viewing session with the children are a complex web of experiences, some
in the distant past, some in recent months, that together prompted Lisa to examine her

experiences as a learner and her beliefs as a teacher. Her inquiry centered on the merits of

small groupwork in her sixth grade classroom.

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isi estions about P ti e

During a Thursday night IMT meeting in late March, 1993, Carole had commented
on the diflicult challenge of really understanding how her students were experiencing the
activities and the discourse in her mathematics class. She had asked the group, ”What do
they make of all of this discussion? Does it seem helpful? What about it is helpful?”
Carole’s concern was one that had come up in the group's conversations before when the
teachers worried together about the "resource room students" or those members of the
class who aren’t "auditory learners." The teachers had asked, “How do we know if what
we are doing is helpfirl? How do we know if what we do is safe and productive for all of
our students?”

These concerns were familiar to Lisa in her own practice. Indeed, her inquiry into
one little girl’s experience in the classroom earlier in the year had been guided by a similar
set of questions. Still, Carole’s comments during this meeting stood out to Lisa and a
couple of months later she came to remember them as the starting point of a new inquiry
in her own practice. Lisa's journal entry about this March meeting reflected how she was
connecting Carole's ideas to her own questions. While Carole's thoughts didn't seem to fit
her situation, they provoked Lisa’s thinking and sustained her attention to the problem.
She wrote:

It was reassuring and seemed a bit coincidental that Carole had recently

been using a chart to record participation. I had been fiustrated with the

same dilemma. Even though I ’m afraid that the chart as she uses it might

be too stifling, I ’m wondering if a more deliberate, obvious attempt is
necessary to expand the number of students participating. I also think it is

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the feeling of pressure to get through the year, I ’m getting less time to sort
things out (Lisa '5 journal, March, 1992).

Origins of the Groupirg Experiment

I first learned of Lisa’s inquiry into her students’ experience in small groups at
another IMT meeting, the second following the group’s return from the annual meeting of
the American Educational Research Association (AERA) in Atlanta, Georgia. It was late
April and on this particular evening some of the teachers met earlier to watch videotape
with Sheryl and a colleague from Sheryl’s school. Because her commute to campus kept
her flom aniving early, Lisa was not a part of this pre-meeting viewing session and so
when she did arrive, she joined Helen and Steve and me in another room. She excitedly
launched into a story of an experiment she was conducting in her classroom:

I’ve been trying an experiment with homogeneous grouping. ...A couple

times ago we [the [M T group] were talking about how the same kids are

talking all the time. I was wondering if it might help to have two groups

divided so that kids who didn ’t talk very much in class discussion were

together and so first day back from the conference—well, I talked about it

with Helen and I talked about it with other teachers, who said, 'Yeah, I

wonder about that.’ Helen told me a story about one of her daughter's

professors who did something like this.

Lisa’s experiment, I learned later, had roots in a conversation she had had with
Helen on a walk through Atlanta’s Underground during the AERA conference. It started

out as a light conversation about kids' perceptions of the things their teachers do. For

example: to many students, cooperative grouping oflen means, “Oh no, I‘m going to have

169

to do all the work.” This led Lisa and Helen into a discussion about “things I believe
professionally, but yet have other reasons to doubt them.” Helen described for Lisa how
her daughters’ personal experiences with groupwork in their college courses had raised
hard questions about her own beliefs in the merits of groupwork. She told Lisa a story
about a professor who asked the students to sort themselves into groups according to the
criterion that they saw themselves as people who talk or people who don’t talk in groups.
When I learned that this story was somehow connected to Lisa's attention to
groups in her sixth grade classroom, I asked Helen about the story and she recounted it for

me:

...And so they did [divide themselves into groups]. They were supposed to
talk about whatever they had written for that day. My daughter said it was
great, it was a really interesting discussion with the people in the group
who had things to say and she wasn't the only one talking. They were all
the people who had talked in class, who had said interesting things, that she
never got to be in groups with. So, great thing number one was that
people who talked were interesting and great thing number two was that
when they all came back together again, all the groups had interesting stuff
to say, including the ‘five don't talk” groups.

(Interview with Helen Featherstone, April, 1993)

Helen's story had prompted Lisa to act on questions about groupwork that had
been bubbling just below the surface of her thinking for some time. In a sense, Helen
stood as a representative of the group, giving Lisa supportive permission to question her

practice. Back to Lisa's telling about her experiment with her sixth graders:

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Lisa said:

So, first day back from Atlanta, I wrote on the board:

[First part of the year]:
Hypothesis: Students learn better in heterogeneous groups
Experiment. Heterogeneous group each marking period
Conclusion: + special qualities, help each other

- good speakers do all the speaking
[The Grouping Experiment]:
Hypothesis: Students learn better in homogeneous groups
Experiment: Put ourselves into new groups
Conclusion ?

Lisa continued:

I thought I ’d tie it into Science. I said [to the class], ‘This year I have
been working on the hypothesis that students learn better in heterogeneous
groups and that metms that they are at different levels card they each have
different qualities that they contribute to the group. So, the experiment
that I ’ve been doing is grouping you heterogeneously each marking period
and then my data, things I've noticed are, on the positive (+), you help
each other in different classes and each group has special qualities and
so, you work pretty well together. The drawback (-) is that it seems like if
every group has a good speaker, those people are always the ones doing
the speaking. I know that when I was in school, I know that there were
times where I would be in a group and I was a very good thinker, but I was
a slower thinker and I would need time to think through my ideas card so,
other people who were quicker thinkers would say, ‘Here ’s how to do it;
do you get? ’ and I would never be able to figure out things on my own and
that was frustrating for me. And so I want you to think about: Are you
someone who gets a chance to talk in your groups and in whole group
discussion? Or, are you someone who needs more time to think?’

After lunch, I had them go into their two sides and there were several kids

in the middle who said that they were in the middle either because they
couldn ’t decide, it depended on what they were doing, or there were a few

171

who said they were in the middle because they didn ’t want to talk. These
are not shy kids; they don ’t want to participate. There are about five in
the middle. I told them this was an experiment and we would all collect
data.

I had a group of boys who were strong speakers; a group of girls who

were strong speakers; another two groups of girls who were quieter. It

was amazing that with most of the groups, even though they were

homogeneous according to how they talk, they really were heterogeneous

according to math ability. There were two groups of girls that were
quieter, but they both had two really strong math students in them. Then

there was a group of boys that considered themselves to be quieter, but

three, really all four of them I thought were strong.

Lisa continued with her lengthy description of the way the children divided
themselves into groups. We had to interrupt her story when it was time to join the rest of
the [MT group to begin our regular meeting. While this web of events continued to spin, I
was watching and wondering from the periphery. What was Lisa’s sense of all this? I was
eager to talk with her. I was curious about her reaction to the little girl who told her, ‘I
really like this because I get a chance to talk. In my old groups, they'd say this is how you
do it; do you agree?’ Lisa said she knew exactly what she was talking about. I wondered
how this fit with Lisa's experience in groups?

Over the next few weeks, I collected stories flom Lisa and Helen that helped me to

see multiple connections (see Figure 8.) between her conversations, past experiences,

reflections and current decisions.

172

 

Survey/Discussion with
the Sixth graders

Conversation with
Helen at AERA in
Atlanta ‘ April IMT Meeting ‘

\

\\ Jan’s Survey

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Questions about Groupwork
m the Slxm grade Conversations with
Lauren
Reflections on her Watching Videotape with
Preservrce Expenence the Sixth graders

 

 

 

 

Figure 8. Events highlighted in Lisa's inquiry into groupwork

In the late April IMT meeting, when Lisa shared with us her story of the first 10
days of the experiment, she acquired another tool for her inquiry. When the whole IMT
group convened for their regular meeting, Jan described a survey she had just given to her

third graders that week. She had asked them to respond to the following questions:

1) I usually, sometimes, or never feel that others are interested and care about
what I have to say in class;

2) I usually, sometimes, or never feel that my teacher is interested and cares about
what I have to say in class;

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Lisa picked this up and said she wanted to borrow the idea. She thought it fit with
the discussion she was having with her students. The group discussed it and Helen
suggested she might add a third question:

3) I, myself, am usually, sometimes, or never interested and care about what's

being discussed.

It is this survey that Lisa was discussing with the sixth graders on May 4'”, when
she shared with them her concern over the responses and her curiosity about what they

might learn about their groupwork by watching a videotape of their mathematics class.

The Connections Continue

The issue of the students not liking the small group discussions became the focus
of my next telephone conversation with Lisa. I asked her to tell me more about her
surprise at the students’ perspective; I said I thought she sounded troubled. She said she
was troubled; the students' responses had caught her off guard. I asked if she shared her
surprise with the students. She told them it seemed odd to her, it surprised her, and she
wondered why they felt that way. As a class, they had a firrther discussion about people
not listening to each other, people not really hearing what each other has to say, or not
paying attention. As she talked with me, I was struck by how our conversation now, in
April, contrasted with my images and memories of the class when I was at the school in
November. Then, they had said things like, “Mrs. Pasek's class is different because we

talk and we share ideas and we listen to each other and that's what this math class is

174

about.” Now it seemed they were saying that ‘yve don't listen to each other and we aren't
sharing.” I told Lisa about my recollections and she added that despite what looks to be
this warm and fuzzy cooperative conversation, “there are people that don't feel like they
are being heard at all and it's not a good thing!”

I told Lisa of my curiosity about what might happen if we showed the students a
videotape of their small group discussions, one we had flom last fall. This made sense to
her and together we realized that this was the next focus of our work with videotape; this
was what we should videotape, view, and discuss. Over the telephone, then, we planned
how to document her students’ reflections on their discourse so she could study them and

perhaps share them with colleagues.

den n T h Res h rs nd Coll ° min o m

On May 4“, I arrived at the school just before 9:00 am. Lisa had already reviewed
quite a bit of the videotape. She said she wanted to show the kids the same clip that she
had shown to the IMT group. At 9:30 the students arrived. Lisa set them up to take
notes on what they saw and to try to capture as much of their thinking as they could about
what they were noticing. She talked about finding patterns, watching for patterns and
what's happening in the class that strikes them, what they would want to say about it. I
added to her introduction that they might also note any questions that they would want to
ask. So, we watched the lS-minute segment of tape without stopping and then Lisa began

a discussion about what they saw.

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Lisa had crafted four questions while the students were watching the videotape.
First, before they began to talk, she gave the students an opportunity to write whatever
they were thinking about; an open-ended, ‘What did you see?’ Second, she asked them
to write about anything that had surprised them, anything that they had seen on the tape
that they didn't remember happening. The third question was, ‘How is this class that we
just observed similar to other math classes; how is this like their math class usually? What
things about it are the same?’ And then, fourth, the flipside of that question, ‘What was
difl'erent about this math class flom their math classes usually?’ The class wrote for about
10 minutes.

Susan spoke first and two or three students followed her lead to explain that they
didn't think people were camera shy, they didn't see a lot of kids making faces or turning
away flom the camera as Lisa had suggested they might see; ‘that probably wasn't as big a
deal as we might have thought it was.’ They noted and described some “first viewing”
surface features. Then, their discussion shifted.

With Susan's lead, the group began to talk about what was happening in the small
groups. They described how it didn't seem that people were really listened to in the small
groups. In the video segment that they watched, Mike and Susan had worked together
quite intensely and then turned and explained what they had been working on to Doug.
Doug had had a hard time engaging with the group, looking away or making comments
and asking questions that were not connected to the group’s discussion. Frequently he

nodded his head, as a sign of understanding, but his gestures didn’t fit with his comments.

176

In viewing the video segment Susan and Mike were not convinced he had connected with
them or the ideas.

Lisa and I had talked about Doug's participation before the day began. During the
survey on Monday, he did what Lisa called “middle of the road responding” by saying that
he sometimes, or usually, does feel listened to and feels like he's interested in others. Lisa
had said he played it safe and she expected that this videotape was going to show him
something quite different. She had wondered ahead how he might react to the images.
Now, the students had picked up on what was going on. Bill made a sophisticated and
articulate observation about Doug's interaction with Susan and Mike. He asked, “He says

he gets it, but how do we know he understands?”

Lisa’s Reflections On Learning From Her Practice:
The “Rut” Is No Longer A Threat

At the end of this school day, Lisa wrote a journal entry in which she listed several
of the recent experiences in her ongoing inquiry. She worked with several students’
reflections of the grouping experiment to formulate questions she could take to the IMT
group for firrther discussion. Perhaps most important to this close look at a teacher’s
sense of self and knowledge of self as a learner are Lisa’s reflections on her discoveries
about herself:

So many things have been coming together since returning from AERA:

* “presenting ” to the stafl; using choral reading from the WT 's Georgia
tour

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* The beginnings of The Grouping Experiment in my own class:
- Procedure
- Experiment
- Observations (Data)
- Revision as a result of some very impressive class discussion
* Jan ’s questions to her class, Helen ’s suggestions for a further “angle ”
*Linking these questions to some foundational wanderings about the true
advantages and disadvantages of heterogeneous groupings-what service
are we really doing for these kids if we put them by someone who will just
give them the answer?
--The importance of social skills in Cooperative Learning (esp. checking
for understanding and equal participation)
—-But how much do we really practice these social skills, even as adults! !
(Paley) How can we depend on these sorts of interactions as basis for our
classroom learning routines... ?!
Before I get too deep into today 's video discussion with the students, there
are two things I have discovered about myself:

# 1-1 am much less worried about getting into a rut during my career
because even as much as I think something through and feel strongly
about it, I still see myself as being open to thinking through other
perspectives. The heterogeneous/homogeneous dilemma was never an
issue for me before. In general, I still believe that heterogeneous groups
can provide support and extension for all students involved but in a
“socially constructing ” learning community, kids also need to be
discovering for themselves at their own pace. I believe I ’m very open to
dusting of my own mirror and looking more carefully and more deeply at
what I am doing. One of my pm'ent helpers was marveling at our
grouping experiment and told me how courageous I was! I think it is just
a matter of perspective. If scientists who keep trying to find the best way
to fight a virus or cure a disease are courageous, or if the figure skaters
who continuously strive to make the newest, most challenging maneuver
look easy we courageous, I guess I am courageous, too. Risk taking
requires courage and trust. Trust in yourself that you have solid reason
for your actions, trust in yourself that whatever happens, you ’1! figure it
out—or at least try to. Trust in those around you...that they ’11 help and
support you in whatever way they can...which leads me to notion #2.

#2—1 often ask myself perhaps as a questioning of character, would I
continue to do all this “stuff” if there were no [M T , no MS U affiliation,
no researchers, no official audience for my inquiry and investigations? I

178

might try to tell myself “Oh sure! I’d do it for the pure exhilaration of
reveling in kids" and in my own insights! However, even after an
outstanding morning of kids’ thoughtfulness and insights bowling me
over, an afternoon of chatty kids, a staff meeting, and a common cold are
enough to make me reconsider...And if there were no audience with which
to share and collaborate, all my work, alone in a vacuum, would seem
unimportant and not nearly worth the effort!

And I suppose this is why when my husband asks, “Is this [M T group
going to last forever? ” my first impulse is, “I hope so I ” In some way,

shape, or form, teachers need teachers in dialogue that is more sustained
than “And guess what Johnny did T ODA Y?! ”

Predictions: And to think I was afraid of overestimating what the kids
would notice about the videotape. Such an interesting play-out of first,
everyone seeming to agree that the small group worked well, like a group
is “supposed to by “helping ” and giving the answers- and then, the
pivotal issue from Bill and Jamie:

Jamie: “The person still didn ’t understand, I don’t think. "
Bill: “How do you know when someone knows... ? ”

WOW! The kids should just take over writing up the agenda for our [M T
group and any other educational societies—the students zeroed in on BIG
ISSUES--not because they ’re obviously big issues. In fact, they seem
subtle, but so crucial.

“We can learn that the kids need time to work so everyone gets the
problem and the answer. We have to have time to explain our ideas. "
- Tammy, sixth grader

“Maybe if we have a person go up and explain their ideas right at the
beginning of math discussion, then we can have a small group talk and we
can explain that one person ’s idea. ”

"Susan, sixth grader

This idea that whole group is somehow more productive than small
group? Or is it safer? Less intense than one-on—one work? A more
powerful combination of ideas? More trust in what the whole group
discusses and agrees upon? A good question for the [M T group: Are
these small “safe ” small groups serving their purpose ? How do we know?
Small groups contain fewer people, perhaps one or two people, explaining

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and re-explaining their one or two ways of tackling the problem while
large group has many more “teachers ” involved—struggling students can
pull away fiom intense scrutiny, “DO YOU GET I T?! But, there ’s always
the dilemma of the struggling student.

“Learning—I think we can learn that watching a second time, you really
notice things that you didn ’t before. Like someone doesn ’t understand so
someone else helps to try to help that person understand... Wow, this is
neat. There are lots of wonderful ideas about helping and giving advice.
I am now understanding what really happened ”

-Emma, sixth grader

This comment of Emma ’s may have something to do with why I chose to
have the kids view the same tape segment as I shared with the M
getting another view of “what really happened ”

“We can learn that kids understand each other better than adults. Most
kids think the same way. Teachers were taught different. It was a good
discussion. ”

-Wanda, sixth grader

“Susan is asking Doug “Do you agree why .515 is bigger? That is good
checking for understanding. ”
-Sam, sixth grader

Wanda 's comment gives me some insight into why kids can so often
understand and pick out each other ’3 misconceptions so easily. She ’s
right. They do have a more common background together than teachers
have with them—especially as curriculum changes and teachers who are
struggling with change have even less of an idea of what new fangled
methods students may have been exposed to in an earlier year. They have
less of an ideas of what they can “connect to ”-

Sam's comment highlights the debate in class between the advantage of
how a group works together versus the disadvantage of kids not really
understanding, even though others try to “tell them. ” This tendency for
“This is how you do it—Do you get it? Do you agree? And what a skewed
way to use the language of “agreeing ” with an idea .....

(Lisa's journal, 5-4-93)

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A Conversation about Learning from Experience

A week later Lisa and I met in her classroom after school. Trying to piece
together this web of events and to explore their educative potential for us, I guided Lisa
through a series of retellings. I had a hunch that there were interesting connections
between/among several parts of the stories and events that had occurred in recent weeks:
Lisa’s conversation with Helen in Atlanta; Lisa's revisiting her experience in Glenda's
class; Lisa trying the homogeneous grouping experiment with her class; an IMT meeting
and Jan's questions; the students watching a videotape of their mathematics discussions. I
wanted to get all of this on the table where we might work with it together; I was curious
about the ties between her past experiences, recent interactions, and what she was doing
with her students. I had a hunch that she was drawing on several sources of thinking, of
experience, of support, of intersecting learning communities, to make sense of what she
knows and believes, about groupwork in her classroom. I asked her to retell these pieces,
some that I had only heard in part; some that I had heard second hand; and others Ijust
wanted to hear again, all in the same conversational workspace (Denyer and Pfeiffer,
1996)

As she retold these stories, Lisa drew on her journal, her notes flom teaching, and
her conversations with others. She talked at length; I didn't want to adhere too closely to
a structured set of interview questions. I wanted to see how she might pull together the
telling of these stories--what she connected. The following is an excerpt flom our three-

hour conversation on May 7, 1993. Here, Lisa describes connections between her current

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investigation into groupwork with her sixth graders to her experience as a group member

in her teacher education classes:

Lisa:

Lauren:

Lisa:

In each of the three [math] classes, I did those questions and I
had told you how struck I was when my class said, ‘Well, are
you asking about whole group or small group?’ I said, ‘Well,
whole group; that’s what I’m most worried about. Do you
think it would be different?’ They said, ‘Oh yeah, it’d be
different! ’

I thought, well, OK. And I told you [Lauren] that I thought for
sure, small groups are safer. So, they are going to feel more
listened to; there are only three people there; people are going
to listen to me (student) in small group. People might not listen
to me in whole group. I was just devastated that it was the
opposite; people felt less listened to in their small group or that
there were people-more often--there were people that felt
never listened to in their small groups.

...Helen’s suggestion for the third question, I myself am
usually, sometimes, or never, interested and care about what '5
being discussed, is what really hooked me into doing this
survey with my students. I hadn’t linked the survey to the
grouping experiment; the kids saw it that way.

...I hadn’t linked this survey to my teacher preparation
experience until some of the groups talked about why they
didn’t talk. That made me think about my own experience
when I was in my own preservice math education class. I was
in a group of four students. We worked in cooperative groups.
And really, once we were set; it wasn’t assigned seating, but we
just sat in the same place. There were 25 of us and for 2 years
we had the same group pretty much.

The same foursome?

Pretty much. Maybe you’d switch around a little bit but you
know, we were responsible students and we were supposed to
take care of our grouping. In my group was myself; there was
Amy who was an older student and she was very unconfident in
math; there was Lucy and she was my roommate. She was real

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Lauren:

Lisa:

sharp in math; and then there was Jerry who was sharp in math
but whatever he lacked in understanding, he made up--with his
mouth. If he got a problem that he didn’t quite understand,
instead of looking at it quietly, he’d--I’d look at a problem and
kind of think, quietly; He would look at it and say, ‘OK, what
do we know, here. OK, we know that 1/2 = 1/2. OK, right
now, we know that 1/2 is not equal to da da da date da. And
he would just talk! Non-stop. And what ever you were
thinking, he just grabbed it right away with his mouth. He was
very enthusiastic and I liked him as a person but it made it hard
for me to learn math for myself. So, there is Jerry and Lucy and
Amy and myself.

And what is the parallel description of you? This person was
really sharp in math and this person was really sharp in math
and made up for what he didn’t know with his mouth, and this
person was sharp in math but unconfident.

I would say, I was--I was unconfident in math and--I don’t
know; I could have figured the things out, but I never had the
time. I was never given the time because of the group. And I
didn’t really notice that when I was in the class. I just-~they’d
say work in a group and we’d always get it. Once it was
explained to me I did understand it but there are things, still,
like when someone says, ‘remember this problem flom our
class’, I’m like, “No.” Or, ‘remember the line through the
forest problem’? I remember I never got that one! I remember
people trying to explain it to me and I never did get that one...
Our experiences were so different. Most of the time, I
remember the problems and I can tell you what I learned but
there are some, like the line through the forest that I never did
quite get it. And I remember the flustration of being in that
group. I guess at the time I didn’t realize I was flustrated
because that was how it had been.

So, all those things were building up and remembering what
that group was like, helped me really pinpoint-J thought about
that—my own group—and I thought, that was a heterogeneous
group! Lucy was the highest; I was the medium or Jerry and I
were the mediums and maybe Amy was the low because she
lacked a lot of concepts, too. Or at least she seemed like she
did because she had so little confidence. I was not confident

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Lauren:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

but I was willing to try but she was not confident and berated
herself a lot.

And just pulled out.

Yes. She’d get real flustered and say, ‘Oh, I can’t do it;
explain it again.

It makes me think of Rosey [in your class].

Yes. And it struck me that that was a heterogeneous group
right there. And I was, technically, a good student and I still
suffered from--I guess--from what I could have maybe done if I
would have had the chance to discover it on my own.

Describe for me what it was like.

It was--it is a lot of things I see played out here in my
classroom. Someone kind of getting stuck and then a pair
works on it and it’s, ‘Oh yea, maybe that’s it’ and then when
they get in their small whole group it’s, ‘yeah, yeah, that’s what
it is.’ Or, or, two are sure and the other two aren’t sure and
they get together and say, ‘yeah, that must be what it is.’

It’s not necessarily negative either. You know, I usually sat
across from Lucy and next to Jerry. That image is so strong of
the four of us! I learned a lot in that class but it is just-the
affective results. There were a lot of wonderful affective results
flom that class but in the group, I remember that feeling--but,
you know, there is another side of it. If I hadn’t been with
people who were a little bit stronger than me, would I have
gotten it all--as much as I got? I had a lot of questions.

When?

Thinking back on it, after Atlanta I had a lot of questions about
that group. How did it help? How did it hurt? Would I have
learned as much if I hadn’t been in a strong group of people?
Or, would I have learned more if I had a chance to puzzle it out
myself? What do I remember; what do I not remember because
of that group?

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Lauren:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

Mathematically?

Mathematically. So, I was--that was kind of happening all at
once; all this thinking about it. By the time I got back flom
Atlanta, I knew I wanted to try the experiment with my class on
the following Monday.

Was this the first time you questioned your experience in your
teacher preparation group?

Pedagogically. This is the first time I ever questioned the
theory behind the grouping.

Is it the first time you ever thought hard about what happened
to you as a learner in your preservice class?

No. As a result of all of the things I’d thought about as part
of the research project, I had done a lot of reflecting about how
I, myself, changed as a learner and about how my ideas about
math changed; ideas about myself as a mathematician. But, I’d
never before thought about my, um, maybe my learning style?

Social constructivist theories of learning describe the power of having learners

value and own their sense of understanding rather than relying on external authorities--

their teachers and their books--to tell them what they know and don’t know. Memories of

her preservice education included experiences in which Lisa was encouraged and

supported explicitly in knowing herselfas a valued thinker in a community of thinkers.

She told me a story about a conversation she had with one of her professors during her

junior year in college. This particular conversation was pivotal in Lisa coming to know

herself as a valued thinker:

Lisa:

He asked me if he could talk to me in his office; he wanted to
‘talk to me about the way I think.’ I was dying!

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Lauren:

Lisa:

Lauren:

Lisa:

Why?

Well, I was afraid. I didn’t know what he meant. So after class I
went up and I said, ‘What do you mean, how I think?’ And he
said, ‘Well, I’ve been watching you. A lot of students have their
hand up and nothing to say. You don’t always have your hand up
but you have a lot to say and I want to talk to you about how you
think.’ He said he thought I was a very careful thinker and that I
was analyzing things but not necessarily getting into the
conversation as quick as other people. I definitely agreed with
him because I was aware that Lucy and Jerry were—always—
raising their hands and there were a lot of people that were
argumentative. There were a lot of people who had real strong
personalities.

So, I thought this professor had a good point. He told me he
thought I could really pull some things together as far as
curriculum development, pull together some innovational kind of
things. He said that’s were curriculum is going, toward
integrating things. He said, ‘It just seems to me that you could
really do some good work in that area.’

How did that strike you?

I was just thrilled! I guess that helped give me confidence as far
as--and that’s a big part of it too, valuing deep thinking, even if
your not a quick thinker, valuing thoughtfirl thinking. I guess
that’s where I really got that message, good and strong.

Lisa’s experience as a preservice teacher, including this explicit naming of her as a

thinker by a respected teacher, contributed in compelling ways to Lisa's embarking on a
path of identity development that includes a self image as a valued thinker. In contrast to
her schooling experience where she received messages that “quick thinkers” were more
valued, a descriptor she would not apply to herself, she was helped in recognizing that as a

carefiil, analytical thinker she had a great deal to offer her learning community. It seems

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important to consider this pivotal event in Lisa's experience in the larger context of her

preservice experience where she was being introduced to new ideas and perspectives on

children's learning in classrooms. Lisa realized she would need to be an active analytical

thinker herself in order to support her students’ development as thinkers and valued

members of a learning community. She was able to connect how others know her with her

own lived experience and then use it as a resource in thinking about her aims for students:

Lisa:

Lauren:

Lisa:

Lauren:

Lisa:

WHhoooaa! That’s weird. I knew that was part of it but, and I knew
that it was very influential; I guess I just hadn’t thought of it being
directly tied to the grouping experiment.

Where are you now in thinking about groupwork?

I am reaffirmed in the ideas that the progression flom
individual to team--individual, partner, team; get some different
ideas generated; go to the whole group; compare ideas; get as
many different strategies as you can so people have multiple '
ways of understanding the same problem. I’ve tried to work in
more closure; closure even if it is not necessarily the closing of
a problem but, capturing on paper what your ideas are at the
end of class. I usually have done that, but I’ve started being
more deliberate about it; leaving more time and not just saying,
‘0. K., jot a few things down.’ I am more deliberate in leaving a
cushion of time where everybody has to be writing and then
putting the paper carefirlly into their notebooks so they have it
for the next day.

...The idea of going back into small groups after having a whole
group discussion; that seems to have some merit.

And that’s new since all of this exploration?

Uh huh. I mean, it’s not that it never happened, but it seems to
have more of a purpose, to reflect and to bring closure. Explain
to a partner; explain to your team; make sure you have a chance
to explain what you think happened in the large group
discussion.

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Learning About Self As Learner And Self As Teacher

Lisa’s grouping experiment and her use of videotape with her students supported
her image of self as a collaborative learner, in this instance, in company with her sixth
graders. She had the personal-professional resources (self, me, IMT) and her ongoing
history of participation in the reform work to guard against her fear of not “pulling off”
this inquiry. Part of what Lisa learned, indeed what she marks as key, is not that she
“pulled off” the inquiry and learned something profound about heterogeneous groups but
rather that she learned she is and will continue to become a thoughtful, learning teacher:

I had written some about the grouping experiment but as far as trying to
pull it altogether into some kind of document, I have never done that. One
of the things I was worried about was that if I talked to people, saying that
I did this grouping experiment and they would asked me what it was about
and what did you learn about heterogeneous groups? If I had written
about it back then, I probably would have tried to come to some
conclusions about heterogeneous groups, but having had some distance, I
have an idea that the grouping experiment was not-~that what it taught me
of value is not so much about heterogeneous groups, because I still don’t
know what I think about heterogeneous groups. But, what it taught me is
that I have more confidence in myself that I am not just going to fall into a
rut and be stuck there forever. If I was willing to question, in a very
serious way, and involve myself and my students and a lot of people in a
very serious inquiry, into something that I really believe in; ifI was willing
to seriously question and to dig into something that I believed in then, that
must mean that I am open and changing. I guess, when we wondered what
we would find out from a year of working with videotape, we have pulled
together some interesting ideas about how to use videotape and some of
the benefits and some things that can happen and some reasons why those
good things might or might not happen, but the most important lesson for
me is what I have learned about my own development as a teacher. (edited
quote flom a conversation/interview with Lisa, December, 1994)

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As a result of my study of Lisa’s learning flom her experience, I think about the
reflective practitioner in new ways. I have a new sense of the multiple dimensions of
analytical sensemaking when a teacher examines her experience. For Lisa, a goal of her
work is to continue becoming a teacher who raises questions about her practice and seeks
collegial support and participation in her inquiries. In her original request for my help in
videotaping her classroom Lisa was asking for help in supporting her development as a
reform-oriented teacher. The notion of fitting images of the possible with what happens in
the classroom underscores for me the rareness of imagery as a resource for teachers to
gather and study representations of their experience for the purposes of continued learning
to teach. Lisa's experience in learning about the powerful influence images of teaching can
have on her thinking and on her work gives me a sense of the many missed opportunities
for learning flom experience resulting flom teachers' isolation.

Believing that learning happens through social interaction with others, Lisa sought
the company of colleagues with whom she could continue to learn about teaching.
Worrying that she "may too quickly settle for her own perspective,” she sought the
different perspectives, different experiences, different ways of making sense of classroom
life that other teachers can bring to conversations about teaching.

She first knew this work in her preservice teacher education program and her first
year of teaching was a bridging experience that showed her the potential for situating her
continual study of teaching in practice. This early experience also introduced her to the

real challenges of enacting and articulating her vision of practice to parents and

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colleagues. Lisa maintained her ties to the university, the source of her commitment to
intellectual engagement about her work. With each course or study group she seemed to
strengthen her sense of self as a thinker and deepen her commitment to the identity she
would craft as a practicing teacher, grounded in inquiry and experimentation.

When Lisa joined the IMT group, in the fall of her second year of teaching, her
efforts to grow intellectually were placed in tension with the culture of her school. To
belong there, to establish and sustain collegial relationships with colleagues in her district,
she felt pressed to adhere to deeply entrenched norms of sameness. She felt pressed to
join her teaching colleagues in presenting themselves as alike in style, perspective, routine
and belief so as not to be too different, or to threaten the predictable, manageable
homogeneity of the faculty. It seemed that her ticket to successfirl socialization in her
school faculty was to hide her own and ignore others' difl‘erences in competence,
philosophy, and knowledge. Yet hiding this diversity would block the very resource—the
community—that could contribute significantly to her aims to become a reform-oriented
teacher. Hiding this diversity could limit her opportunities to raise questions about
teaching, to consider alternative perspectives, to reflect on the multiple experiences of
other teachers.

And so, the IMT group became a transitive support community in which Lisa might find
both a sense of belonging and sense of becoming that would support her identity

development and her learning of a reform-oriented practice of teaching.

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CHAPTER SIX

Constructing Professional Participation Knowledge For A Teaching Practice

We are living and teaching in times when the struggle to affect changes in the
professional development of teachers is more conscious and more visible than ever. In this
study, I have explored some of what it takes for a teacher to support her own continued,
self-directed professional development; what helps and what hinders her development as a
practicing teacher in a period of intense educational reform; and how my own learning as a
researcher can both contribute to and be served by a collaborating partnership.

The context of this study was my collaboration with Lisa Pasek, a sixth grade
teacher in a mid-size, Midwestem school district. Lisa was interested in how the
videotapes of her own teaching might inform her efforts to develop a discourse with
children in which they explore multiple perspectives on solving particular mathematical
problems and look to themselves and to their peers as sources of support for their own
learning. She was also curious about how she might use videotapes of her teaching to talk
with her faculty colleagues and administrators about her practice.

My goals for the study were two-fold. I wanted to pursue an inquiry rooted in the
ongoing work of a classroom teacher. I also wanted to design a study that involved the
kind of work I plan to continue doing as an educational researcher and as a teacher

educator. Specifically, I knew I wanted to use the dissertation project as an opportunity

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to learn about a kind of collaborative work that is called for in the literature yet, is neither
easy or obvious how to begin and sustain. This question guided the research project: What
and how does a teacher learn from conversations around videotapes of her teaching?

In looking back at the three contexts in which Lisa engaged in conversations
around videotapes of her teaching: in a meeting discussion of a teachers’ group, in a
dialogue with me, and in a classroom discussion with her sixth grade students, I learned
that Lisa’s use of videotaped records of her teaching required that she construct and
employ new kinds of knowledge about teaching and learning. The kinds of knowledge
needed to support Lisa in critical examination and articulation of her understandings, her
beliefs, and her practices are different flom the knowledge of learners, subject matter,
pedagogy, for example, that is identified as part of a knowledge base for teaching. Lisa’s
learning in this study reflects her development and use a domain of knowledge for a
teaching practice that supports her capacities to work with colleagues on individual and
collective inquiry into teaching and learning. In what follows I offer a description of this
knowledge, setting this domain in relation to an existing domain of teachers’ knowledge
for teaching. I explore a flamework in which these two domains taken together constitute
a teachers’ knowledge for practice and respond to the calls for reform in teachers’
professional development. I draw on my analysis of Lisa’s use of videotapes of her
teaching to identify a preliminary set of categories within this domain of knowledge that
may be distinct and significant to her ongoing professional development. Finally, I

explore what this study might offer researchers, teacher educators, and teachers about

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what practitioners may need to know to share their wisdom of practice and to transform it
into tools and resources that support their continual learning and development as reform-

oriented teachers.

Learning In A Different Domain Of Knowledge

At the time I proposed this study I expected that, through this work with Lisa, I
would better understand how a teacher might learn about pedagogy, for example, by
examining her actions in a lesson; or how a teacher might learn more subject matter by
assessing the content students explored during a classroom activity; or how a teacher
might learn about her learners by analyzing their interactions— all recorded on videotape
and used in discussions with other teachers. At the close of this work, I believe that
indeed Lisa may have increased her understanding in these areas and perhaps deepened her
knowledge of pedagogy, subject matter, and learners through conversations about the
video records she revisited. I believe, too, that our awareness was heighten about the
collegial relations that surround her conversations about her own teaching. Her journal
writing and our ongoing conversations clearly reflect the safety, trust, and care needed to
engage in this work.

The teacher learning of significance, in response to my research question, however,
is of a diflerent domain. Lisa's participation in conversations around videotapes of her
teaching—and her preparation for and reflection on these conversations—supported a

kind of learning that differs in its form and in its fiinction from the kinds of learning

193

supported during her preservice education program and her early inservice work. While
Lisa may have been working on her knowledge of pedagogy for elementary mathematics
teaching she was also using and deepening her knowledge of participation with colleagues
around representations of her teaching, questions, and ideas about that pedagogy. In her
pursuit of collegial conversations that would aflirm, push, and develop her thinking about
pedagogy, Lisa became critically thoughtful about what kinds of collegial interactions she
was seeking. She also created and nurtured opportunities to become skilled at how to
create these interactions.

Another way to described the domain of learning highlighted in this study is to
return to the notion of a secondary discourse for teaching. In order to engage the IMT
teachers in a conversation around her videotape, Lisa drew on the knowledge and skill she
acquired in her apprenticeship of observation and her early socialization into teaching, her
primary discourse for teaching (Denyer and Florio-Ruane, 1995). Additionally, for the
same purpose, she drew on her introduction to a secondary discourse for teaching she was
acquiring through, in part, her membership in the Investigating Mathematics Teaching
group. Her activities in this study reflect an active engagement in the kind of transitional
work Brufi‘ee (1993) describes as necessary for meaningful enculturation, supported by
boundary conversations in a transitional support community.

What stands out from the study reported here as a response to my question, What
and how does a teacher learn from conversations around videotapes of her teaching?, is

that conversations around one’s own videotape of teaching can create opportunities to

194

construct and use meaningful, educative forms of participation in a professional discourse.
In the context of a transitive support community, a teacher can construct knowledge
needed—both understanding and skills—to engage in a kind of continual learning situated
in a reform-oriented practice. The evidence presented in this study suggests that Lisa’s
knowledge of situated learning to teach with colleagues is of a different domain than her
knowledge of curriculum or pedagogy. That is, Lisa's knowledge of curriculum has at its
center student learning, instructional design and student achievement; her knowledge of
pedagogy has at its center classroom contexts, the relation of content to activity, and
community building. In contrast, Lisa's knowledge of the culture of teaching has at its
center teachers, practice made public, and discourse strategies for support and inquiry,
both in the service of student learning, and also as a valued focus of her own personal
professional development.

Knowledge needed for meaningful participation in a reform-oriented discourse, a
secondary discourse for teaching (Denyer and Florio-Ruane, 1995), is knowledge that
enables teachers to move theirpractices to public forums where they can be shared and
problematized for collective learning. This knowledge holds promise of enabling teachers
to shift their conversations about teaching toward critical examination of understandings,
beliefs, and actions. This knowledge holds promise of enabling teachers’ personal grth
to become intentional and more integral to their professional practices of teaching and
learning.

To articulate fithher what I have learned from this work, I continue describing the

195

kind of knowledge Lisa was using, constructing, and refining in our work together, as
professional participation knowledge for teaching in the context of reform. My aim is to
articulate what I have learned in a way that suggests a framework for the complex
knowledge base developing in and among teachers who are pursuing real and sustained
changes in their teaching; that is, in and among reform-oriented teachers. This framing
offers two ideas: First, the calls for reform in teaching require teachers’ development and
use of two broad domains of knowledge: knowledge for teaching and professional
participation knowledge. Together, these knowledge domains are comprised of many
varied and complex kinds of knowledge a reform-oriented teacher needs to create and
sustain a practice that includes thoughtful work in and around classroom instruction (see
Figure 9). Second, the relationship between these domains of knowledge is such that the
extent to which a teacher can develop her knowledge for teaching in response to the
reforms may be dependent on her development and use of professional participation
knowledge for a teaching practice.

In their recent writing on the reform of teachers’ professional development,
Deborah Ball and David Cohen (in press) sketch an ambitious and intriguing approach to
the reconstruction of teachers’ professional education. They distinguish their proposal
from those that call for the restructuring of roles, time, and relationships. Acknowledging
that such restructuring may be needed, they argue that these alone will not lead to better

instruction or learning.

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Rather, they propose:

...new ways to understand and use practice as a site for professional

learning, as well as ways to cultivate the sorts of inquiry into practice fi'om

which many teachers could leam...To affect what teachers might learn, one

must consider the curriculum and pedagogy of professional development:

what teachers would have opportunities to learn, and how they would be

taught (Ball and Cohen, in press, p. 5).

I am eager to explore beyond this study how a conception of teachers’ knowledge that
includes professional participation knowledge, for inquiry into practice, for example, might
contribute to the reconstruction of teachers’ professional development.

To help distinguish professional participation knowledge from knowledge for
teaching, I draw on the oft-cited work of Lee Shulman to begin to outline how Lisa’s
knowledge about collegial interactions, specifically, teachers’ conversations, and about
herself as a learner, functions in special relation to her knowledge for teaching. I speculate
about Lisa’s knowledge for practice then, as comprised of her knowledge for teaching

surrounded, supported, and further developed, in part, because of her knowledge of

professional participation with colleagues.

 

Professional Participation Knowledge

...............................................................

...............................................................

Professional Participation Knowledge

 

 

 

Figure 9. A Framework for Teachers’ Knowledge for Practice.

197

Following my description of professional participation knowledge, I turn to the
examples in this study to illuminate a preliminary set of categories in this domain of

teachers’ knowledge for practice.

Protessional Particimbn Knowledge For Teaching In The Context Of Reform

In Knowledge and Teaching: Foundations of the New Reform (1987 ), Lee
Shulman outlines a set of categories of knowledge that underlie teachers’ understanding
needed to promote comprehension among students. In the decade that has followed,
numerous other researchers have also asked, What do teachers need to know and be able
to do in order to teach in ways envisioned by reformers? (see for example, Wilson,
Shulman, and Richert, 1988; Feiman-Nemser & Remillard, 1995; Larnpert & Ball, 1998.)
A debated issue in our field, researchers and teacher educators continue to pursue their
understanding of the complex kinds of knowledge teachers use and develop for their work
with students.

A common and emphatic response to this question stresses the importance of
teachers’ knowledge of the subject matter they teach. In addition to subject matter
knowledge, Shulman offers six other categories of knowledge: pedagogical knowledge,
curriculum knowledge, pedagogical content knowledge, knowledge of learners,
knowledge of educational contexts, knowledge educational ends, purposes, and values

(p8). Offering firrther organization, Shulman describes four major sources for the

198

teaching knowledge base: 1) scholarship in content discipline, 2) materials and settings,
3) research on schooling, and 4) wisdom of practice itself.

Of particular interest to this study is the notion of teachers’ wisdom of practice as
a source of knowledge for teaching. In 1987, Shulman argued for a more systematic
gathering, studying, and organizing of the individual and collective knowledge held by
teachers. His focus was on the need for researchers to glean and codify what teachers
already know but have “never tried to articulate” (p. 8). He reasoned that close work with
teachers would bring forth and contribute to organizing teachers’ wisdom of practice in
ways that offer the field a deeper understanding of the principles, theories and beliefs that
shape and direct teachers’ practices. And I believe the last decade of work has
demonstrated the benefit of close work with teachers and supported the emergence of not
just cooperative partnerships in which teachers grant researchers access to their
knowledge base, but also collaborative work in which teachers and researchers together
generate new understandings in response to questions about teaching and learning.
Building on the last decade of innovative research relationships with teachers, I think there
may be another path to pursue for what we might understand about teachers’ knowledge
by working closely with them as they make explicit and use what they know in their work.

It seems there are two places to look inside teachers ’ wisdom of practice. One
territory, as Shulman describes it, includes the theories, beliefs, and principles teachers
hold about content, learners, contexts, and curriculum. Teachers develop wisdom about

multiple aspects of their work and often use it in unarticulated ways. This wisdom

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includes things they have learned to do in situ but have talk about in an explicit or analytic
manner. When tapping teachers’ wisdom of practice, we are asking them to make explicit,
to talk about, to make visible their knowledge for teaching. This is a premise of much of
the collaborative research of the last decade and it has provided critical contributions to
the collective knowledge base of researchers and teacher educators.

How to tap into, to gather, and to organize what is gleaned from teachers has been
a topic of methodological debate. Gaining access to what teachers know requires
teachers’ active participation and thoughtful engagement with other educators. This is a
second territory inside a teachers’ wisdom of practice. It is this participation—a teacher’s
capacity to participate—that has raised a related but different question through the course
of this study: What do teachers need to know and be able to do to articulate their
knowledge for teaching: to converse, examine, and debate about what they know about
subject matter, students, and classrooms? What might be the professional participMon
knowledge teachers need in order to construct and use their wisdom of practice in critical
conversations about teaching and learning?

Conscious of the magnitude of the claim that what Lisa and I engaged in together
was a domain of knowing and learning distinct from other kinds of knowledge, I want to
proceed with my description of this distinction. I do so with confident uncertainty (Ball,
personal communication, 1995) that others engaged in the reforming of teachers’
professional development may affimt, challenge, or clarify the framework I set out in ways

that contribute our efl’orts to understand what “teachers need to know, and know how to

200

do, in order to offer instruction that would support much deeper and more complex
learning for their students?” (Ball and Cohen, in press).

Professional participation knowledge includes understandings and skills that enable
a teacher to construct contexts for and to engage in shared public work on learning about
teaching and learning. Where knowledge for teaching includes, for example, knowledge
of subject matter, knowledge of learning and learners in context, and knowledge of
curricula, professional participation knowledge supports active public engagement,
investigation, and sense-making of problems, questions, and issues that emerge as teachers
act on their knowledge for teaching. I return to Shulman’s work and draw on an example
he uses to illuminate what I am calling here professional participation knowledge.

Shulman and his colleagues observed, documented, and studied the expertise and
skill of a secondary teacher. They drew on Piaget’s methods of study and began to
identify, label, and organize what this teacher was able to do: what she knows and how
she uses what she knows to engage her students in the study of literature. Shulman and
his colleagues were interested in learning how Nancy, the cooperating teacher in their
study, used a conceptual framework in planning and teaching her high school English
class. The researchers drew on her explanations, in part, to frame a developing knowledge
base of teaching which Shulman likened to a chemist’s periodic table, containing cells or
categories yet to be identified. The question raised in the light of my work with Lisa is:
Would this English teacher explain her conceptual framework as she did to Shulman if she

were talking to an immediate peer? What else might she say; what might she not say?

201

How else might she use that framework to look at her teaching or her students’ learning?
What does that framework tell her, not her visiting researchers, about her growth as a
teacher? It seems that these are questions that reference a different kind of work inside a
teacher’s practice.

I turn now to my work with Lisa in this study to firrther explore the notion of a
domain of professional participation knowledge for its potential in helping us address the
professional development needs of reforrn-interested teachers. To fully engage in
professional development work where videotape might be helpfirl, that is, in conversations
with like-minded critical colleagues, teachers may need to develop new categories of
knowledge about teaching that reach beyond the knowledge they use inside their
classrooms. They may need to develop knowledge that support their efforts create a
professional learning community and to know how to participate in it in ways that are
educative.

While I am acutely aware that the insights I have gained from my work with Lisa
and the IMT group are only a beginning foray into a domain of knowledge I imagine is
quite complex, I believe I can articulate four categories of professional participation
knowledge reflected in the analyses reported here. Four categories of professional
participation knowledge illuminated in this study are: (1) Knowledge of conversational
rights and duties; (2) Knowledge of language use and meaning in dialogue; (3)
Knowledge of selfas teacher: relation of beliefs and actions; (4) Knowledge of self as

learner: reflection on personal/professional growth.

202

Knowledge of Conversational Rights and Duties

In sharing a videotape of her teaching, Lisa drew on her understanding of the
culture of teaching to create a conversational workspace around a videotape of her
teaching. In preparing for a viewing session with her IMT colleagues she articulated her
goals of wanting to see what others might see and to be pushed to think carefully about
her mathematics teaching. She was seeking a conversational workspace in which to work
on her knowledge of learners, contexts, and pedagogy—her knowledge for teaching. Her
knowledge of the culture of teaching shaped the discourse and the extent to which the
group could engage in critical examination of the video record. As the analysis showed,
the rights and duties that governed the IMT discussion were more reflective of the culture
of teaching that socialized Lisa to be an informant of her practice, than her envisioned role
as an inquirer. In her reflections on the viewing session discussion, we saw Lisa construct
an understanding of the importance of her framing and posing a question when using her
videotape and the potential of the question to shift the discourse pattern of the group’s
talk. This understanding, constructed out of her reflections, stands as an example of the
kind of professional participation knowledge Lisa needs to engage in critical conversation

about her mathematics teaching.

Knowlggge 9f language use and meaning in dialogue

Throughout the course of our work together, Lisa used what she knows about

conversations with teachers in the [MT group to tailor her conversations with me so that

203

she could examine her own understanding of a set of concerns in her practice: her sixth
graders’ meaning in a description of their math work, the relation between her belief about
student authority in the classroom and her own physical positioning in the room, her
meaning and use of the term curriculum in discussions with other educators. Each
concern emerged, in part, from Lisa’s knowledge for teaching, specifically, her knowledge
for reform-oriented teaching: knowledge of learners, knowledge of pedagogy, and
knowledge of curriculum development. However, without knowledge of a kind of
conversation that will value and support the exploration of this knowledge for teaching,
Lisa’s opportunities to intellectually scrutinize her meanings, her understandings and how
they compare and contrast with the understanding of others was limited. Her
conversations with me, in the context of this work, supported her continued practice in

creating and participating in meaningful examinations of her work.

Knowledge of self as teacher: relation of beliefs to actions

To push her understanding of her own development as a reform-oriented teacher,
Lisa initiated an inquiry, a small action research project, in company with her sixth-
graders. Perhaps her struggle to achieve the kind of conversation she sought with the IMT
group provoked her curiosity about her own students as resources for her learning about
her teaching. In her journal writing and in conversations with me, Lisa used her growing
awareness and understanding of her own experience as a learner to look for connections
between her knowledge of pedagogy—small group discussions—and her knowledge of

learners—their constructive participation.

204

Knowledge of self as learner: reflection on personal/professional growth

Working with Lisa in the context of her inquiry into groupwork highlighted some
of the personal/professional costs to a teacher beginning to cross boundaries in the
direction of new norms of collegial interaction: the problem of being too different; the
challenge of leading and teaching others how to present their practice as part of trying to
figure hers out for herself; and the realities and risks of being misunderstood. Lisa’s
inquiry illuminated how important it was to her that she keep inching her way forward in
this direction; to succeed in crafting new ways of talking about her practice is in support
of her commitment to continuing to learn to teach in response to the reforms. She used
her knowledge of active intellectual engagement about her work to maintain her ties to the
university, to join the IMT group, and to explore the potential of meaningful conversations
in her school. With each course or study group she seemed to strengthen her sense of self
as a thinker and deepen her commitment to the identity she would craft as a practicing
teacher, grounded in inquiry and experimentation.

These four categories are a starting set and a beginning attempt to describe Lisa’s
development and use of her professional participation knowledge. I think it is important
to note that within this study other categories of professional participation knowledge may
have been employed as Lisa and I explored her use of videotapes of her mathematics
teaching. Such possibility reflects the potential for me and perhaps others to continue

learning from this work and these gathered research materials.

205

Continuing The Reform Of Teachers’ Professional Development

I think there is a distinction in the current discourse about reforms that may be
helpfirl in considering the significance of professional participation knowledge to a
teacher’s capacity to craft and sustain a reform-oriented practice. I think current reform
efforts can be grouped into two categories (see Figure 10). In the first, education reform,
reformers are concerned with re-conceptualizing the content and the processes involved in
educating our youth. Education reforms address concerns about the core subject matter
areas, ideas, principles, and skills needed for a productive citizenry in the 21 st century.
Additionally, education reform is concerned with the processes by which learners acquire,
learn, and practice new knowledge and skills.

In the second category, school reform, the focus is on the re-organizing and the re-
structuring of contexts in which new content and new learning processes are employed—
where education reform take place. School reform addresses concerns about the
resources and structures (temporal, organizational, and financial) that operationalize

educational programs.

206

   

   
 

  
    
   
     

Education
Reform

School
Reform

  

Professional
Development
Reform

Figure 10. A view of the contexts of reform: education reform, school reform,
and professional development reform.

The work of the reforms is complex, interrelated, and labor intensive. It seems the
complexity lies, in part, in historical and paradigmatic forces that enable schools to operate
and that permit them to attempt innovation without much real change to the culture that
defines and directs life in schools. Many have tried to change what gets taught in school
or how children engage in their work. But, in doing so without fundamentally changing
the structure of the school day or the year, or without reconceptualizing the organization
of groups of teachers and learners, or without reconceiving of the use of resources these
would be reforms have only distorted and weakened a shared vision for improved

education in schools.

207

The work in these arenas is and will continue to be labor-intensive, as all reforrn-
oriented educators work upstream against long standing conceptions of roles, work
relations, authority stmctures, perspectives on where professional knowledge comes from,
and the decision making about what happens specifically in the classroom.

Many reformers aim to create real change through the work of classroom
practitioners. Reflected in the increasing visibility of teachers engaged in action research,
organizational leadership, and professional development facilitation, many reformers
believe it is the teacher who will make the kinds of sustaining changes that result in quality
improvements for student learning. It seems easier to think of teachers as central to
education reform—changing what students learn and how they learn it—than to think of
teachers as central to financial, organizational, or structural change. However, the extent
to which these arenas become interdependent, influencing, guiding, and supporting
authentic change in each, is dependent in large measure upon classroom teachers who can
imagine the possible impact of new approaches to teaching, enact experimentations, and
articulate meaningful connections to others outside the classroom.

And so, it follows that a third arena of reform is the professional development of
teachers (see Figure 10). To influence real and lasting change in schools, we must place a
tremendous amount of attention and resources on the professional learning and
development of the classroom practitioner who will shape and revise and enact the visions

of education and school reform.

208

Reflecting on my work with Lisa and the lessons learned in our collaboration, I
have generated the following descriptors of this reform-oriented teacher:

1. Has active working knowledge for teaching in the classroom. This
includes knowledge of content, pedagogical content, curriculum,
pedagogy, learners, contexts, and purposes.

2. Holds models and images of what is possible for student learning, as
proposed in education reform literature. This involves a paradigm shift
in perspective on the kind of learning that can take place in school
settings. This shift is a move away fi'om the teacher's apprenticeship of
observation or early teaching career, likely both.

3. Acts on a critical awareness of the culture of teaching: that it exists; that
it has powerfirl influence on teacher communication and action in
school; that a different culture is needed to support sustained reform
work, and that s/he must have a role in shaping such a culture.

4. Acts on a view that the work of teaching extends beyond the classroom
and therefore requires different skills beyond pedagogical work, for
example. Specifically, she seeks skills for creating and sustaining critical
conversations with colleagues about teaching practices, beliefs, and
questions.

5. Reflectively attends to her identity as a teacher who engages in critical
colleagueship. That is, she possesses a stance toward moving beyond
sharing ideas and supporting one another through the change process
“to confronting traditional practice—the teachers’ own and that of his or
her colleagues—with an eye toward wholesale revision” (Lord, 1994,
p.193)

A reform-oriented teacher is a practitioner who has the knowledge and skill to
contribute to the profession at both the micro-level of classroom work and the macro-level
of institutional work. I think it is becoming clearer to reformers and teacher educators——
and to many teachers—that the changes called for cannot be realized if microwork is the

concern of the teacher and macrowork is the concern of everybody else outside the

classroom. A reform-oriented teacher must have the intellectual resources, skills, and

209

support to move back and forth between these levels of reform. Such a shift in our
profession’s perspective on individual classroom teachers’ work, emerging with our
increasing clarity about the complexity and magnitude of current reforms, requires a shift
in the kinds of knowledge teachers need to fiilly participate as reform-oriented
practitioners. This study, my collaborative work with one teacher learning to teach math
in new ways, offers some insight into what teachers may need to know to share their
wisdom of practice and to transform it into tools and resources that support their

continual learning and development as teachers.

New Questions For New Work

Through this study I have gained an understanding of the need for teachers to
construct and use what I have called professional participation knowledge in order to
engage in sustainable reform-oriented practices. Learning that this knowledge for
participating with colleagues is distinct from other knowledge teachers hold and use raises
many questions. As a field, we might advance our understanding of teacher knowledge
for practice by exploring fiirther what is involved in creating and sustaining the transitive
support communities in which teachers construct the professional participation knowledge
needed for the “critical practices” (Little, 1982) called for in the reform literature.

As researchers, both university-based and school-based, we can pursue questions
that help us further define the nature and content of professional participation knowledge.

Ifknowledge “categories” is seen as an appropriate structure, what are the categories of

210

knowledge teachers develop and use when working with colleagues?

Reflecting on the preliminary categories suggested by this study in relation to
current literature on professional development I can imagine questions about additional
categories that may be explored in future research work: What is the nature of teachers’
knowledge of argument and is it transformed through reform-oriented work with
colleagues? In what ways? What knowledge do teachers hold about evidence and its
relation to claims made about teaching and learning. What is the relation of teachers’
knowledge of research literature to professional interactions around instruction? What is
the nature of teachers’ knowledge of theoretical frames and how is this knowledge used in
interactions with other educators?

Exploring a range of possible categories that might be included in a domain of
professional participation knowledge creates opportunities for researchers and teachers
together to build a language that clarifies and delineates this kind of knowledge in relation
to other forms that constitute a knowledge base for a professional practice.

As teacher educators, both university-based and school-based, we can create and
sustain transitional support communities in which teachers can observe, develop, and
practice professional participation knowledge in use. The rapidly expanding literature on
teacher groups offers a wealth of imagery and language for crafting communities in which
reform-oriented educators can create and participate in boundary conversations about
practice. I think there is great promise for real change in education through learning

communities that foster exchanges of knowledge and norms between university- and

211

school-based practitioners. Such exchange support teachers moving out from their
knowledge community of instruction into meaninng participation in arenas of work
formerly conducted by administrative leaders and researchers. Likewise these exchanges,
support teacher educators and researchers in acquiring the necessary understanding and
skill to authentically participate in long term work with classroom practitioners.

As teachers, both university-based and school-based, we can seek out and
participate in opportunities to work collectively in tasks that require our collaborative
engagement as educators across cultural boundaries of research, innovation, and practice.
In such continual collaboration, I believe, lies the potential to develop and use a shared
language for the teaching as a practice. As I bring this research project to a close,
completing my graduate studies and creating new contexts for my continued learning, I am
struck by a rapidly growing spectrum of professional development opportunities. Many
teachers are finding ways to respond to the tug of intellectual hunger without leaving their
work in classrooms. I have met teachers who are striving to continue developing as
intellectually alive adults and thoughtful practitioners by keeping their learning grounded
in daily interactions with children, parents, and other educators. These teachers’
commitment to stay in the classroom brings with it a profound psychological and social

struggle, about which the field of education is only beginning to raise questions.

212

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