THE MEANING OF TEACHING MATHEMATICS:
TEACHER POSITIONINGS AS EMBEDDED IN ALGEBRA TEACHERS’ GUIDES
By
Heejoo Suh

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Curriculum, Instruction, and Teacher Education—Doctor of Philosophy
2017

ABSTRACT
THE MEANING OF TEACHING MATHEMATICS:
TEACHER POSITIONINGS AS EMBEDDED IN ALGEBRA TEACHERS’ GUIDES
By
Heejoo Suh
Teacher educators have been examining the professional status of teaching, including
defining central practices of teaching, comparing teaching to other professions, and
understanding teachers’ own perspective via interviews, surveys, and observations. The
present study intends to contribute to the discussion by examining the meaning of teaching as
reflected in teachers’ guides.
I chose to examine teachers’ guides because they are known to have impact on
teachers. Being a resource that is close to teachers’ everyday practices, curriculum materials
inspire teachers with what they could do in their classroom. Educators intending large-scale
educational reform pay attention to curriculum materials. Careful use of linguistic features
therein could enhance thus further support teachers’ guides in effective communication with
teachers.
I investigated four 8 th grade Algebra teachers’ guides, which were selectively chosen
to represent variety. Drawing on positioning theory, I observed positionings regularly
appearing in each of those four. Then I turned to idiosyncratically-observable positionings.
Two research questions sought understanding of what teaching mathematics entails as
presented in the TGs, hence how each guide constructs teaching mathematics. Last, I
examined the guides’ linguistic features. This was for understanding the degree of teacher
professional judgment acknowledged by the guides.
My results indicated that, as constructed by each guide, teaching mathematics does
not differ much across the guides. Those guides presented various types of knowledge as
entailed in teaching mathematics. Compared to aspects on teacher professionalism in the

literature, the guides occasionally addressed teacher research, interaction with colleagues,
utilizing knowledge, and acknowledging uncertainty. In addressing these aspects, the guides
in most cases did so with insufficient support. Examining idiosyncratic positionings, I found
two types: i) positionings occurred idiosyncratic only, and ii) positionings occurred
idiosyncratically in addition to their regular appearance. The latter can be classified into two
types: i) one that succeeds the context of the communication actions associated with the
general positioning, and ii) one dissociated from the context. My linguistic examination of
the guides suggested that they varied in their use of voice. Some are more directive, others
are more suggestive, indicating different levels of acknowledgement of teachers’ professional
judgment.
In this dissertation’s last chapter, I present ways in which this study contributes to
understanding of curriculum materials and of teacher professionalism. I end this dissertation
with implications for curriculum authors, teachers, teacher educators, and researchers.

Copyright by
HEEJOO SUH
2017

Dedicated to f;
we have survived another day.

v

ACKNOWLEDGEMENTS

My sincerest gratitude to my Michigan State University professors, namely Dr. Alicia
Alonzo for introducing me to critical issues in teacher education, Dr. Tonya Bartell for your
support and insights into how I better could address prospective teachers’ needs as an
instructor, Drs. Kristine Bieda and Janine Certo for your support and advice on how I
successfully could enact my duties as a field instructor, and Drs. Mary Juzwik and Ralph
Putnam for your guidance during my early stage in the program.
I also sincerely thank leaders of the College of Education and the Department of
Teacher Education: the current and former department chairs, Drs. Margaret Crocco and
Avner Segall; the current and former program coordinators, Drs. Sandra Crespo and Peter
Youngs; and staff members Linda Brandau, Ann Castle, Terry Edwards, Lisa Keller (from
the PRIME program), Lindsay Metiva, and Amy Peebles.
Thank you also to professors at the University of Michigan and at Ewha Womans
University. Thank you to Dr. Vilma Mesa for her patience and support when I was lost in the
woods; to Dr. Edward Silver with whom I was honored to work in a research project and in
the school of education at Dearborn; to Dr. Mary Schleppegrell for her guidance into the
world of discourse analysis; and to 고응일교수님 (Dr. Ko, Eung Il), 윤정호교수님 (Dr.
Yoon, Jungho), and 이향숙교수님 (Dr. Lee, Hyang-sook) for mentoring me in my Ewha
time and beyond.
Drs. Jillian Cavanna, Kate Johnson, Alex Theakston Musselman, and Samuel Otten,
thank you for the enjoyment you gave me in my being your office mate. Thank you to Dr.
Heather Howell for your mentoring, research opportunities, and writing opportunities, in
addition to emotional support and encouragement you gave me to enable me to complete my

vi

dissertation. And thank you to 김성식교수님 (Dr. Kim, Sungsik), 김수철교수님 (Dr. Kim,
Soochul), 양희준박사님 (Dr. Yang, Heejoon), 이성회박사님 (Dr. Lee, Sunghoe),
이현선생님 (Mr. Lee, Hyun), 최유림선생님 (Dr. Choi, Yourim), and 황지원교수님 (Dr.
Hwang, Jiwon), for patiently supporting me in my dissertation work while I adjusted to the
Korean educational research community. I also thank 유정애 센터장님 (Dr. You, Jeongae),
the director of the Institute of Curriculum Excellence at Chung-Ang University, for believing
that I could complete my dissertation. I am deeply grateful for the opportunity to become a
part of your center.
I sincerely thank my dissertation committee due largely to whom I have come this far.
Thank you to Dr. Beth Herbel-Eisenmann – my dissertation chair, academic advisor,
researcher role model, and US mother – for her huge intellectual and emotional support; her
close advising deeply impacted me as researcher and a writer and instilled in me the
aspiration to be in future the kind of mentor she is. And for your questions, inspiration and
support in my dissertation process, thank you Dean Robert Floden, Dr. Corey Drake, and Dr.
Amy Parks. My dissertation’s contributions are possible because of you. Its flaws are mine.
I thank those in the popular culture industry, thanks to whose hard work I could relax
and refresh myself and my thoughts and keep on dissertating, a la “All work and no play
makes Jack a dull boy!” Last, I am appreciative of my immediate family: 김상숙 (Kim, Sang
Sook), 서정호 (Suh, Jung Ho), 서희연 (Suh, Heeyeon). And my lovely nephew 신윤호
(Shin, Peter Yoonho). You believed in me even when I did not. Thank you.

vii

TABLE OF CONTENTS

LIST OF TABLES ..................................................................................................................... x
LIST OF FIGURES .................................................................................................................xii
KEY TO ABBREVIATIONS ................................................................................................ xiii
CHAPTER 1: INTRODUCTION .............................................................................................. 1	
Organization........................................................................................................................... 3	
CHAPTER 2: RELEVANT LITERATURE ............................................................................. 6	
Review of the Literature on Curriculum Materials ................................................................ 6	
Review of the Literature on Teacher Professionalism ........................................................... 9	
Knowledge Base .............................................................................................................. 10	
Teacher research .............................................................................................................. 11	
Interaction with Colleagues ............................................................................................. 12	
Utilizing emergent bilinguals’ knowledge as a resource ................................................. 13	
Acknowledging Uncertainty ............................................................................................ 14
CHAPTER 3: METHODS ....................................................................................................... 16	
Theoretical Framework: Positioning Theory ....................................................................... 16	
Positionings ...................................................................................................................... 16	
Storyline ........................................................................................................................... 21	
Communication Act ......................................................................................................... 23	
Research Questions .............................................................................................................. 24	
Data Sources and Data Analysis .......................................................................................... 26	
Data Sources .................................................................................................................... 26	
Data Analysis Plan for Research Question 1: What teacher positionings regularly are
observable from the four selected mathematics TGs? How do these positionings
compare with research on teacher professionalism? What teacher positionings are
pervasive in the four guides? ........................................................................................... 28	
Data Analysis Plan for Research Question 2: What teacher positionings irregularly are
observable from the four selected mathematics TGs? ..................................................... 33	
Data Analysis Plan for Research Question 3: What is the range of voices across the four
TGs? How might these voices shape the degree of obligation to the teacher positionings
as duties? .......................................................................................................................... 34	
Structural Comparison of the TGs ....................................................................................... 37	
Reflexivity and Expert Debriefing ....................................................................................... 40	
Researcher Reflexivity: My Motivation to This Study ........................................................ 40	
Myself as a Reader of the Guides ........................................................................................ 46	
CHAPTER 4: RESULTS ......................................................................................................... 49	
Results for Research Question 1: Regularly Occurring Positionings .................................. 49	
Narrow List of Positionings ............................................................................................. 49
Knowledge base. .......................................................................................................... 50
Teacher research. ......................................................................................................... 52
Interaction with colleagues. ......................................................................................... 56

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Utilizing emergent bilinguals' knowledge as a resource. ............................................. 57
Acknowledging uncertainty. ........................................................................................ 58
Common Positionings ...................................................................................................... 60
General information of the TG. ................................................................................... 62
Specifics of the content. ............................................................................................... 63
Assessment................................................................................................................... 64
Pervasive Positionings from each TG .............................................................................. 65	
Degree of Support ............................................................................................................ 68
Teachers have a duty to know vocabulary. .................................................................. 69
Teachers have a duty to know potential student errors. ............................................... 69
Teachers have a duty to know the pacing of the curriculum/chapter/lesson. .............. 70
Results for Research Question 2: Idiosyncratically Occurring Positionings ....................... 71	
General Descriptions ........................................................................................................ 71	
Idiosyncratic-Only Type .................................................................................................. 72	
Idiosyncratic-Regular Type ............................................................................................. 74	
Closing Remarks .............................................................................................................. 78	
Results for Research Question 3: Voices of the TGs........................................................... 79	
General Description ......................................................................................................... 80	
Pronoun: General Findings .............................................................................................. 82	
Pronoun You ..................................................................................................................... 83	
Pronoun We ...................................................................................................................... 85	
Pronoun I.......................................................................................................................... 85	
Modality ........................................................................................................................... 87	
Imperatives ....................................................................................................................... 91	
Conclusion from the Three Results.................................................................................. 93	
CHAPTER 5: DISCUSSION................................................................................................... 95	
Returning to the Research Questions ................................................................................... 95	
Research Question 1 ........................................................................................................ 95
Narrow list of positionings........................................................................................... 95
Commonly-observed positionings. .............................................................................. 98
Pervasive positionings from each TG. ......................................................................... 98
Degree of support. ........................................................................................................ 99
Summary. ................................................................................................................... 100
Research Question 2 ...................................................................................................... 100
Idiosyncratic-only type. ............................................................................................. 100
Idiosyncratic-regular. ................................................................................................. 101
Research Question 3 ...................................................................................................... 103	
Looking Backward ............................................................................................................. 106	
Looking Forward ............................................................................................................... 107	
Implications for Curriculum Authors............................................................................. 107	
Implications for Teachers and Teacher Educators ......................................................... 108	
Implications for Future Research ................................................................................... 109	
APPENDICES ....................................................................................................................... 112
APPENDIX A: LIST OF THE REGULARLLY APPEARING HEADINGS .............. 113	
APPENDIX B: TABLES OF REGULAR AND IDIOSYNCRATIC POSITIONINGS
........................................................................................................................................ 119	
REFERENCES ...................................................................................................................... 128

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LIST OF TABLES

Table 1. Subdomains of the Knowledge Base of Teaching Mathematics ............................... 10	
Table 2. Phases of Thematic Analysis Table, from Braun and Clarke (2006, p. 87). ............. 29	
Table 3. General Structure of the Four Guides ........................................................................ 38	
Table 4. Phases of a Lesson ..................................................................................................... 39	
Table 5. Positionings Addressing Teacher research ................................................................ 53	
Table 6. A Positioning Addressing Interaction with Colleagues ............................................. 56	
Table 7. A Positioning Addressing Utilizing Emergent Bilinguals’ Knowledge as a Resource
.......................................................................................................................................... 57
Table 8. Positionings Addressing Acknowledging Uncertainty .............................................. 59	
Table 9. Common Positionings ................................................................................................ 61	
Table 10. Regularly and Idiosyncratically Occurring Positionings ......................................... 72	
Table 11. Idiosyncratic-Only Type Positionings ..................................................................... 73	
Table 12. Idiosyncratic-Regular Type Positionings................................................................. 75	
Table 13. General Findings ...................................................................................................... 81	
Table 14. The Use of Pronoun: General .................................................................................. 82	
Table 15. The Use of Pronoun You .......................................................................................... 84	
Table 16. The Use of Pronoun We ........................................................................................... 85	
Table 17. The Use of Pronoun I ............................................................................................... 86	
Table 18. Modality per Explicit and Implying......................................................................... 88	
Table 19. Excerpts from Halliday and Matthiessen’s (2014, p. 116) Table for Finite Verbal
Operators .......................................................................................................................... 88
Table 20. Modality with Explicit and Implying Combined ..................................................... 89	
Table 21. Modality by Suggestive and Assertive .................................................................... 90	
Table 22. Imperatives: General Results ................................................................................... 91	

x

Table 23. Range, Mean, Median, Mode of the Frequency of Imperative Incidences .............. 92	
Table 24. Aggregated Table ..................................................................................................... 93	
Table 25. Headings Examined from the Phase of IntTG ....................................................... 113	
Table 26. Headings Examined from the Phase of IntCh ........................................................ 114	
Table 27. Headings Examined from the Phase of IntLe ........................................................ 115	
Table 28. Headings Examined from the Phase of BeLe ........................................................ 115	
Table 29. Headings Examined from the Phase of MiLe ........................................................ 116	
Table 30. Headings Examined from the Phase of EnLe ........................................................ 117	
Table 31. Headings Examined from the Phase of EnCh ........................................................ 118	
Table 32. Standards and Goals............................................................................................... 119	
Table 33. Resources ............................................................................................................... 121	
Table 34. Accommodation ..................................................................................................... 122	
Table 35. Tasks ...................................................................................................................... 122	
Table 36. Assessment............................................................................................................. 124	
Table 37. General Information: Features and Structures of the TG ...................................... 124	
Table 38. General Information: Mathematics ........................................................................ 126	
Table 39. Additional Features ................................................................................................ 127	

xi

LIST OF FIGURES

Figure 1. Positionings observed from more than three phases. ............................................... 66	

xii

KEY TO ABBREVIATIONS

TG

Teachers guide

IntTG Introduction to a TG
IntCh Introduction to a chapter
IntLe Introduction to a lesson
BeLe Beginning of a lesson
MiLe Middle of a lesson
EnLe Ending of a lesson
EnCh Ending of a chapter

xiii

CHAPTER 1: INTRODUCTION
Teachers’ beliefs about what their profession entails, or about their professional
selves, can impact their practice (Zohar, Degani, & Vaaknin, 2001; Zohar & Dori, 2003).
Therefore, understanding sources of teachers’ formation of their professional selves is
important to making productive changes to their practice. By understanding sources, I mean
first to know what the sources are, and, second, what each source presents as to what teaching
mathematics entails.
In this study, I conceptualize self as a dynamic construct combining internal and
external factors (Harré, 2012; Hermans, 2013). I paid particular attention to external factors. I
did so because people rely on “[their] personal background knowledge, and their attitudes
toward each other, sociocultural assumptions concerning role and status relationships, as well
as social values associated with various message components” (Gumperz, 1977, p. 191).
Research about beliefs suggests similar points. A belief becomes stable when it is shared with
others or is reinforced in multiple contexts (Leatham, 2006; Walkerdine, 1988). Teachers’
beliefs are less an individual phenomena, but more a reflection of the perspectives that are
shared in a professional community (Parks, 2010; Parks & Wager, 2015; Taylor, 1996).
Applying these insights to teaching, I see teacher professional self as what shaped by
both individual self-reflection and interaction with the outside world (Cooper & Olson, 1996;
Hand & Gresalfi, 2015; Parks, 2010; Parks & Wager, 2015). Outside-world factors include
teachers’ self-concepts, expectations by the professional community, and images society
broadly shares on teaching (Beijaard, Meijer, & Verloop, 2004; Reyes & Rios, 2003). Also
relevant is that teachers with innovative ideas likely would find it challenging to manifest
those ideas if a majority of peers regard such innovations as only barely aligning with their
perceptions of what teaching is and should be, or if the school system does not understand the
value of innovative ideas teachers are hope to implement (Davis, 2002; Deemer, 2004).

1

Among a vast range of potential external factors, in this dissertation I attend to TGs.
Research indicates that the external factor in teachers’ landscapes impact teachers’
development of their professional selves, regardless whether messages are explicit or implicit
(Cooper & Olson, 1996; Rennert-Ariev, 2008; Reynolds, 1996; Sugrue, 1997). Mathematics
education research, too, reports the on-reader impact of messages embedded in written texts
(e.g., Dowling, 1996; Herbel-Eisenmann, 2007).
Building on this research, I explored externally-assigned professional selves by
drawing on positioning theory as expounded by Harré and colleagues (see Harré, 2010). In
particular, I gave attention to teacher positionings from four TGs, following the storyline of
teacher professionalism. When identifying positionings, I adopted two approaches. First, I
attended to those guides’ range of duties presented for model teachers. In so doing, I aimed to
demonstrate teaching mathematics as constructed by each guide, hence the kinds of duties a
professional teacher should fulfill. My assumption was that the guides provide contents
seeming relevant and important for teaching mathematics well, rather than random
information that may or may not support teaching of mathematics. Then, I attended to the
form of the language used in the guides. Drawing on the notion of voice (Herbel-Eisenmann,
2007; Remillard et al., 2011), I examined the imperatives, personal pronouns, and modality in
each TG. Examining the tone used throughout the guides, I sought to understand the guides’
suggested space in which teachers may maneuver. Such collective analysis allowed me to
provide a multifaceted understanding of external positionings relative to teachers’
professional selves.
Although I use the word teacher, this study is more about teaching practices than
teachers’ personal qualities (see Kennedy, 2010). This study paid attention to teaching as a
profession and to what society expects of that profession, as constructed by TGs. In this
study, I did not intend to examine the teacher professional self an individual teacher holds;

2

rather, this study focuses on the professional selves as presented in the surroundings of
teachers’ environments. Positioning theory was particularly useful for such analysis because
it acknowledges self as reciprocally constructed. In other words, teachers develop their
professional self not in a vacuum, but while interacting with the external world. The
professional practice as constructed by external world may not be individualized, but it is a
source that can influence individual teachers’ sense of professional selves. In addition,
positioning theory attends to “taken-for-granted practices” (Harré, 2010, p. 53) conceived as
natural by the external world. Therefore, the theory allowed me to discuss teaching practices
the guides assumed to be natural.
Organization
This dissertation comprises five chapters. The Introduction supra is the first, an
overview of this study’s context and infra this dissertation’s organization. Chapter 2 provides
this study’s theoretical background and presents its research questions. First, I reviewed
literature on curriculum materials, thereby seeking to unfold what is known about written
curriculum materials as an external factor with a potential to impact teachers’ construction of
their professional selves. In addition, I attended to literature on teacher professionalism. In
particular, I focused on five aspects, namely i) knowledge base, ii) teacher research, iii)
interaction with colleagues, iv) utilizing knowledge, and v) acknowledging uncertainty.
In Chapter 3, I turned to positioning theory, the theoretical framework of this
dissertation. In particular, I explained each of the three main concepts of the theory, namely i)
positioning, ii) storyline and iii) communication act. Following the theoretical framework, I
presented three research questions, two about the positionings embedded in the selected TGs
and one about the voice the guides are using. In addition, I expanded on the notion of rights
and duties, two terms widely used when defining positioning. In so doing, I explained why I
chose to attend to duties only and not rights in this study. Then, I outlined and discussed my

3

method and my rationale for choosing Algebra TGs as my data source. For each of the three
research questions, I gave a data analysis plan. In addition, I made explicit how I approached
the guides when observing positionings, as a way to be explicit with the analysis process,
hence enhance this study’s rigor. Following my approach to the guides, I described who I am
in the subsection named researcher subjectivity.
Chapter 4 describes my results. First I attended to generally-observable positionings. I
compared these findings to the literature about teacher professionalism. Then, I discussed the
seven positionings present in all the selected guides. Following this, I presented for each
guide the positionings revisited multiple times. I closed my reporting of findings for the first
research question by sharing the differences I observed in terms of the degree of support.
With the idiosyncratic positionings, I presented idiosyncratic-only types followed by
idiosyncratic-regular types of positionings to present how idiosyncratic positionings are
occurring. I closed my examination of positionings by presenting pervasive positionings
counting idiosyncratic cases. Following the positionings is the examination of voice, to
examine which I attended to pronoun, modality, and imperatives. For an across-guides
comparison, I provided the ratio of each of the three aspects (pronoun, modality, and
imperatives) to the totals of sentences and of pages examined, instead of using the number
counts.
Chapter 5, the last, presents my discussion, in which I revisited my results in light of
the research questions. Answering the research questions, I found that the regularly occurring
positionings were more similar than different across the teachers’ guides I examined. In
addition, I identified idiosyncratic positionings occurring in at least three different ways,
which showed that idiosyncratic occurrence is key to understand the presence of a
positioning. Further, I found that the teachers’ guides are, in general, more likely to use
linguistic features that restrict teachers from using their professional judgements. Following

4

this is a retrospective on what writing this dissertation taught me about research. I also
offered suggestions looking forward to possible extensions of this study: first by considering
implications for curriculum authors; second for teacher educators, and teachers. Last, I
suggested possible future directions for research.

5

CHAPTER 2: RELEVANT LITERATURE
This chapter is my review of literature on curriculum materials and on teacher
professionalism. Regarding curriculum materials, I focused on empirical research on
teachers’ engagement with those materials, their potential as an external factor that may
impact teachers’ sense of professional self, and ways to maximize those materials’ potential
as a resource for teacher education. Regarding teacher professionalism, I attended to five
aspects: i) knowledge base, ii) teacher research, iii) interaction with colleagues, iv) utilizing
students’ knowledge, and v) acknowledging uncertainty. To be clear, these five aspects are
by no means a comprehensive list of what the educational research field suggests in relation
to teacher professionalism.
Review of the Literature on Curriculum Materials
In this section, I discuss how teachers engage with curriculum materials, and those
materials’ potential for impacting teachers’ sense of professional self. Researchers suggest
that teacher development can be effective i) when it is connected to teachers’ classroom
practices, ii) when it goes through several iterations over time, iii) when supports are
ongoing, and iv) when teachers can experiment and reflect on what they learned (Collopy,
2003; Remillard, 2000). Curriculum materials satisfy these conditions, which means that
those materials have strong potential to bring changes to teachers’ sense of professional self.
Collopy’s (2003) empirical study well supports this point: the teacher in the study changed
her practice as she adapted ideas from curriculum material she was using.
How the materials impact teachers’ sense of professional self is a combination of the
material-authors’ intentions, and the teachers’ readings of the materials. In other words, the
impact that materials can have on practice depends on what teachers take from the materials
(Collopy, 2003; Remillard, 2000; Remillard & Bryans, 2004; Sosniak & Stodolsky, 2007;
Stein & Kim, 2009). Observing two mathematics teachers’ use of curriculum materials,

6

Remillard (2000) concluded textbooks are unlikely to have direct impact on enacted
curricula, because teachers modify contents within those books. Yet she also recognized
curriculum materials’ potential as a tool for teacher learning. Teachers appreciate textbooks
because those texts save their planning time, and help them pace even when they did not
follow exactly what the textbook asked them to do (Sosniak & Stodolsky, 2007). This
variability is reflected well in Sherin’s and Drake’s Curriculum Strategy Framework (2009),
a framework for understanding teachers’ engagement with curriculum materials. The
framework includes reading, evaluating, and adapting. When teachers engage with
curriculum materials, they do their own reading of selected parts that address their needs.
They then approach their reading with their own evaluation stances, and with their own
orientation toward adaptation. The term adapting, instead of enacting it with fidelity, signifies
existing variability in teachers’ use of curriculum materials.
Despite that the materials’ impact on teachers’ sense of professional self depends on
how teachers engage with them, some researchers attend to the substantial potential impact
which curriculum materials have for teachers’ sense of professional self. Curriculum
materials are known to have large-scale influence on classroom practice (Ball & Cohen,
1996; Collopy, 2003; Stein & Kim, 2009). To implement reform-based instruction in a large
number of classrooms, educators strategically chose to promote curriculum materials of
innovative design (Ball & Cohen, 1996) with the expectation that teachers could teach
themselves and develop teacher professional self as intended by the reform from reading the
curriculum materials (Sherin & Drake, 2009). Curriculum materials’ potential as tools for
teacher professional development becomes more significant when considering beginning
teachers. Because they newly are starting their careers, it is unrealistic to expect them to
invent effective teaching materials. Although teachers’ use of curriculum varies by individual
teachers, and well-experienced teachers may choose not to use textbook materials (Sosniak &

7

Stodolsky, 2007), less-experienced teachers tend to rely more on their curriculum materials
(Ball & Feiman-Nemser, 1988; Remillard & Bryans, 2004). A more realistic expectation
might be, as Ball and Feiman-Nemser (1988) have suggested, orienting beginning teachers
“toward learning from teacher’s guides and other curriculum materials in a way that allows
them to move toward building their own units of study, units that are responsible for subject
matter goals and responsive to students” (p. 421). That is, teacher education programs should
aim to encourage prospective teachers in flexibly adapting curriculum materials rather than
ignoring or totally relying on them (Drake, Land, & Tyminski, 2014). Because beginningteachers tend to rely on curriculum materials – and such reliance is reasonable to expect from
them – curriculum materials’ impact on beginning-teachers’ development of professional self
is not to be ignored.
Several researchers have given serious attention to maximizing the potential of
curriculum materials as a resource for teacher development (Ball & Cohen, 1996; E. A. Davis
& Krajcik, 2005; Drake et al., 2014). Using the term educative curriculum materials, Davis
and Krajcik (2005) suggested that well-designed curriculum materials can “help to increase
teachers’ knowledge in specific instances of instructional decision making” while helping
them “develop more general knowledge that they can apply flexibly in new situations” (p. 3).
Ball and Cohen (1996) also explored the potential of curriculum materials and how these
materials can contribute more to teacher learning. More recently, Drake, Land, and Tyminski
(2014) pointed out that “educative curriculum materials can and should be utilized in teacher
preparation to support PTs [prospective teachers] in developing not only knowledge and
practices related to curriculum materials and their use, but also the broader knowledge bases
needed for successful novice teaching” (p. 155). In other words, curriculum materials have
potential to strongly impact teachers’ sense of professional self. Curriculum authors can

8

achieve this by designing curriculum materials with a clear intent of making them tools for
teacher learning.
Taken together, although curriculum materials do not have control over teachers’
learning and practice, they can and do serve as a source of input for the formation of
professional selves. In this dissertation, I pay particular attention to this potentiality that
curriculum materials have. Among the range of curriculum materials, I chose to focus on the
guides written specifically for teachers. By so doing I hope to make visible what teachers
guides (hereafter, TGs) consider teaching mathematics to entail. I also hope to understand the
amount of teacher professional judgment acknowledged by the guides. Thoroughly
understanding teachers’ professional selves is complex because many factors influence it,
including teachers’ personal experiences, their past experiences as prospective and/or
practicing teachers, common sense shared in the community (of which the teachers are a
part), policy expectations, school leadership, and more. By examining TGs assumed to be
close to teachers’ practices and learning, my dissertation will contribute to understanding a
portion of so complex a matter.
Review of the Literature on Teacher Professionalism
Here, I discuss the literature addressing teacher professionalism in order to use it in
the results section as a guide to interpret the positionings I observed from the TGs. The
teacher professionalism aspects included in this review are that of i) knowledge base, ii)
teacher research, iii) interaction with colleagues, iv) utilizing students’ knowledge, and v)
acknowledging uncertainty. This review’s purpose is not to provide a comprehensive map of
all aspects extant in this research area, nor on presenting the five most-widely accepted
aspects. Instead, this dissertation’s readers might consider the abovementioned aspects as five
example contexts. I am making such suggestion because this review locates the results of this
study.

9

Knowledge Base
One line of research on teacher professionalism attends to the multiple knowledge
bases that successful teachers possess (Ball, Thames, & Phelps, 2008; L. Shulman, 1986).
The expectation here is that in addition to their knowledge of mathematics, mathematics
teachers have other knowledge bases. Three decades ago, Shulman (1986; 1987) questioned
whether the then-current version of teacher evaluation standards were sufficiently
comprehensive to address properly what teaching entails. Shulman suggested further
specifying types of knowledge required when teaching. Instead of using “content knowledge”
to cover multiple types of knowledge, Shulman subcategorized knowledge into i) subjectmatter knowledge, ii) pedagogical-content knowledge, and iii) curricular knowledge.
Table 1. Subdomains of the Knowledge Base of Teaching Mathematics
Subdomain
Common content
knowledge
Specialized content
knowledge
Horizon content
knowledge
Knowledge of
content and students
Knowledge of
content and teaching
Knowledge of
content and
curriculum

What it is
“[T]he mathematical knowledge and skill used in settings other
than teaching.” (Ball, Thames, & Phelps, 2008, p. 399)
“[T]he mathematical knowledge and skill unique to teaching.”
(Ball, Thames, & Phelps, 2008, p. 400)
“[A]n awareness of how mathematical topics are related over the
span of mathematics included in the curriculum.” (Ball, Thames,
& Phelps, 2008, p. 403)
“[K]nowledge that combines knowing about students and knowing
about mathematics.” (Ball, Thames, & Phelps, 2008, p. 401)
“[C]ombines knowing about teaching and knowing about
mathematics.” (Ball, Thames, & Phelps, 2008, p. 401)
“[R]epresented by the full range of programs designed for the
teaching of particular subjects and topics at a given level, the
variety of instructional materials available in relation to these
programs, and the set of particular curriculum or program
materials in particular circumstances.” (Shulman, 1986, as cited in
Ball, Thames, & Phelps, 2008, p. 391)

Extending Shulman’s idea, Ball and colleagues (2008) suggested that mathematical
knowledge for teaching can be bisected into subject matter knowledge and pedagogical
content knowledge. Subject matter knowledge consisted of common content knowledge,
horizon content knowledge, and specialized content knowledge. Pedagogical content

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knowledge consisted of knowledge of content and students, knowledge of content and
teaching, and knowledge of content and curriculum. Table 1 describes each of these
subdomains. Since this groundbreaking work began, a number of researchers focused on
mathematical knowledge for teaching in a variety of settings, or improvised the subdomains
list (e.g., Bell, Wilson, Higgins, & McCoach, 2010; Kleickmann, Richter, Elsner, Besser, &
Krauss, 2013; Kunter et al., 2010; Ryve, Nilsson, & Mason, 2011; Speer, King, & Howell,
2014; Steele & Rogers, 2012; Tatto et al., 2008). In my data analysis, I adopted Ball and
colleagues’ (2008) classification to understand which of the six subdomains are addressed in
TGs, and which are not.
Teacher research
Another line of research related to teacher professionalism expects teachers to utilize
their classroom practices as a source of professional development. Cochran-Smith and Lytle
(1990) suggested that teacher research is likely to differ from research conducted by
university researchers, but the difference is the main reason that makes teacher research a
fruitful source of information. Teacher research is valuable because it focuses on current
issues from the classroom. It also satisfies participating teachers. When university-generated
knowledge is not seen to be superior to knowledge generated by teachers in their classrooms,
and when the knowledge from two different sources is equally appreciated, teachers benefit
more than when knowledge from one source is less appreciated (Cochran-Smith, 1991). At
the heart of this approach is acknowledgement of the importance of the local knowledge
produced by teachers within their own context (Lytle, 2006). Some may question the value of
teacher research by pointing out that teachers’ observations are not generalizable to other
classrooms; their documentation process may not be scientific, and often their research is not
grounded in theories. Yet these critiques cannot be a reason to refute teachers’ roles as
researchers: first, teacher research should not be treated as a subset of rigorous academic

11

research (Cochran-Smith & Lytle, 1990); second, teacher research provides valuable
information to teachers so that they can enhance the quality of teaching (Cochran-Smith &
Lytle, 2006). In addition, work on teacher-action research suggests it to be an effective tool
for professional development, attesting to its pragmatic nature (Gore, 1991; Sales, Traver, &
García, 2011). Examples of teacher research are journaling, writing essays with varied
lengths, oral inquiries, classroom studies, and any activities contributing to teachers’
systematic examination of local classroom context (Cochran-Smith & Lytle, 1990). Reading
this line of research, I attended to the positionings that foregrounded the aspect of teacher
research. Among the options for conducting a teacher research, most positionings I found
were about collecting data from students via assessment. In the results section, I discuss this
in more detail.
Interaction with Colleagues
Researchers suggested collegiality as what professional teachers recognize and
practice to improve their teaching. Unlike the literature about multiple knowledge bases,
which focuses on individual and cognitive aspects of teaching, Research expects teachers to
be social and interactive. Teaching involves being a member of a learning community of
teachers. Shulman and Shulman (2004) stated that “[an] accomplished teacher is a member of
a professional community who is ready, willing, and able to teach and to learn from his or her
teaching experiences” (p. 259), emphasizing the power of interaction in a collegial
community. Mathematics-teacher study groups, in particular, are found useful because
teachers can reflect on their own practices and perspectives through active engagements often
involving dissonance (Crespo, 2006; Drake & Cirillo, 2009; Males, Otten, & HerbelEisenmann, 2010). In fact, researchers argue that such dissonance is what gives a teacher
interaction productivity. The naïve approach of “every teacher has to find his or her own
style” may contribute to a warm atmosphere, but the approach prevents teachers from

12

learning, and has them talk past and around each other (Ball & Cohen, 1999; 1994).
Questioning what a teacher said is more likely to push the teacher to articulate her
assumptions, and provides opportunities for teachers to think about how to deal with an issue
together (Ball & Rundquist, 1993; Little, 1990; S. Wilson & Berne, 1999; Zech, Gause-Vega,
Bray, Secules, & Goldman, 2000). According to Lord (1994),
[k]ey features of professional development, in the light of national content standards,
are to support teachers in their efforts to bring to the surface these questions and
concerns, to help teachers expose their classroom practices to other teachers and
educators, and to enable teachers to learn from constructive criticism (p. 184).
This set of key features reflects the expectation that teachers should interact mutually (i.e.,
with each other). When teachers openly talk about their concerns, question assumptions about
teaching, and produce productive disequilibrium in traditional concepts and daily routines,
collegial interaction becomes meaningful. Building on these studies, I examined which
positionings encourage teachers to interact with other teachers.
Utilizing Emergent Bilinguals’ Knowledge as a Resource
A number of researchers suggest that teachers with professionalism pay attention to
what students can do, rather than what they cannot, in order to support students from a range
of backgrounds, including those from lower socioeconomic status, who are emergent
bilinguals (i.e., second- or even multilingual), with cultural backgrounds different from
school culture, and from under-represented racial groups (Aguirre et al., 2013; Battey, 2012;
Civil & Andrade, 2002; Domínguez, 2010; Domínguez, LópezLeiva, & Khisty, 2013;
Gutiérrez, 2002; Ladson-Billings, 1998; Turner, Domínguez, Empson, & Maldonado, 2013).
These researchers consider students’ background knowledge as a resource for having them
engaged in learning school mathematics. Instead of focusing on the mismatch between
students’ home culture and school culture, these researchers question whose cultural contexts

13

are included and excluded when teaching and learning mathematics. By changing their
beliefs to how students’ home culture and home language can be a resource rather than an
obstacle, in teaching mathematics, researchers and teachers can be open to search for better
pedagogical supports. In their two-step empirical study with teachers, Planas and Civil (2009)
found that teachers’ beliefs about immigrant students can be altered through having a series
of teacher study-group meetings. During the second phase of their research, the authors
followed teachers to their classrooms to see to what extent their talk was reflected in their
practice. Although teachers did not dramatically change their practice, they did provide more
space to immigrant students than before, and were much more reflective on their interactions
with those students, which may lead to change in teachers’ practice in the future. In my
analysis, I searched not only for the positionings asking teachers to make teacher moves to
meet those students’ needs, but also for whether any of those teacher moves are in fact
drawing on what bilingual students bring in.
Acknowledging Uncertainty
The last type of expectation on professional teachers in this review is to acknowledge
uncertainty. Multiple components contribute to uncertainty – from instructional content
(Capobianco, 2010; Floden & Buchmann, 1993; Melville & Pilot, 2014), to pedagogy
(Meister & Nolan, 2001; Midthassel, 2006; Wheatley, 2002; 2005), to student traits or school
culture (Friedman, 1997; Labaree, 2003; Roeser, Skinner, Beers, & Jennings, 2012;
Villaume, 2000). Consider students’ emotional state as an example of uncertainty: teachers
neither can control nor predict what emotionally impacts a student when she is at home. For
the sake of improving classroom practice, acknowledging uncertainty is much more
constructive than denying it. The acknowledgement is indeed a sign of expertise (Floden &
Chang, 2007). This is so because the denial gives teachers the impression that everything is
fine, hence prevents teachers from searching for alternatives (Cohen, 1988; Helsing, 2007). A

14

number of studies have shown that by acknowledging uncertainty, teachers were able to
search proactively for effective pedagogical moves (Bennett, Woods, Wise, & Newton, 2007;
Capobianco, 2010; Friedman, 1997; Meister & Nolan, 2001; Melville & Pilot, 2014;
Midthassel, 2006; Villaume, 2000). To support teachers’ professional development, Jordan,
Kleinsasser, and Roe (2014) suggested, teacher educators should push teachers to confront
uncertainty with critical thinking so that they can avoid settling down on simple but less
effective pedagogical moves. During my data analysis, I looked for incidences where TGs
attend to possible uncertainty or encourage teachers to be flexible in finding effective
pedagogical moves.
So far, I have reviewed background literature explaining why I attended to TGs and
the five aspects that have been proposed as duties to be fulfilled by professional teachers. In
the following chapter, I present research questions and methods I used for this study.

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CHAPTER 3: METHODS
In this chapter, I introduce positioning theory, the theoretical framework of this study.
Before I explain my research methods, I present the three research questions I attended to in
this study. Then, I examine the following: First, I discuss why I chose four algebra TGs as
my data sources. Then, I provide specifics of my analysis processes to answer each of those
three research questions. Following this, I provide a structural comparison of selected TGs,
and a description of who I was as a reader of the guides during the analysis process. I end this
chapter by explaining my effort in maintaining the rigor of this study, in that effort. I make
explicit my researcher subjectivity.
Theoretical Framework: Positioning Theory
In my dissertation study, I used positioning theory to analyze how teaching and
teachers are constructed in the chosen texts in order to better understand teachers’ sense of
professional self. Positioning theory has three mutually-constituted components: positioning,
storyline, and communication acts, each of which I explain in more detail. In explaining
positioning, I extend the relationship between the notions of rights and duties because
positioning often is defined as a cluster of these two.
Positionings
Harré (2010) described positionings as “clusters of beliefs about how rights and
duties, or expectations, are distributed in the course of an episode of personal interaction and
the taken-for-granted practices in which most of these beliefs are concretely realized” (p. 53).
Positioning is a cluster of beliefs because the theory is more interested in “what a person
‘may do and may not do’” than in “what he or she can do” (p. 52, emphasis added). The
terms rights and duties depict the illocutionary nature of actions that are acceptable, expected,
or natural at a moment. Rights and duties, or positionings, frame what a person can do or say.
Different sets of rights and duties are associated with different positionings.

16

Coherency is not an essential characteristic of positionings, nor is intentionality
(Wagner & Herbel-Eisenmann, 2009). Positionings may vary across settings. In addition,
people can intentionally negotiate self and other’s positionings, but the process of positioning
can be unintentional. Positioning theory does not assume the existence of a mental first
person, which is the consistent self that oversees and controls other selves (Louis, 2007).
Instead, an individual’s positionings change over time and space. Also, a person can be
positioned in multiple ways by herself and others. Embracing incoherency, positioning theory
sees positioning as ephemeral and negotiable (Harré, 2010). Because positioning is
ephemeral, for example, my positioning as a daughter can fade when I interact with people
other than my parents. In short, I do not carry a positioning with me, but let positionings
emerge from the situation in which I am interacting. One can position oneself or a
counterpart in an interaction (i.e., first-order positioning), refute a positioning imposed by
others on oneself (i.e., second-order positioning), or position others who are not present at the
scene of interaction (i.e., third-order positioning). Second-order positioning happens when
people try to negotiate imposed positionings. Interaction here includes written
communication in addition to spoken communication. For example, a TG construes firstorder positionings for teachers by describing what teachers need to do to teach the content.
When teachers read the guides, some might disagree with the rights and duties described
therein, hence engage in second-order positioning. Because the guide is written for teachers,
its description of students can be considered as third-order positionings.
Earlier, I presented literature suggesting that teachers engage with curriculum
materials in varied ways. Using language from positioning theory, I focused on identifying
first-order positionings from the TGs I chose for this study but this does not mean that
teachers readily will accept those observed positionings. Rather, those observed positionings
are open to refutation. Teachers can and do cast second-order positionings when they

17

disagree with first-order positionings from the guides. In this study, I attended to a smaller
slice of this whole picture, which is the first-order positioning presented by the TGs I selected
as my data sources.
Now I turn to the discussion of rights and duties. A positioning often is defined in
terms of rights and duties. In this dissertation, I chose to use duties rather than rights. Here, I
explain my rationale for such decision. In Harré’s early work, a positioning was defined with
rights, duties, and obligations. Examples of early definitions are these:
1. In so far as the content of a position is defined in terms of rights, duties and
obligations of speaking, and these “moral” properties are locally and
momentarily specified. (Harré & van Langenhove, 1991, pp. 404-405)
2. Technically a “position” is defined by a certain set of rights, duties and
obligations as a speaker. (Sabat & Harré, 1999, p. 93).
3. To position someone or to be positioned is implicitly (and sometimes
explicitly) to assign or remove contributing rights. (Harré, 2002, p. 618).
In Harré’s recent contributions, however, a positioning is consistently described as a
cluster of rights and duties. For example,
1. [Complaining] is embedded in a complex weave of ‘positions,’ that is of
clusters of rights and duties with respect to what can legitimately be said and
done by whom. (Harré, 2005, p. 186)
2. Positions, as clusters of right and duties, exist more in the practices of social
actors than in structural demands. (Moghaddam, Harré, & Lee, 2007b, p. 9)
3. Positions are clusters of beliefs about how rights and duties are distributed in
the course of an episode of personal interaction and the taken-for-granted
practices in which most of these beliefs are concretely realized. ( Harré,
Moghaddam, Cairnie, Rothbart, & Sabat, 2009, p. 9)

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4. [T]he application of positioning analysis—that is, how rights and duties are
distributed among the actors in the course of complex discursive interactions,
sometimes personal, sometimes in the newspapers and television media.
(Moghaddam & Harré, 2010, p. 6)
5. [P]ositioning theory looks at what a person “may do and may not do.”
“Rights” and “duties” are shorthand terms for clusters of moral (normative)
presuppositions that people believe or are told or slip into and to which they
are momentarily bound in what they say and do. (Harré, 2010, p. 53).
These definitions show that the more refined version of definitions of positioning draw on the
notions of rights and duties. Thus, to understand the meaning of positioning, an examination
of rights and duties is central.
Although a position is described as a cluster of rights and duties, the relationship
between rights and duties were not clearly explored by the leading scholars of positioning
theory. This invites researchers using positioning theory to decide themselves whether to
describe an act as an implementation of a right or of a duty. Some researchers did not use
rights and duties to describe the positionings (de Freitas, Esmonde, Knipping, Lunney
Borden, & Reid, 2012; Fahlgren & Sawyer, 2011; Glazier, 2005; Herbel-Eisenmann &
Wagner, 2010; Langer-Osuna, 2011; Turner, Domínguez, Maldonado, & Empson, 2013).
Other researchers used the language of rights and duties, without explaining their criteria for
classifying as a right or a duty (Anderson, 2009; Barnes, 2004; Redman, 2007; 2013).
Fathali Moghaddam, who actively coauthored and coedited with Rom Harré about
positioning theory (Harré et al., 2009; Harré & Moghaddam, 2013; Moghaddam, Harré, &
Lee, 2007a), discussed rights and duties elsewhere (Moghaddam, 2000; 2004; 2011;
Moghaddam & Riley, 2005; Moghaddam, Slocum, Finkel, Mor, & Harré, 2000). Although
Moghaddam’s work on rights and duties had no explicit connection to positioning theory at

19

the surface level, his work clarifies the uncertainty that researchers confront when attempting
to explain a positioning in terms of rights and duties.
Moghaddam (2004) described rights as “a demand placed on others by the person
who possesses it” and duties as “a demand placed by others on the person who owes it” (p.
126). Having a closer look at the relationship between these two, however, Moghaddam
makes explicit that “rights and duties are almost always replaceable” (p. 126). In other words,
“a right can be reinterpreted as a duty, just as a duty can be reinterpreted as a right:” (p. 126).
Cultural conditions, or the situations of the person doing the interpreting of an act, are what
impact the decision of whether an act is a right or a duty (Moghaddam & Riley, 2005). The
law is one of a “few exceptions” that is clearly a duty (Moghaddam & Riley, 2005, p. 76).
Regarding the law, there is “duty to obey the law” but it is absurd to say that one has a “right
to obey the law” (Moghaddam, 2004, p. 126). Regardless of one’s agreement to the law, one
has no choice but to obey the law or one will be punished. Therefore, for an act to be a right
or a duty mostly depends on the situation and the interpretation; there are a few exceptions
that the replacement between the label rights and the label duties is more complicated.
In practice, people do act as though they feel obligated when the obligation is not a
law. Moghaddam acknowledges rights and duties that are informal and implicit in everyday
social life (Moghaddam & Riley, 2005). Following Finkel’s (1995) work, Moghaddam names
such rights and duties as “commonsense rights and duties” (Moghaddam & Riley, 2005, p.
75). Among the commonsense duties, some can be categorized as “supererogatory duties,”
meaning the “duties an individual will be praised for performing, but not morally blamed for
omitting” (Moghaddam, 2004, p. 126). People performing supererogatory duties do so with
conscious recognition and intention (Moghaddam et al., 2000). Performing supererogatory
duties is voluntary and personal. In the imaginary world that all duties are supererogatory, all
people have rights to obey the law (Moghaddam et al., 2000).

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In this dissertation, I conceptualize the positionings from TGs as supererogatory
duties. Behind this conceptualization is the understanding that the curriculum authors will
include content that they think i) could be useful or even crucial for teachers to know to
perform the work of teaching, and ii) teachers do not know well enough to perform without
supports from TGs. It is supererogatory because teachers are not blamed by refusing to
implement everything suggested in the guides. Rather, teachers are encouraged to make
selections and modifications using their professional knowledge when reading the guides. In
my data analysis, I first attend to positionings as supererogatory duties in the guides. Among
the supererogatory duties, some are more strongly recommended than others. That is, there is
a spectrum of supererogatory duties from mild suggestions to strong ones. This spectrum also
will be addressed, especially by examining linguistic features of each guide.
Storyline
Storyline is a larger context in which positionings are located and the storyline at play
relates to positionings possibly available to those interacting with spoken language or with
written documents. Storyline “draws on knowledge of cultural structures and positions
recognizably allocated to people within those structures” (Ritchie, 2002, p. 37). When one
practices a certain act, the act may be welcomed in one context but discouraged in another,
because the unfolded storylines are different in those contexts. Unfolded storylines are not
necessarily exclusively revealed in interactions (Harré, 2010). Depending on what storyline
to follow, the positioning of curriculum materials might vary. For example, within the
storyline of mathematics being abstract and should be taught abstractly, project-based
curriculum materials are unlikely to be considered as quality material.
For a given positioning in a given situation, multiple storylines can be involved while
those also vary within the scales of interaction (Herbel-Eisenmann, Wagner, Johnson, Suh, &
Figueras, 2015). For example, imagine a student who rarely participates during whole-group

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discussions. A teacher can draw on the storyline that students might participate less when
feeling unwell. Alternatively, the teacher can draw on the storyline that classroom norms or
the interaction pattern among students influence students’ participation. The scale of the
former storyline, which lasts for a school day, is smaller than that of the latter storyline,
which lasts for a semester or a school year. This often needs several months to develop.
When a positioning is challenged, refuted, and negotiated, new storylines not
previously part of the scene may unfold. In other words, positionings and storylines are
concepts that affect and are affected by each other. Henriksen (2007) explained this
relationship by comparing positioning to role, and storyline to structure:
…roles are constituted by structure, but structure is unaffected by the enactments of
these roles. In comparison, the post-structuralist line of thinking employed by
positioning theory considers the relationship between the positioning and the
structuring storyline as mutually constituting. Whereas roles are given by structure,
positions are created, occupied, held and abandoned through social interaction,
including both the spoken and the written. Similarly, norms, values, rights and duties
are structurally provided within role-theory, whereas they are negotiable within
positioning theory. (p. 48)
The excerpt above addressed that positionings are not dominated or controlled by storylines
but positionings and storylines are “mutually constituting” (p. 43). That is, changes in
storylines can bring changes in positionings, as much as changes in positionings might bring
changes in storylines. Therefore, suggesting alternative storylines can be a strategy to
challenge imposed positionings.
Because positionings and storylines are closely interconnected, fixing a storyline to
follow allows me to delve deeply into one changing variable (i.e., positionings) instead of
chasing two changing variables (i.e., positionings and storylines). In this study, I chose to

22

pick a storyline – the storyline of teacher professionalism – with larger scale than smaller
scale to reserve enough space to recognize a range of positionings from the four TGs, which
are written with different goals and assumptions. In addition, this fixation allows me to
consider teachers only. Considering the reciprocal aspect of a positioning, texts directed at
teachers might contain positionings of students or mathematics. In the sentence “You may
want to assign these tasks as homework,” teachers are positioned to assign homework to
students. Reciprocally, such a statement positions students as people who can be assigned
homework from their teacher. Another possible read of the sentence is that mathematics is
positioned as a subject matter that can be learned by solving tasks, individually. Although the
storyline of my choice is broad, it is not too broad to drag my attention from the positionings
of teachers.
Communication Act
In positioning theory, the communication act means meaningful practice of actions.
Drawing on speech act theory, positioning theory distinguishes an act from an action. An
action is “a meaningful, intended performance” such as speech or gesture (Harré, 2012, p.
198). An act is the meaning of action or how the action functions in the given context. For
example, a teacher action of gazing at a student could be an act of enforcing behavior
management. Both linguistic and nonlinguistic discourses including gestures and spatial
distance are considered as sources of communication acts (Slocum & van Langenhove,
2003).
Although more work has been done with spoken communication acts, some
researchers have used positioning theory to examine written communication acts. For
example, Rothbart and Bartlett (2007) examined media reports on the Rwandan genocide of
1994. These communication acts are different from face-to-face spoken interaction in that the
reports were prepared for a wide range of audiences rather than for the person in front of the

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author. Additionally, there was a time gap between the initiator, or author, and receivers, or
readers. The authors drew on systemic functional linguistics (Halliday & Hasan, 1985) and
borrowed the notions of field, mode, and tenor to identify events and situations, their recontextualized form, and speakers, accordingly. Rothbart and Bartlett’s (2007) examination is
relevant to my study in that curriculum authors write their TGs for a wide range of audiences,
or teacher readers, rather than for a particular teacher in front of them.
Scheer (2013) also conducted media analyses by examining articles from news cites
influential in the U.S., in addition to news articles the author had been surveying. The
purpose of the study was to understand Wall Street’s positioning after the U.S. economic
collapse circa 2007-2008. Scheer’s approach was thematic in that the author discussed the
themes observed and supported the existence of such themes by citing the news articles.
Allen and Moghaddam (2013) analyzed introductory psychology textbooks to understand
their representation of hostility and friendships. The authors assembled a list of terms (e.g.,
enemy, friendship, aggression, violence, peace, etc.) and searched in which context and how
often those terms were used. These examples show that positioning theory is a framework
useful for investigating written texts. In this study, communication actions are texts written in
the TGs. Then, the communication act of these actions is, roughly speaking, assigning duties,
the specifics of which may vary depending on the content of the communication action. Thus
far I explained positioning theory by examining each of the three inter-connected components
of positioning, storyline, and communication act. Now I turn to the research questions that I
used to guide this study.
Research Questions
In this dissertation study, I focused on external expectations others have of
mathematics teachers in written texts close to teachers’ daily practice and professional
development. In particular, I analyzed texts, or communication actions in algebra TGs. I did

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so to understand teaching of mathematics as constructed by the guides, and to what extent the
guides acknowledge teachers’ professional judgment to accept, revise, or refute the TGs’
suggestions. Following the storyline of teacher professionalism, specific research questions I
examined in this dissertation are:
1. What teacher positionings regularly are observable from the four selected
mathematics TGs? How do these positionings compare with research on teacher
professionalism? What teacher positionings are pervasive in the four guides?
2. What teacher positionings irregularly are observable from the four selected
mathematics TGs?
3. What is the range of voices across the four TGs? How might these voices shape the
degree of obligation to the teacher positionings as duties?
Examining the first and the second research questions, I explored the TGs’ construction of
what teaching mathematics entails. Examining the last research question, I described to what
extent teachers’ professional judgments are welcomed in each TG. That is, the first two
questions are about the kinds of duties assigned to teachers, and the last question is about the
degree of dutifulness of the assignment. If my examination of the first and the second
research questions show that the TGs cover a range of different duties, this might be a sign
that the TGs recognize teaching mathematics as a complex activity that only professionals
could do. If my examination of the third research question suggests a low degree of
dutifulness, this might indicate high appreciation of teachers’ ability to make professional
judgments rather than mindlessly follow what the TG tells them to do.

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Data Sources and Data Analysis
Data Sources
In this dissertation study, I narrowed my focus to TGs for middle-school algebra. I
compared four TGs from different group of authors. To control possible noise from
mathematical content being different, I chose algebra as a subdomain. Algebra is known to
have significant impact on students’ futures. Algebra has been conceptualized as a gateway to
later academic achievement (Bush & Karp, 2013; Gamoran & Hannigan, 2000; Liang,
Heckman, & Abedi, 2012; Smith, 1996; Stein, Kaufman, & Sherman, 2011; National
Mathematics Advisory Panel, 2008). From both educators and policymakers’ perspectives,
algebra significantly impacts students’ advancement in future mathematics and science
courses and, in turn, influences their academic success (Liang et al., 2012). According to the
Mathematics Advisory Panel (2008), algebra drew extra attention from those interested in
educational policy because students’ mathematics achievements drop drastically when they
begin algebra coursework. The Panel further pointed out that “completion of Algebra II
correlates significantly with success in college and earnings from employment” (p. xiii). The
chance for college graduation was more than twice higher for students who took Algebra II
than for those who took fewer mathematics courses. Access to algebra is better when it is
given at earlier grades, because early access positively impacts students’ high-school
mathematics performance (Smith, 1996). Spielhagen (2006) mentioned that students who
began algebra in Grade 8 enrolled in more high-school mathematics courses than did those
who began it in Grade 9. Further, the author found that students who began algebra in Grade
8 were more capable of taking advanced courses in high school.
Despite such importance of algebra on students’ future, I could find only a small
number of research studies focused on teachers teaching algebra (Stein, Kaufman, &
Sherman, 2011). Among the few, some researchers focused on developing frameworks and

26

measures that could advance the field with understanding on the knowledge matters when
teaching algebra (Buschang, Chung, Delacruz, & Baker, 2012; Izsák, Çağlayan, & Olive,
2009; McCrory, Floden, Ferrini-Mundy, Reckase, & Senk, 2012). Others attended to specific
subdomains of algebra in relation to teaching (Even, 1993; Haimes, 1996; Nathan &
Koedinger, 2000; Sánchez & Llinares, 2003; Stein & Baxter, 1990; Stump, 2001; M. R.
Wilson, 1994). One observation from these efforts is that teachers’ perception or knowledge
on algebra and algebraic practice affect students’ learning (Even, 1993; Nathan & Koedinger,
2000). With the potential of curriculum materials as a resource for teacher learning, the
research so far reviewed suggests that teachers’ sense of professional self, as represented in
algebra TG, is a topic worthy of careful investigation. Echoing Doerr’s (2004) point that
“there is a significant shortage of research about how teachers learn to teach algebra, how
they understand their own practice, and how they form and are formed by their own practice
within their own specific cultural contexts” (p. 282), I paid specific attention to TGs as an
external source of impact on teacher professionalism, rather than a container of a collection
of algebraic contents with more impact on students than teachers (U.S. Department of
Education, 2008). In so doing, I hope to suggest what authors can add or revise to better
support algebra teaching by contributing to the understanding of teachers’ sense of
professional self.
For middle-school algebra TGs, I chose CMP (Lappen, Phillips, Fey, & Friel, 2014),
Eureka (Great Minds, 2017), UCSMP (Brown et al., 2008), and Pearson (Charles et al.,
2015). In choosing TGs, I not only considered market share, but also included curriculum
materials with a range of design principles and structures, while keeping the number of
materials manageable. To be clear, although I wanted to include a range of types of texts, I
did not intend these four TGs to be a representative sample of any kind, but more of a
purposeful sampling. This dissertation study’s purpose is to explore what is being

27

communicated to prospective and practicing mathematics teachers because those positionings
may contribute to teachers’ professional selves. By exploring this set of TGs, I hope to
provide an in-depth description of a smaller part of the whole picture.
Data Analysis Plan for Research Question 1: What teacher positionings regularly are
observable from the four selected mathematics TGs? How do these positionings
compare with research on teacher professionalism? What teacher positionings are
pervasive in the four guides?
In my dissertation study, the analysis utilized a combination of thematic analysis
(Braun & Clarke, 2006) and the analytic process described in the literature on positioning
theory (Anderson, 2009; Barnes, 2004; Esmonde & Langer-Osuna, 2013; Harré &
Moghaddam, 2013; Herbel-Eisenmann & Wagner, 2010; Moghaddam, Harré, & Lee, 2007b).
Thematic analysis is “a method for identifying, analysing and reporting patterns (themes)
within data” (Braun & Clarke, 2006, p. 79). It is extremely flexible and has been used in a
number of studies, including cases when they did not explicitly claim to use thematic
analysis. The flexibility is in fact the strength of the method. Grounded theory analysis is
similar to thematic analysis in that both seek patterns. Grounded theory analysis, however,
ultimately aims to develop a theory from data (Suddaby, 2006). Thematic analysis does not
require researchers to develop a theory to explain data. Patterns or themes need not be
determined by quantifiable measures such as how much it is present in data (Braun & Clarke,
2006). An example of thematic analysis process is described in Table 2 below.

28

Table 2. Phases of Thematic Analysis Table, from Braun and Clarke (2006, p. 87).
Phase
1. Familiarizing
yourself with your
data:
2. Generating initial
codes:
3. Searching for
themes:
4. Reviewing themes:
5. Defining and
naming themes:
6. Producing the
report:

Description of the process
Transcribing data (if necessary), reading and re-reading the data,
noting down initial ideas.
Coding interesting features of the data in a systematic fashion
across the entire data set, collating data relevant to each code.
Collating codes into potential themes, gathering all data relevant to
each potential theme.
Checking if the themes work in relation to the coded extracts
(Level 1) and the entire data set (Level 2), generating a thematic
‘map’ of the analysis.
Ongoing analysis to refine the specifics of each theme, and the
overall story the analysis tells, generating clear definitions and
names for each theme.
The final opportunity for analysis. Selection of vivid, compelling
extract examples, final analysis of selected extracts, relating back
of the analysis to the research question and literature, producing a
scholarly report of the analysis.

To observe the positionings, I attended to written-for-teachers texts often provided at
the margins of the guides. Following the storyline, I did not necessarily exclude the
positionings that are contrary to teachers as professionals. In fact, my assumption was that the
guides are providing such information because the curriculum authors think it is useful for
teachers to know, and there is a possibility that authors include the information because they
do not know whether teachers know it or not. What I planned to exclude are texts directed to
others, for example, students. Positionings identified within the storyline have the potential to
shape teachers’ productive professional selves.
When observing positionings, I attended to explicit and pervasive communication
actions. I acknowledge that teachers can be positioned in certain ways from what is absent in
the TG. For example, the absence of solution paths (as opposed to a strong presence of
answers to mathematical tasks), positions teachers in certain ways. Naming and explaining
what those “certain ways” are requires an in-depth look at all aspects of the TGs. To make
claims from what is not present in the TGs is an extremely complicated project, even when

29

additional sources of information (e.g., interviews with textbook authors) are provided.
Because of this difficulty, I attended only to explicit and pervasive communication actions
that are stated closely and revisited repeatedly in the TGs. To this end, I attended to the
communication actions firmly embedded in the design of the guides. If a certain
communication action is embedded in the design, it means such communication action
appears in most, if not all, lessons in the guides. When answering this research question, I did
not examine communication actions with sporadic presence. I focused on those
communication actions when answering the second research question. Drawing on the
thematic analysis, I revisited the data multiple times to generate a list of positionings per each
of the four selected TGs. To make the analysis process manageable, I drew heavily on the
first 19-28 lessons of the four guides, and reviewed the rest of the chapters to verify the
consistency of my observation from the first 19-28 lessons. The number of lessons reflects
the lengths of first three chapters of UCSMP (23 lessons) and Pearson (27 lessons). CMP has
19 Problems in the first additional unit for use with Algebra 1. Eureka presents 28 lessons in
Module 1.
To keep data to a manageable size, and to enable my comparison across the guides, I
grouped portions of TGs into seven phases, then attended to each phase individually. These
phases are: introduction to a TG (IntTG), introduction to a chapter (IntCh), introduction to a
lesson (IntLe), beginning of a lesson (BeLe), middle of a lesson (MiLe), end of a lesson
(EnLe), and end of a chapter (EnCh). I considered structural features, or the headings, from
the four TGs when deciding on which to group as a phase. I found the phases useful
especially because each TG uses different headings for the portion that essentially serves a
similar purpose. By using phases, I was able to compare TGs despite their varied wordings
for the headings.

30

I attended to texts written for teachers, including those at the margins and those
between lessons or chapters. Their placement varies, depending on publisher. My primary
criterion is to attend to texts written for teachers only, hence ignore texts in student versions,
often presented at the center of the guide per each lesson. For the same reason, I did not
analyze texts in the exercise section or the worksheet, unless they contained there a
significant amount of text to guide teachers. When identifying positionings, I planned to
prioritize headings repetitively appearing across lessons in the first 19-28 lessons, or first
three chapters. The goal of the first research question was to devise an overview of the types
of positionings in four TGs, which reflect a range of design principles.
I paid attention to each heading individually and compared all texts under headings
from the first three chapters. My goal was to generate one positioning per heading that
described commonality among texts. For example, UCSMP has the heading Warm-Up in its
introduction to the chapter (IntCh) phase. To examine the positioning observable from this
heading, I reviewed all warm-ups from the first three chapters of UCSMP and looked for
common features across the texts. A common feature was that the warm-up was presenting
something for teachers to use to open a lesson in class. Some warm-ups presented
mathematical tasks, others presented activities. Some drew on real-life contexts, others were
without such contexts. Therefore, I described initially-observed positioning in the warm-up in
the following way: teachers are duty-bound to know how to open each lesson with
mathematical tasks or activities, either contextualized or not. After examining all the
headings in the IntCh of UCSMP, I turned to the same phase of the other three TGs.
For each phase, I made a table with each column allocated to a TG and each row to an
initially-observed positioning. In the cell was the TG heading from which I read the initial
positioning. For example, the cell where the column UCSMP intersects with the row teachers
have a duty to know how to open each lesson with mathematical tasks or activities, either

31

contextualized or not, I wrote the heading Warm-Up. Then, I examined the row for
positionings to find those essentially addressing a similar aspect of teaching. For example, in
Pearson I observed the initial positioning that teachers have a duty to know questions to ask
when facilitating the opening task. Similarly, in CMP I observed that teachers have a duty to
know how to introduce lesson-content. I combined these two initially-observed positionings
with one from UCSMP to the following observed positioning: teachers have a duty to know
tasks/activities/questions for opening a chapter/lesson. As a result, I observed 17 positionings
from Introduction to a TG (IntTG), 30 from Introduction to a chapter (IntCh), 12 from
Introduction to a lesson (IntLe), 6 from beginning of a lesson (BeLe), 8 from middle of a
lesson (MiLe), 14 from end of a lesson (EnLe), and 12 from end of a chapter (EnCh).
Through the process of identifying positionings, I chose to use the phrase “teachers
have a duty to know.” I made such a decision to foreground the intentionality behind the
presence of certain content in TGs. TG authors are more likely to examine carefully the
contents they want the teacher readers to know. The authors, however, choose not to provide
every detail needed when teaching the lessons. For example, TGs rarely explain how teachers
properly could move hands and arms when handing out sheets to students. In other words,
content present in the TGs reflects the authors’ assumption on what teachers do not know, or
at least what they need to be reminded of for successful teaching of the lessons.
My next step was to aggregate these tables into one comprehensive table. Columns
were the TGs, and rows were positionings, but this time the cell was filled in with the phases
instead of the headings, which are the labels in each of the phases. Headings might provide
rich information about the TG and positioning, but similar richness could be reached with
phases while causing the comparison to be more practical and manageable. In the aggregation
process I again was able to refine descriptions of the positionings so they are not overly
specific yet retain enough detail to articulate the duty implied.

32

Although my initial approach was to allocate one positioning per heading, some
headings are coded multiple times in the aggregated table (see Appendix B). Pearson’s
heading Teaching Resources is one such case. The positioning I observed from this heading
in the IntTG table was that teachers are duty-bound to know the range of available resources
per type and purpose. In the aggregated table, I revised the positioning to: teachers have a
duty to know, generally, what supplementary resources are available. I made such a revision
so that the three other TGs could also be covered by the positioning. Later in the aggregated
table, I found the positionings, observed from different headings, that teachers were dutybound to know supplementary information to make accommodations, and to know how to
support emergent bilingual students. These two aspects were observable from the texts under
the heading Teaching Resources. Between obligating to the rule of one positioning per
heading versus providing a rich picture of the data, I chose the latter. By so doing, I could
avoid misrepresenting a TG as not addressing a positioning when it really is really addressing
it. Therefore, I coded the heading to address these two positionings also. To identify those
cases, I provided in the aggregated table headings in blue that are coded multiple times.
Data Analysis Plan for Research Question 2: What teacher positionings irregularly are
observable from the four selected mathematics TGs?
The danger of giving so much attention to the headings is that I might miss
positionings that appear sporadically through the guide. For example, if a TG provides tips
for supporting tactile learners whenever such opportunity came but not in all lessons, it is
misleading to ignore such communication action of the guide. To avoid misrepresentation of
the guides, I attended to less pervasive positionings that are worth mentioning.
To answer the second research question, I began with the aggregated table from the
first research question. The aggregated table represents positionings regularly observable.
Cells left blank in this table mean that positionings are not regularly observable from the TG.

33

This does not mean, however, that such positionings are completely unobservable in the TG.
From my reading of TGs, I observed positionings present in it, although their appearance was
irregular. For example, the table might indicate that Positioning A is present in Guides 1, 2,
and 4, but not in Guide 3. What is possible for Guide 3 is that it actually does not say
anything about Positioning A. Alternatively, it is possible that Positioning A is construed in a
couple of lessons only. In such a case, Positioning A is present in Guide 3, although its
presence is not as strong as in the other three guides. Because of the possibility of the
positioning to be present sporadically rather than consistently, the list from the first research
question cannot be evidence of nonexistence of the positionings.
To fully understand a guide’s potential as an external factor in developing
professional selves, I paid attention to the blank cells of the aggregated table, and verified
whether those positionings are not at all addressed, or addressed in an irregular manner in
each TG. The irregularly-observed positionings are indicated by the phase using red in
Appendix B.
Data Analysis Plan for Research Question 3: What is the range of voices across the four
TGs? How might these voices shape the degree of obligation to the teacher positionings
as duties?
In addition to the examination of less pervasive positionings, I examined the voice of
the guides by taking a finer-grained linguistic approach. The dataset for this part of analysis
is the texts from Chapter 1 of UCSMP (7 lessons) and Pearson (9 lessons), Investigation 1 of
CMP (3 Problems), and Topic A (5 lessons) of Eureka. My initial informal examination of
the guides told me they are consistent with their language use. For example, the guide using
the pronoun “we” to refer to textbook authors (e.g., “We expect this task to help students
with…”) almost always use this pronoun when referring to authors in the later part of the TG.
Similarly, the guide using sentences with low modality (“You might solve this task with

34

students.”) used modality in other sentences, too. Analyzing linguistic features of sentences
written in some number of lessons, I discussed the strength in which the duties are imposed
on teachers.
This part of my analysis focused on the use of pronouns, imperatives, and modality,
because these can be indicators of the voice (e.g., Herbel-Eisenmann, 2007), or “how the text
communicates to the teacher, what it communicates about, and how the text positions the
teacher as a reader and user of it” (Remillard et al., 2011, p. 3). Any text can have multiple
voices that might even be contradictory (Herbel-Eisenmann, 2007). Examining voices of
TGs, Remillard (2000) distinguished when a TG spoke through teachers versus when it spoke
to teachers. Depending on what language a TG uses, it might end up speaking through
teachers by offering “steps to follow, problems to give actual questions to ask, and answers to
expect” (Remillard, 2000, p. 347). Such an approach emphasized the outcomes of teaching.
When a TG speaks to teachers, it foregrounds “the rationales, assumptions, or agendas
supporting them” (p. 347), which in turn encouraged teachers to engage with the guide’s
decisions and suggestions, in addition to its underlying ideas. The notion of voice allows
researchers to consider external teacher positionings done via the form of the communication
actions. My analysis for the first and the second research questions attended to the content of
the texts. By conducting such analysis, I expected to understand external expectations on
what teachers do when teaching mathematics. The analysis of voice provides information on
the degree of teachers’ autonomy assumed by the authors, or the degree of dutifulness the
guides imposed on teachers. In other words, are the positionings in the guides presented as
what teachers should think through using their professional knowledge and make productive
modifications as needed, or are the positionings presented as strong duties that teachers
should obey?

35

I drew on the notion of speaking through versus speaking to. Curriculum materials
speak through teachers when they guide actions, offer steps to follow, and give actual
questions to ask. Materials speak to teachers when they give rationales, assumptions or
agendas supporting information provided (Remillard et al., 2011). My assumption is that a
subtle difference exists between “Give manipulatives to students” versus “Consider providing
manipulatives to students,” and “This task connects mathematics and real-life context” versus
“We designed this task to connect mathematics and real-life context.” Teachers are likely to
develop authoritative professional selves when exposed to the latter type because of the
consistent invitation from the guides for teachers to recognize their authoritative selves. From
this, what I saw as central is acknowledgment of the presence of teachers as those who can
make professional judgments, rather than those who merely follow given directions. I paid
attention to this particular aspect of the speaking through versus speaking to dichotomy.
Therefore, I examined the presence of teachers and space available for them to either accept
or refute suggestions from the guides.
I drew on Herbel-Eisenmann’s (2007) work for a specific analytic process. In her
work on the voice of mathematics textbooks, Herbel-Eisenmann drew on Morgan’s (1996)
articulation of systemic functional linguistics and attended to imperatives, personal pronouns,
and modality to examine the interpersonal function of the books. According to HerbelEisenmann’s use of Rotman (1988), imperatives can be either inclusive or exclusive.
Inclusive imperatives, such as “consider” or “define,” position readers as thinkers, whereas
exclusive imperatives, such as “use” or “copy,” position readers as those who perform
actions. Because of such nature of imperatives, I examined imperatives in TGs to see when
the guides were speaking to teachers with inclusive imperatives, and when they were
speaking through teachers with exclusive imperatives. Pronouns are important because they
portray the guides’ (or guide-authors’) personal involvement (Herbel-Eisenmann, 2007). By

36

attending to when and how I, we, and you were used, I expected to unveil whether the
developers’ design decisions are presented in the way those are being talked to teachers and if
teachers are supported to make decisions while enacting the curriculum. Modality is another
linguistic form that matters when examining voice of a text. Modality is to be found in the
modal auxiliary verbs, adverbs, adjectives, and hedges (Herbel-Eisenmann, 2007). Modality
reflects the degree of certainty of the voice. By attending to modality, I expected to uncover
when the guides were using assertive voices and for what purpose.
Structural Comparison of the TGs
Before sharing my researcher reflexivity, I present a structural comparison of the
four TGs, showing their structures and providing background information for the results
section. Then I describe how I read the guides, an effort to maintain rigor of the study by
being reflexive to what I did.
TGs structures were similar to each other but with subtle differences (Table 3). Both
UCSMP and Pearson were two-volumes in hardcover; each volume of both had several
chapters, each chapter had several lessons, and each lesson was designed to be taught in one
day unless the lesson is blocked. CMP came with eight books, each representing a unit, each
unit consisting of four to five investigations with a similar number of problems, and by
design each problem was likely to be covered in one day. Eureka was provided digitally in
five pdf files, each file a module, each module a couple of topics, each topic a number of
lessons, and each lesson intended to be covered within a day. For ease of discussion, I used
the label lesson to indicate lessons in UCSMP, Pearson, and Eureka, and problems in CMP.

37

Table 3. General Structure of the Four Guides
UCSMP
2 volumes
(13 chapters total)

Pearson
2 volumes
(12 chapters total)

Chapter
(7-10 lessons)

Chapter
(6-10 lessons)

Lesson

Lesson

CMP
1 set
(8 units)
Unit
(4-5 investigations)
Investigation
(2-5 problems)
Problem

Eureka
5 pdf files
(5 modules)
Module
(2-4 topics)
Topic
(3-15 lessons)
Lesson

To compare TGs structurally, I followed a 7-phase classification based on my initial
observation of the TGs: introduction to the TG, introduction to a chapter, introduction to a
lesson, beginning of a lesson, middle of a lesson, ending of a lesson, and ending of a chapter.
This classification covers every set of content across the four TGs, each of which has all
seven phases, excepting CMP (for the introduction to the TG) and Eureka (for the beginning
of a lesson). Introduction to the TG (IntTG) is texts placed at the very beginning of a TG; this
phase communicates overall design and organization, main features, TG strength, and
messages from curriculum authors to teacher readers. Structure and length varies across the
four TGs. Introduction to a chapter (IntCh) is where the TG provides a general overview of
the chapter; often included is chapter pacing, standards/claims/objectives addressed in the
chapter, and relevant resources. Each lesson consists of introduction to the lesson (IntLe), its
beginning (BeLe), its middle (MiLe), and its ending (EnLe). Ending of a chapter (EnCh) is a
comprehensive review of the whole chapter; long-term projects, assessment tasks, and
reflections are common features.
I show lesson phases in Table 4 below and describe in detail for each TG because a
lesson is the most frequently repeated structure in the TGs.

38

Table 4. Phases of a Lesson
IntLe

BeLe

MiLe

EnLe

GOAL; SPUR
Objects;
Materials/Resource
s; HOMEWORK;
Local Standards;
Background

1 Warm-up

2 Teaching

3 Assignment; 4
Wrap-up

Pearson

Preparing to Teach

1 Interactive
Learning;
PowerAlgebra.co
m

2 Guided
Instruction;
PowerAlgebra.co
m

3 Lesson Check; 4
Practice; Lesson
Resources;
PowerAlgebra.co
m

CMP

Problem Overview

Launch

Explore

Summarize

Classwork

Closing; Exit
ticket; Exit ticket
Sample Solutions;
Problem Set
Sample Solutions

UCSMP

Eureka

Student Outcomes

Lesson flow in each TG is similar but with minor variations; generally, they begin
with an overview including goal, standards, and background information. Then follows the
main teaching part where teachers interact with students; this comprises a lesson beginning, a
middle, and an ending; in those, respectively, teachers invite students to the lesson (typically
a warm-up activity), then a main part (one task or more), then an ending wherein i) via
discussion or an exit ticket teachers assess students’ understanding of what has been taught so
far, and ii) homework is assigned. This structure of beginning, middle, and ending of a lesson
somewhat aligns with the exposition-examples-exercises model common in textbooks (Love
& Pimm, 1996).

39

Reflexivity and Expert Debriefing
To be explicit with my positionality I present myself first as a researcher and second
as a reader of the TGs in a later part of this chapter. For a study to be accepted by the
research community, it should be rigorous. Researcher reflexivity is a validity practice
whereby researchers “report on personal beliefs, values, and biases that may shape their
inquiry” (Creswell & Miller, 2000, p. 127). To practice reflexivity, researchers need to
acknowledge their strengths and limitations when conducting the research, and present them
to the readers (Tracy, 2010). A researcher can write a separate section on herself/himself,
provide interpretive commentary in discussing the findings and in describing personal
experiences, and so forth (Creswell & Miller, 2000). In any form, researchers are asked to
make explicit their orientation to the readers.
For the expert debriefing, I consulted members of my dissertation committee. They
had read my work from the early stage of proposal, and provided feedback and support until
this study’s completion, including the data analysis. Expert debriefing, or peer review, is “the
review of the data and research process by someone who is familiar with the research or the
phenomenon being explored” (Creswell & Miller, 2000, p. 129). Although experts are
expected to be familiar with the research, they are not members of the research team. Their
distance from the research is key, as such distance allows experts to provide with fresh eyes a
wide range of feedback, including both positive and skeptical, with fresh eyes (Creswell &
Miller, 2000; R. B. Johnson, 1997). Researchers can ask experts for written feedback or at the
developing stage can consult with them on ideas, preferably through the whole process of the
research than at the end of the analysis (Creswell & Miller, 2000).
Researcher Reflexivity: My Motivation to This Study
It was March of 2011. I was at the third annual Teacher Education Accreditation
Council (TEAC) writing workshop. Other members from the TEAC preparation team at the

40

University of Michigan-Dearborn (UMD) were there with me. At that time, I was working as
an administrative assistant at the School of Education at UMD, who worked preparing TEAC
accreditation. The workshop was full of people from Michigan and Ohio. They, too, came to
the workshop to prepare an audit of their teacher education programs. Representatives from
TEAC facilitated the workshop. The engagement was unbelievable. People actively raised
questions and responded to each other. They were eager to share their understanding of what
makes teaching a real profession (rather than a para-profession) and what teacher educators
could do to guide prospective teachers to meet those standards. Behind this engagement, I
noticed a tension between protecting teachers and the field of education. Participants of the
workshop had seen outsiders, who were not necessarily interested in education, trying to
determine what defined teaching. Workshop participants were correct to be sensitive to such
an assertion of power from outsiders because despite shallow evidence, the public bought
into these outsiders’ claims. Letting outsiders define what teaching entails can be more
harmful than helpful. Often, it seemed threatening. Defining teaching based on insufficient
experience and knowledge is indeed a threat to practicing teachers, to rigorous teacher
education programs, to prospective teachers, to schools, to students, and to the future of the
community at the local, national, and international level.
Defending one’s stance is important, especially when the teaching profession is being
attacked, from local interactions to interactions on a larger scale. At times, the assumptions
underneath larger scale interactions are deeply embedded in the system, hence pervasive yet
invisible. I learned this growing up as a woman in Korea, an east-Asian country that ranks
116th among 144 countries in terms of gender inequity.1 I am lucky to have been born, given
that in the 1980s, aborting female children was not unusual. Abortion was, and still is, illegal,
but the social norm of boy preference forced women to clandestinely terminate their

1

http://reports.weforum.org/global-gender-gap-report-2016/rankings/

41

pregnancies at a rate that was tantamount to female-infanticide, which is a distinct category
of genocide. I remember very young males who sexually harassed me but were forgiven by
adults because these boys liked me. My will, however, was not considered. Because adults
forgave them, I had to do the same, because in Korean society obedience is expected. I
attended an all-girls middle school and high school. There, I met male teachers who enjoyed
verbally harassing students as well as female teachers who asserted that girls should behave
like girls. Despite freezing temperatures, school regulation required us to wear black
stockings under a knee-length skirt. Teachers punished girls who wore gym pants underneath
their skirts to offset the cold. The university where I did my undergraduate studies is a
famous (and prestigious) women’s university. Because I enrolled there, many people
assumed my only interest (or my duty) was to an affluent husband. All the time and energy I
spent on intellectual activities were acknowledged only by the people in the university.
Underlying these unpleasant and disrespectful attitudes is misogyny. No matter how often or
how much I protested, nothing seemed to change. After much struggle and countless upsets, I
gave up. I gave up speaking up for myself. Instead, I chose to escape. After all, Korea was
never a country for women.
In May 2016, a man committed a random murder at the Gangnam station area. To be
precise, the murder was random in the sense he killed a woman he did not know. Yet, it was
not random, in the sense he killed the seventh person he met, letting six men go. In other
words, he killed the first woman he saw. An undertone in pertinent press descriptions was
that the victim was not as careful as she could have been. Some social media comments
blamed her. However, others protested the victim-shaming by gathering at a Gangnam
Station. Again, us women knew from past experience that we were lucky to be alive. I knew
that as a woman in Korean society that my life was a matter of daily survival, as gender
discrimination resulted not only in continuous acts of disrespect but also in the death of

42

countless women. There we stood, finally spelling out the violence we had to endure and the
fears we live through. At the station, we recognized each other. Sharing our personal
experiences that should not be as general as how it is then, we sensed support and oneness. It
became clear that defending my gender equality is the matter of survival. Misogyny was
profound at the level of actual physical murder. Despite of the dire situation, only a few
women have spoken out against gender inequality in Korea. From now on, however, things
will be different. This incident, the so-called Gangnam murder case, was a wakeup call for
the society. Although misogyny did not disappear after the protest at Gangnam station,
people became more proactive.
Another form of misogyny is not allowing women to earn enough money to live
independently. In the past, these low wages pushed women into marriage. Divorce was
impossible. Women had to endure verbal and physical abuses merely to survive. Today, more
opportunities are given to women than before, but the gender wage gap is wide. By limiting
women’s professional and economic possibilities misogynists still control women. This
approach, however, is no longer as powerful. Kim, a voice actress, is a perfect example. On
July of 2016, Kim uploaded a photo on her personal Twitter account. The photo was her
wearing a shirt with an imprint “Girls do not need a prince.” Because of this, she received a
notice from Nexon, a game company, that they would discontinue the contract with Kim. At
that time, she was acting the voice of a character named Tina. Those who welcomed this
decision argued that the shirt is evidence of Kim’s participation to Mersgall, which they
declared as a socially harmful and unjust online community for “feminazi.” They considered
the shirt as evidence of Kim’s participation to the community. In fact, the shirt was a gift for
the participants of the fundraising by Mersgall4. Mersgall4 was collecting funds for the civil
suit against Facebook Korea. According to Mersgall4, Facebook Korea used their media
power to discriminate women. Mersgall4 claimed that Facebook Korea repeatedly deleted

43

pages that introduced feminist issues in Korea and around the world, while leaving the pages
posting images and videos with misogynic messages. The funding was successful – 4,103
people participated and it collected about $134,000. Misogynists started to call Mersgall4
feminazi because they posted feminist issues, even though no one member of Mersgall4
killed or physically harmed any Korean men. In addition, Kim said she was not a member of
Mersgall4. She happened to have the shirt because she participated to the funding, being
aware of the potential harm from misusing media power to the society. Of course, no
evidence of her participation of the community was found, but Nexon did not take back their
decision. People who recognized how outrageous Nexon’s decision was actively voiced their
support of Kim. This protest was difficult to imagine before the Gangnam station case. It sent
a clear message that Kim’s voice will always be welcomed and there are people waiting to
hear her voice t. Although the game company is unlikely to ask Kim again to act their
characters, we can hear Kim’s voice on Cartoon Network Korea (e.g., Powerpuff Girls),
Disney Channel Korea (e.g., Star vs. the Forces of Evil), and more.
We are not afraid of anymore. We know if someone has to resign due to sex scandal,
it has to be the offender, not the victim. People on Twitter shared the sexual harassment they
experienced in their workplace using the hashtag “ㅇㅇ_내_성폭력
(#sexualharassmentin____).” In particular, the hashtag “문단_내_성폭력
(#sexualharassmentinliteracy)” took several senior male writers to court, and ultimately, it led
publishers to stop publishing these male writers’ books. Female writers, inspired by the
hashtag, established a crowdfunding to legally and medically support victimized writers.
Their campaign reached its fundraising goal on its first day. Ultimately, 2,321 people
donated, and the campaign reached 309% of its funding goal.

44

This fight is our fight. No one else can do it for us. More women are acknowledging
the solidarity among us. In February 2017, a voice actress Chae posted on her blog that she
would not act commercially sexualized female characters. As expected, while some people
were disturbed by Chae’s post, other supported her decision. I, too, support her decision.
Now I can see that running away is not a solution. We will defend ourselves and we will win
the fight. The world will become a better place for everyone. This is what I believe in. Yes,
우리는 서로의 용기야 (you are my courage as I am to you).
From these personal experiences, I learned two lessons. First, we can change society
by proactively generating stories from our perspectives. Second, a sense of solidarity
prevents exhaustion. Being a teacher is different from being a woman. To become a teacher,
one has to go through some level of training or education. One can refuse to be recognized as
a teacher by discontinuing teaching at schools. When it comes to biological sex, one is
recognized as a female as soon as she is born. Once a person is recognized as a woman by
others, it is challenging to ask people to see the person as a different gender. All this is to say
that the identity as a teacher is not the same as the gendered identity. My gendered
experience, however, has shown me that if people come together they can make changes to
the world. I hope teachers and others in the education field to show the world that teaching is
a serious profession requiring special kind of knowledge and skills. Also, I hope this
dissertation could serve as a source of solidarity to those people fighting to persuade the
world that teaching is a profession.
This dissertation contributes to the effort to understand the potential of curriculum
materials in teachers’ sense of professional self. Herbel-Eisenmann and Wagner (2007), in
their study on how textbooks position students, suggested that “[l]anguage indirectly indexes
particular dispositions, understandings, values, and beliefs” (p. 10). With such an approach to
language, the authors explored language choices made in textbooks to unveil the constructed

45

model student reader. Following this approach, I examined how curriculum materials position
teachers in their writing, and I want to investigate who the model teacher reader is.
Myself as a Reader of the Guides
For observation of teacher positioning, I built a reader persona. As reader, I was
interested in learning from the TGs, whose texts I regarded as the minimum information I
should know before teaching the lesson, and to whose suggestions and directions I was
receptive. Further, I believed in TG authors’ expertise and good intentions. Rather than
raising questions, including productive questions, I inclined to accepting it as is. Because my
reader persona was sensitive to visual representation, I by nature was attracted to larger-size
and/or eye-catching color texts. I was more attentive to repetitive contents than to only
occasional mention; this translates into my closer attention to contents with headings
embedded in the design. For instance, if a tip for addressing potential student error is given its
own heading and repeated in every lesson, I took it seriously, whereas if it was embedded in
texts under a different heading – for instance ‘Notes on the task’ – I paid less attention to it.
My reader perspective was that content possessed of its own heading means such content is
more important than content without.
Another catalyst of my closer attention was multi-repetitive headings and associated
contents in TGs. An interesting aspect of repetition is that teachers might develop positive
attitudes to positioning that endures throughout a TG. Labeled Mere Exposure Effect,
repeated exposure to a stimulus can engender a liking for that stimulus (Colman, 2015). In
addition, frequent exposure to information contributes to considering the information to be
valid or trustworthy (Rindfleisch & Inman, 1998). Accordingly, while not much work has
been done on the effect of frequency of positioning on a person being positioned, repetition
should not be disregarded.

46

An aspect of repetition is that it might reflect widely-shared positionings of teachers,
the more so when different publishers present similar positionings in their TGs. Patterns
observed from multiple sources “demonstrate evidence of particular hegemonic discourses or
majority ‘common-sense’ ways of viewing the world” (Baker, 2006, p. 14) or “stereotypes”
shared by the community (Hansson, 2015, p. 180). If a positioning is presented in four
different TGs, it might indicate the positioning requires closer examination; it might be a
shared stereotype – either welcomed or not – in the mathematics-education community.
To be clear, high number-count by itself cannot be used to claim the importance of a
positioning or the likeliness of teachers’ acceptance of that positioning. For a positioning to
affect teachers, meaningful engagement is key (Gresalfi, 2009). Repetition, however,
contributes to thickening of the position (Polman & Miller, 2010). Gresalfi (2009) echoed
this point in an empirical study following four students for a year to examine shifts and
lasting of their dispositions toward learning. Repetition reflects the number of opportunities
presented to teachers, hence the higher chance of engagement and reinforcement. My
intention was to discern where to find opportunities to engage with a positioning, because
therein reside opportunities for teachers to engage. If a positioning is pervasive and
repeatedly brought up in a TG, some might develop a positive attitude to the position due to
mere exposure effect. Needless to say, teachers could refute the recognized positioning. In
such case, the TG might end up communicating a limited amount of text (excluding texts
with refuted positionings) or ask teachers to use considerable energy (to accept the
information but separate out the positioning).
When observing positionings, I chose to use the “teachers have a duty to know”
statement. This is a deliberate choice to acknowledge the possibility of modification when
teachers enact the curriculum. Teachers read and make sense of the information and
suggestions in the TG. After that, teachers enact a lesson, with or without modification of

47

what is in the TG. As this study pays attention to the moment when a teacher reads the TG, I
tried to capture such a moment with “teachers have a duty to know” statement rather than
“teachers do.” Another reason for choosing “know” comes from my assumption about
authors’ situations, namely that TG authors choose content they deem meaningful for
teachers to know, so as to teach well within the curriculum. Reality’s conditions (e.g., page
count, budget) are that authors may be blocked from including everything they hope teachers
have a duty to know. In other words, TG texts are selected not random sets of information.
Based on what has been discussed so far, I list headings I found to be repetitive per each
phase and which represent parts on which I focus to observe positionings. See Appendix A
for this list.

48

CHAPTER 4: RESULTS
In this chapter, I presented results for each of the three research questions. I began
with my analysis for the first research question, which attended to positionings regularly
occurring. Then, I provided results for the second research question that focused on
idiosyncratically occurring positionings. Last, I described my examination of the three
linguistic features, which is the third research question.
Results for Research Question 1: Regularly Occurring Positionings
I observed 44 positionings in total. In UCSMP, I observed 30 different positionings:
in Pearson 27, in CMP 23, and in Eureka 24. The full list of positionings with phases I
observed per each TG is in this dissertation’s Appendix B. Here, instead of reviewing each
positioning, I approached the analysis result from four directions. I began by discussing the
identified positionings relative to the literature I reviewed regarding teacher professionalism.
Then I focused on positionings all four TGs have in common. Following this, for each TG I
presented positionings that are pervasive. Last, I provided cases where the TGs presented
varied degree of support for teachers to go beyond the positionings of knowing, to doing.
Based on my examination, I suggested that curriculum authors could enhance their TG’s
potential as sources of teacher education by proactively expanding the kinds of positionings
they provide in the TG.
Narrow List of Positionings
By examining TGs, I found that aspects addressed by the positionings are not as
varied as I had expected. In the literature review, I discussed five aspects related to teacher
professionalism: i) knowledge base, ii) teacher research, iii) interaction with colleagues, iv)
utilizing knowledge, and v) acknowledging uncertainty. These aspects suggested what is
entailed in teaching mathematics. While these aspects are not mutually exclusive, all
positionings I identified were about a teacher’s knowledge base. By definition, all

49

positionings address at least one subdomain of the knowledge base. Some positionings
address the other four aspects, although not as profoundly as in the literature. I now visit, in
turn, each of the five aspects to show how TGs address them.
Knowledge base. Here I follow subdomains suggested by Ball, Thames, and Phelps
(2008), among variations of classifications (e.g., Kunter et al., 2010; Tatto et al., 2008).
Instead of classifying in which subdomain each positioning falls, I attended to whether each
subdomain is addressed, by at least one positioning. From positionings I identified, it is clear
that authors of the TGs are well aware that teaching mathematics requires more than
knowledge of mathematics. Some subdomains were addressed in all four TGs; some others
were addressed in some TGs.
Common content knowledge – i.e., mathematical knowledge required in a setting
more general than teaching – is well reflected in the positioning that teachers have a duty to
know answers to tasks/questions. By asking teachers to be aware of the answer, which falls in
the general mathematical knowledge category, the TGs emphasized some common content
knowledge.
Horizontal content knowledge – i.e., knowledge of the connection between
mathematical topics in the curriculum – is not sufficiently visible to be elected as a
positioning across all four TGs. Closest is the positioning that teachers have a duty to know
information of mathematical topics in addition to algebra. This positioning attends to the
connection between mathematical contents at the multiple-year level, rather than at a year. I
identified this positioning from UCSMP and Pearson. For example, An Articulated
Curriculum Across All Grades, from the IntTG phase of UCSMP, presented a diagram
showing how the whole UCSMP program, including Algebra, can be used in Grades 5-12
classrooms, and by which group of students at each grade level. It showed the same
information for Geometry; Advanced Algebra; Functions, Statistics, and Trigonometry;

50

Precalculus and Discrete Mathematics; and Calculus. Pearson presented big ideas in three
topics namely Algebra, Statistics and Probability, and Geometry, to show how high school
mathematics “fits together” (Pearson, p. T26). Both TGs are similar in that they attempted to
show the placement of algebra to future mathematical topics. UCSMP does it via a diagram
outlining when and to whom to teach each topic. Pearson does it by listing the big ideas.
Specialized content knowledge – i.e., mathematical knowledge specifically needed to
teach mathematics – is emphasized by the following positioning: Teachers have a duty to
know supplementary information to implement a task. This positioning highlights the need for
teachers to have knowledge other than common content knowledge to successfully enact
mathematical tasks in their classrooms. For instance, CMP’s IntLe phase had Problem
Implementation that informed teachers of a general set up for the lesson. This included
whether the task was expected to be completed in a whole group, small group, or individual
setting. Following the phases of MiLe, EnLe, and EnCh, the TG described what to attend to,
when to call on students, how to support students needing more guidance, math facts, etc.
Knowledge of content and students – i.e., knowledge that attends to the intersection of
content and student – is most-closely addressed by the two following positionings: Teachers
have a duty to know potential student errors, and teachers have a duty to know strategies
students might use when solving tasks. The IntCh phase of Pearson, for example, had three
columns in the Math Background page, each with purple headings named after mathematical
activities of the chapter (e.g., creating equivalent equations, solving proportions, working
with percentages as proportions). Following the heading were general descriptions of
strategies which students might apply when engaging with the math activity. Pearson often
presented strategies using a simple math task as an example. Both these positionings
regularly are observable in Pearson, whereas the other three TGs idiosyncratically present
either one or both.

51

Knowledge of content and teaching – i.e., knowledge that attends to the intersection
of content and teaching – is addressed by the positioning that teachers have a duty to know
mathematics for pedagogical purposes. An example of this positioning is UCSMP’s heading
Background in the IntLe phase that explained the chapter’s mathematics with particular
reference to teaching it, including how students might react during the lesson, what to expect
them to know already, and the aspect of the mathematical content related to the purpose of
the lesson. This positioning is regularly observable from all TGs except for Eureka. In
Eureka, this positioning is idiosyncratically observable.
Knowledge of content and curriculum – i.e., knowledge that attends to the intersection
of content and curriculum – is addressed by the positioning that teachers have a duty to know,
in general, supplementary resources available, among others; this positioning asks teachers
to be aware of what instructional materials the TG provided either via supplementary student
materials in reduced size (UCSMP), organizing available resources in a table (Pearson),
listing resources needed to teach the lesson (CMP), and suggesting tools to prepare to solve
tasks in the lesson (Eureka).
Apparent from this examination is that teaching mathematics as constructed by the
TGs involves more than common content knowledge. All four TGs consistently suggested
that teaching is about having specialized content knowledge and knowledge of content and
curriculum, in addition to common content knowledge. Including idiosyncratic positionings,
knowledge of content and students, and knowledge of content and teaching, are addressed in
all TGs. Horizontal knowledge was the least visible subdomain across the four TGs.
Teacher research. Teacher research often involves collecting evidence from students
and using it as data for analyzing one’s own teaching. Teachers’ analyses of such data can
support them in determining possible changes in instructions that are specific to the
classroom environment and which might enrich future teaching. Being as inclusive as

52

possible, I identified in Table 5 six positionings addressing teacher research. Not all
positionings in Table 5 perfectly fit what the literature says about teacher research. I included
those positionings to present the maximum potential of each TG so that this section could
inform those interested in emphasizing teacher research to what they could begin with and
extend on.
Table 5. Positionings Addressing Teacher research
Positionings
Teachers have a duty to know
for each assessment type, when
to administer, its format, and
the standards.
Teachers have a duty to know
where students are at from
student performance on the
task/project/question/quiz using
a rubric.
Teachers have a duty to know
questions and/or activities for
students, to assess their
learning of the lesson/chapter.
Teachers have a duty to know
tasks for students, to assess
their learning of the chapter.
Teachers have a duty to know
what to consider when
reflecting on their teaching to
plan the next stage of the lesson
accordingly.
Teachers have a duty to know
they can make notes as needed.

UCSMP

Pearson

CMP

Eureka
IntCh

EnCh

EnLe

EnCh

EnLe

EnLe
EnCh

EnCh

EnLe

EnCh

EnCh

EnLe

EnCh

MiLe
EnLe
IntCh
EnCh

IntCh
EnCh

Among the six identified positionings, four were about assessing students (teachers
have a duty to know for each assessment type, when to administer, its format, and the
standards; teachers have a duty to know where students are at from student performance on
the task/project/question/quiz using a rubric; teachers have a duty to know questions and/or
activities for students, to assess their learning of the lesson/chapter; and teachers have a duty
to know tasks for students, to assess their learning of the chapter). The four positionings I

53

identified have some aspect of teacher research because they expect teachers to collect data
from students about their understanding of the mathematics taught in the lesson/chapter. To
illustrate, I describe from where I observed the positioning that teachers have a duty to know
where students are at from student performance on the task/project/question/quiz using a
rubric. For specific locations of this and other positionings in each TG, see Appendix B.
Project Rubric, in the EnCh phase of UCSMP, is a guideline for teachers to determine
where students are at, based on their performance on the project. The rubric description is
general so that it can be copied and pasted into other chapters. According to the rubric,
students are either advanced, proficient, partially proficient, not proficient, or no attempt.
Pearson’s Lesson Quiz in the EnLe phase is associated with PRESCRIPTION FOR
REMEDIATION. The prescription is a simple rubric with three ranges of points, and into
which level each range falls. Eureka’s rubric is much more specific than those of UCSMP
and Pearson. A Progression Toward Mastery in Eureka is a table showing for each
assessment task, the CCSS content addressed and the rubric for assessing student learning.
The TG defines four steps: Step 1 is for when the answer is missing or incorrect with little
evidence of mathematical reasoning or application. Step 4 is when the answer is correct with
rich evidence of mathematical reasoning or solid application. The table describes for each
task what student performance would be from steps 1 to 4.
Communication actions associated with this and the other three positionings do not
provide enough support for teachers regarding how they could use assessment data to make
future plans, nor are explicit with the aspect of assessment results as a dataset for teachers.
Therefore, these positionings address teacher research to some extent but less than
sufficiently. Alternatively, communication actions associated with these positionings could
be places for curriculum authors to extend if they are interested in promoting aspects of
teacher research.

54

The fifth positioning in the table, teachers have a duty to know what to consider when
reflecting on their teaching to plan the next stage of the lesson accordingly, more explicitly
addressed teacher research as to what requires teacher professional judgment than do the four
positionings discussed above. CMP had a notable feature providing two explicit opportunities
for teachers to reflect on their interactions with students. In every MiLe of CMP, Planning
for the Summary asked two questions: “What evidence will you use in the summary to clarify
and deepen understanding of the Focus Question?” and “What will you do if you do not have
evidence?” (CMP, p. 44). In EnLe, Reflecting on Student Learning presents questions
directed at teachers to consider to “assess student understanding” (CMP, p. 46). Three main
questions are: “What evidence do I have that students understand the Focus Question?” “How
will I use this to plan for tomorrow? For the next time I teach this lesson?” and “Where will I
have the opportunity to reinforce these ideas as I continue through this Unit? The next Unit?”
(CMP, p. 46). CMP presented these questions, leaving it open for teachers to respond, instead
of providing the authors’ intended answers. By leaving questions open, CMP proactively
invited teachers to collect their thoughts on classroom interaction, and to draw on their
specific contexts so they effectively can enact their professional judgment in their next
teaching move.
The last positioning, teachers have a duty to know they can make notes as needed,
may seem to have the least connection to teacher research among the six identified
positionings. I consider this positioning as somewhat addressing teacher research, however,
because it provided space for teachers to express their own thinking. In particular, UCSMP
and CMP presented spaces for teachers to make notes with no specific instructions. Pearson
occasionally offered teachers some margin spaces wherein to jot notes, and teachers using
Eureka could make digital notes on the pdf file, but such possibility is not explicitly
suggested. In IntCh and EnCh of CMP, there was a lined-blank space with the heading Notes

55

and lines. IntCh and EnCh of UCSMP, too, regularly presented a lined-blank space with the
heading Notes and lines. This simple feature offers teachers the possibility to record their
thoughts/ideas as they wish. By having it, TGs invited teachers actively to utilize perspectives
and conditions specific to them. In other words, teachers can add their teacher research
observations in the TG. In so doing, teachers in effect become TG co-authors.
As to when these positionings are introduced, I identified all of them either in the
introduction or end of a lesson or a chapter. The exception was CMP. Placing positionings
addressing teacher research either at the introduction or the end phase of lesson or chapter is
sensible because teacher research is about collecting data to plan future teaching practice. Yet
teachers can collect evidence at various stages of a lesson. As CMP showed, it is not
necessary to wait until the end of the lesson or chapter to collect such data. Findings so far
support the fact that TGs acknowledged some aspects of teacher research, and that TGs could
make more visible teacher research therein by attending to aspects of teacher research other
than collecting evidence at the end of a lesson or a chapter.
Interaction with colleagues. Interaction with colleagues is another area for teachers
to practice their professional judgment. By interacting with colleagues, a teacher becomes a
participant of a collegial community. I identified one positioning to be relevant to this social
engagement, namely teachers have a duty to know tips from other teachers who have
experience with using the curriculum.
Table 6. A Positioning Addressing Interaction with Colleagues
Positionings
Teachers have a duty to know
tips from other teachers who
have experience with using the
curriculum.

UCSMP
IntTG

56

Pearson

CMP

Eureka

UCSMP listed tips from other teachers, suggesting a possibility of forming a
community of professionals. TEACHING MODES AND STRATEGIES, within the IntTG of
UCSMP, presents suggestions from practicing teachers who have used the curriculum. For
example, suggestions included asking students to solve the questions before class, asking
students to write steps they have taken, sharing additional examples from the TG with
students, occasionally inviting students to read aloud. By presenting other teachers’ voices,
UCSMP established a community of professionals. Sense of community could have been
stronger had teachers’ voices been presented in the lessons, in addition to the introduction to
the TG. Still, UCSMP is the only TG that aired insights from other teachers. Other TGs might
have drawn on experiences of teachers who use a pilot version or a previous edition of the
curriculum, but the TGs did not make explicit the presence of those teachers.
Utilizing emergent bilinguals’ knowledge as a resource. Being responsible to
students with diverse backgrounds is important. Teachers can achieve this by refusing deficit
perspectives about these students and intentionally utilizing what the students already are
familiar with. Pearson and CMP regularly provided information for teachers to support
emergent bilingual students, although the supports are more around compensating students’
deficiencies than utilizing the knowledge they bring in (Table 7).
Table 7. A Positioning Addressing Utilizing Emergent Bilinguals’ Knowledge as a Resource
Positionings
Teachers have a duty to know
how to support emergent
bilingual students.

UCSMP

Pearson
IntTG
IntCh
EnLe

CMP

Eureka

IntCh

In Pearson, ELL Support provides information for how teachers could support
emergent bilingual students.2 These supports include using graphic organizers, focusing on
2

The term English Language Learner is not accurate because everyone, including those whose first language is
English, is a learner of English all the time. Emergent bilingual student is a more accurate term for the student
learning English as an additional language and attending an institution using English as its main language.

57

language, using role playing, focusing on communication, assessing understanding, using
manipulatives, and connecting to prior knowledge. The communication action is crafted
according to lesson content to provide supports specific to each lesson. In EnLe, the TG
mentions the resource available for supporting emergent bilingual students at the intervention
level. The table in IntTG allocates a column for to inform which resources could be used to
support emergent bilingual students. The Resources table in IntCh is asterisked to indicate the
resource is available in Spanish. In IntCh of CMP, it mentions sending English-language or
Spanish-language letters to parents. The student version of CMP has an English-Spanish
glossary, but the TG does not explain how teachers could use it for emergent bilingual
students. UCSMP provides supports but they are idiosyncratic rather than regular.
In both Pearson and CMP, possible teacher moves to support emergent bilingual
students are provided yet less from the direction for capturing their strengths. UCSMP and
Eureka do not regularly attend to supporting emergent bilingual students, although UCSMP
did provide suggestions on supporting emergent bilingual students when possible. This shows
that efforts to utilize students’ strengths is somewhat present in some TGs, but stronger
attention from TG authors might be necessary.
Acknowledging uncertainty. Among the list of positionings I identified, four
addressed uncertainty in teaching as described in the literature, namely that teachers are dutybound to know i) additional tasks not in the student version; ii) how to extend tasks; iii)
potential student errors; and iv) strategies students might use when solving tasks. As I
illustrated in Table 8 and examples below, these positionings center mostly on uncertainty in
pedagogical situations.

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Table 8. Positionings Addressing Acknowledging Uncertainty
Positionings
Teachers have a duty to know
additional tasks that are not in
the student version.
Teachers have a duty to know
how to extend tasks.
Teachers have a duty to know
potential student errors.
Teachers have a duty to know
strategies students might use
when solving tasks.

UCSMP

Pearson

CMP

Eureka

MiLe
MiLe

EnLe
EnCh

MiLe
IntCh
IntCh
BeLe

Pearson and Eureka presented additional tasks that are not available in the student
version. Pearson presents additional tasks with answers at the bottom margin. The purpose
thereof is unclear: Is it scaffolding? Or is it for students who are faster than others?
Suggestions for implementation did not exist. Additional tasks, however, are provided
consistently in the MiLe phase of all lessons. Eureka’s hidden tasks were much more explicit
regarding purpose. These are for assessing students’ learning, either as an exit task in EnLe or
as mid- and end-of-module test in EnCh. It seems that because tasks were intended as an
assessment, they should not be readily available to students.
In terms of the positioning that teachers have a duty to know how to extend tasks,
Additional Examples was available in all lessons of UCSMP except for five in the whole TG
(108 lessons). These examples are not in the student version. Although the TG used the term
additional in the heading, the examples here were more extensions of the existing examples
than additional tasks. Answers were provided for each additional example. In the student
version of Pearson, the main part of the lesson comprised a number of tasks. Each is named
as Problem #. At the margin is a box with suggested questions followed by intended student
answers. The questions asked students to explain their process, explain how they would
check the correctness of their solution, describe the relationships, visualize a measure, etc.

59

Questions did not ask scaffolding questions that guide students through certain solution
processes. No explanation is offered on the designers’ intention, mathematical information,
or what students know.
These examples show that uncertainty is somewhat addressed as what teaching
mathematics entails in the TGs. The spectrum, however, of uncertainty represented in the
TGs has potential to be extended to include other types of uncertainties. In addition, explicit
presentation of the purpose of the communication actions as to what supports teachers
dealing with uncertainty could contribute to enhancing clarity of communication between the
TG and the readers.
Examination of observed positionings with the five aspects from the literature
suggests that TGs narrowly construct what teaching mathematics entails. The construction is
narrow because only a small number of positionings address each of the five aspects,
excluding the knowledge base. In addition, in most cases the presence of those positionings is
limited to one or two phases. Further, the positionings addressing these aspects cover a slice
of each aspect, leaving various points of each perspective unshared with teacher readers. This
indicates that the TGs do provide some positionings for teachers to engage with, but not as
diverse as the literature suggests. In the literature review chapter, I discussed TGs’ potential
as sources for teacher professional developments. Despite such potential, my examination
showed that TGs could expand on the kinds of positionings they provide to teacher-readers.
Common Positionings
Examining positionings with the five aspects, I found that teaching mathematics as
constructed by the four TGs has much potential to be extended, so as to address aspects of
teaching mathematics not actively dealt with so far. To better understand the positionings that
exist in the TGs, I discuss the positionings commonly identified from the four TGs.

60

Among 44 positionings I identified, seven were in the four TGs. I grouped the seven
positionings into three: 1) general information of the TG (teachers have a duty to know, in
general, supplementary resources available; and teachers have a duty to know the pacing the
curriculum/chapter/lesson); 2) specifics of the content (teachers have a duty to know
vocabulary; teachers have a duty to know supplementary information to implement a task;
and teachers have a duty to know answers to tasks/questions); and 3) assessment (teachers
have a duty to know questions and/or activities for students, to assess their learning of the
lesson/chapter; and teachers have a duty to know tasks for students, to assess their learning
of the chapter). I give details of each of the positionings in Table 9 below.
Table 9. Common Positionings
Positionings
Teachers have a duty to know,
in general, supplementary
resources available.
Teachers have a duty to know
the pacing of the curriculum/
chapter/ lesson.
Teachers have a duty to know
vocabulary.
Teachers have a duty to know
supplementary information to
implement a task.
Teachers have a duty to know
answers to tasks/questions.

Teachers have a duty to know
questions and/or activities for
students, to assess their
learning of the lesson/chapter.
Teachers have a duty to know
tasks for students, to assess
their learning of the chapter.

UCSMP

Pearson

CMP

Eureka

IntCh

IntTG
IntCh

IntCh

IntCh

IntCh

IntCh

IntCh

IntTG
IntCh

EnCh

IntCh

IntCh

MiLe
EnLe
EnCh

IntCh
BeLe
EnLe
EnCh
IntCh
BeLe
MiLe
EnLe
EnCh
EnLe
EnCh

IntCh
IntLe
IntLe
MiLe
EnLe
EnCh
MiLe
EnLe
EnCh
EnCh

EnLe

EnLe

EnCh

IntTG
BeLe
MiLe
EnLe
EnCh
EnLe

EnCh

EnCh

61

MiLe

MiLe
EnLe
EnCh

General information of the TG. Two positionings, teachers have a duty to know the
pacing of the curriculum/ chapter/lesson. and teachers have a duty to know, in general,
supplementary resources available appeared in IntTG and/or IntCh. I describe the
communication actions from each TG for the later positioning to illustrate (see Appendix B
for information about other positionings). Chapter Resource Masters, from the IntCh phase
of UCSMP, showed in reduced size supplementary student materials for each lesson. The size
of each resource master was small – with font difficult to read but not impossible. This
overview did not include electronic resources. IntTG of Pearson presented covers of
hardcopy resources and screenshots of electronic resources; its following page had a table for
each resource, whether for students at intervention level, on-grade level, enrichment, or
emergent bilingual students. This table had no information specific to chapter or lesson level.
The lesson-level specific information was in Resources of IntCh. The item Resources was a
table showing resources available for each of the smaller parts of the lessons. Resources
include web-based, printed, and in CD-ROM. Each resource type was annotated. An asterisk
was used for resources available in Spanish. The Planning Charts of CMP had columns for
Materials and Resources for informing about supplementary resources accompanying each
chapter and lesson. Resources included Labsheets and Teaching Aids. In Eureka, Suggested
Tools and Representations provided a list of tools (e.g., graphing calculator) and
representations (e.g., coordinate plane, equations and inequalities) used in the chapter.
Unclear is why Eureka decided to combine tools and representations. Except this, nothing
was observed in terms of hardcopy resources. This may be because the curriculum is already
an electronic version.
As the above description shows, these positionings are difficult to revisit elsewhere
because they are more of an overview of particular aspects of the TGs. Among various
options for an overview (e.g., mathematical concepts covered, general flow of each lesson),

62

those of pacing and of supplementary resources are pervasive and both are important to know
for forward planning.
Specifics of the content. Three positionings were in the group of specifics of the
content: teachers have a duty to know vocabulary; teachers have a duty to know
supplementary information to implement a task; and teachers have a duty to know answers to
tasks/questions. Except for UCSMP, the TGs discussed providing vocabulary at IntCh or
IntLe phases. These TGs asked teachers to remind students about vocabulary during
introduction of a chapter or a lesson. UCSMP presented vocabulary in EnCh, indicating that
vocabulary is to be reviewed before working on the end-of-chapter assessment tasks. All TGs
except Pearson simply listed the terms.
The positioning that teachers have a duty to know answers to tasks/questions
appeared in more than three phases of each of the four TGs. The positioning that teachers
have a duty to know supplementary information to implement a task appeared in more than
three phases of UCSMP, Pearson, and CMP, and in two phases of Eureka. In other words,
these two positionings were not only pervasive across the TGs, but also pervasive within
each TG. The TGs, however, placed relatively less attention on solution strategies. The
positioning that teachers have a duty to know strategies students might use when solving
tasks was observed idiosyncratically in UCSMP, CMP, and Eureka. Pearson addressed the
positioning regularly in IntCh and BeLe, but not in MiLe, which was the main part of a
lesson.
In general, teachers, at least those using one of the four TGs, are left alone to find
strategies students might use to solve tasks. A possible explanation for this omission is that
providing solution paths for all tasks requires significant space thus increases production cost.
Another possibility is that omitting solution paths is so widespread as to have become the
norm for curriculum authors. Alternatively, those authors might assume that teachers will

63

have no problem in devising multiple solution paths. Whatever the reason, as a result the
positioning of knowing the answer appears more dutiful than the positioning of knowing
solution paths. This imbalance in the degree of obligation might create in teachers the
impression that, provided the answer is known, solution paths matter less. Further research is
needed to understand how this imbalance impacts the practice of teachers aware that
correctness of the answer does not guarantee correctness of the mathematical thinking
involved in task solution, that solution paths are important evidence for formative
assessment, and that attending to solution paths could support students’ development of
mathematical understanding.
Assessment. Two positionings about assessing students’ learning of the
lesson/chapter, Teachers have a duty to know questions and/or activities for students, to
assess their learning of the lesson/chapter. and Teachers have a duty to know tasks for
students, to assess their learning of the chapter, are observed from EnLe and EnCh phases of
the TGs, suggesting that assessment is to be done at the end of each lesson and chapter. These
two positionings together indicate that summative assessment is conducted not only with a set
of tasks, but also with classroom interaction and small activities. Yet, this could mean also
that the TGs foregrounded summative assessments and paid less attention to formative
assessments.
The phase EnLe of UCSMP presented Ongoing Assessment, which suggests to
teachers what to do to conclude the lesson. The suggestion included mathematical tasks for
individual or small-group work, writing a definition or a paragraph of explanation, and using
the graphic calculator. Chapter # Self-Test, from EnCh of UCSMP, presented texts
accompanying Self-Test in the student version. The text read that this is an opportunity for
students to receive feedback and correction, hence experienced an improvement on their
performance after completing it. Pearson presented a set of mathematical tasks in EnLe and

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pre-written questions in EnCh. In terms of the tasks, EnCh of Pearson had # Chapter Test and
Common Core Cumulative Standards Review, both which supported teachers in conducting
summative assessment of student learning. Two headings from EnCh phase of CMP, Possible
Answers to Mathematical Reflections and Possible Answers to Mathematical Practice,
provided ways to close a chapter by asking students to reflect on their learning. ACE
Assignment Guide in EnLe of CMP listed tasks assignable to each lesson. Closing, from
EnLe phase of Eureka, introduced a range of suggestions across the lessons. Those
suggestions included discussing definitions of mathematical terms, revisiting mathematical
processes used during the lesson, giving a set of tasks to students and discussing solutions,
reminding of the goal of the lesson, and directing questions to students. Regarding tasks,
Eureka had a Mid-Module Assessment Task and an End of Module Assessment Task in EnCh
phase for teachers to give students.
To understand where students are at from their performance on the assessment, all
TGs except CMP provided a rubric. These positionings might reflect the widely-spread
perspective that teachers’ duties include ensuring students’ learning at the end of each lesson
or chapter. Another perspective possibly reflected in this positioning is that assessment can
be other than by paper-pencil tests. TGs support teachers practicing in such perspective by
providing alternative ways to assess students’ learning.
Pervasive Positionings from each TG
My examination so far showed positionings common to all TGs. In this section, I
analyze in each TG, the positionings that are pervasive and particular to each TG. To address
this, I examined from each TG the positionings identified in more than 3 phases. By so doing,
I sought to understand for each TG the positionings repeatedly suggested as to what
mathematics teaching entails. I organized those positionings in Figure 1 below. Underline
indicates that the positioning is one of seven commonly appearing in the four TGs.

65

UCSMP
Teachers have a duty to know supplementary information to make accommodations.
Teachers have a duty to know answers to the tasks/questions.
Teachers have a duty to know supplementary information to implement a task.
Pearson
Teachers have a duty to know CCSS MP relevant to the TG content.
Teachers have a duty to know Big Ideas and essential questions/understandings.
Teachers have a duty to know what electronic resources are needed.
Teachers have a duty to know supplementary information to make accommodations.
Teachers have a duty to know how to support emergent bilingual students.
Teachers have a duty to know questions to ask.
Teachers have a duty to know answers to the tasks/questions.
Teachers have a duty to know supplementary information to implement a task.
CMP
Teachers have a duty to know answers to the tasks/questions.
Teachers have a duty to know supplementary information to implement a task.
Eureka
Teachers have a duty to know answers to the tasks/questions.
Figure 1. Positionings observed from more than three phases.
Across the four TGs, the positioning that teachers have a duty to know answers to the
tasks/questions was pervasive. Except for Eureka, the positioning that teachers have a duty to
know supplementary information to implement a task was pervasive also. This positioning
about knowing supplementary information was present in Eureka, although not as
pervasively as in three different phases. This mirrors a pervasive description of traditional
pedagogy that the most central aspect of teaching mathematics is solving mathematical tasks
and checking their answers.
In addition to the two positionings mentioned above, UCSMP frequently presented
the positioning that teachers have a duty to know supplementary information to make
accommodations. This positioning is mostly about supporting students at different levels.
Example: Differentiated Options in IntCh of UCSMP is a table showing, for each lesson, on
what page teachers can find making accommodations for learners, how to support vocabulary
development, and ongoing assessment. The last column presents materials (e.g., graphing

66

calculator, Computer Algebra System, paper clips) needed in each lesson. The first two
columns and the title of this table remind teachers that making accommodations is part of
what teachers do. Regularly, MiLe of UCSMP presents what teachers could do, using the
heading of Accommodating the Learner. Suggestions include questions, scaffolding
mathematical tasks, and possible reactions from students. These are for “those learners who
could benefit from more basic activities” (UCSMP, p. xxi). Occasionally the TG presents tips
for students “who could benefit from more challenging activities” (UCSMP, p. xxi) under the
heading Extension. Recommended Assignment of EnLe distinguishes tasks for all students
and tasks for extra credits. Identical information is given in HOMEWORK in IntLe. Taken
together, teachers using UCSMP are likely repeatedly to be exposed to the duty to make
accommodations, as well as implementing tasks and knowing answers.
Reading Pearson, teachers are invited to engage at high frequency with eight different
positionings. The three positionings pervasive in UCSMP also are pervasive in Pearson.
Here, too, making accommodations meant differentiating instruction for students at basic,
average, and advanced levels. The difference between the two is that Pearson’s
supplementary information is mostly about distributing worksheets to students at the end of
each lesson (i.e., EnLe), whereas UCSMP’s is more is about practices teachers could try
during the main part of each lesson (i.e., MiLe).
Unique to Pearson is that the obligation to engage with CCSS MP and Big Ideas is
heavy. Yet the TG is not necessarily consistent with presenting CCSS MP and Big Ideas. I
illustrate via the instance of CCSS MP. In EnLe, Mathematical Practices lists the MP
addressed by the exercise tasks. The TG first lists a selected set of MPs then places the task
number next to the relevant MP. The MPs listed, according to the TG, is that of “supported in
this lesson” (Pearson, p. 8). To be precise, the list is the MPs addressed by the tasks, not in
the lesson. The MPs listed here do not match the MPs listed at the first page of the student

67

version where it provides CCSS content standard and MPs related to the lesson. Some lessons
give more MPs than in the student version, while other lessons give fewer. An unexpected
inconsistency is encountered with the TG’s representation of the MPs addressed at the lesson
level. Preparing to teach a lesson, teachers are asked to crosscheck texts about CCSS MP and
Big Ideas and decide what to do with the inconsistency.
Apart from these positionings, Pearson users have obligations to attend to electronic
resources, to predesigned questions to students in class, and to supporting emergent bilingual
students. The positioning regarding emergent bilingual students is the only positioning
pervasive in any of the four TGs addressing one of the five aspects I found from literature. As
previously discussed, communication actions associated with this positioning focus more on
providing additional support within the flow of dominant school culture than on actively
utilizing students’ knowledge. Yet, this positioning being pervasive, the TG constantly
reminds teachers to consider emergent bilingual students when planning and teaching each
lesson.
So far, I showed for each TG the positionings regularly occurred in more than three
phases. The number of pervasive positionings varied across the TGs, as well as the kinds of
positionings. I suggest two questions to consider. First, do most, if not all, of the pervasive
positionings address the qualities that the TG seeks from a professional teacher? Second, are
all the qualities of a professional teacher addressed by the pervasive positionings?
Curriculum authors could intentionally place the positionings they would like to emphasize in
multiple phases so that teacher-readers could gain sufficient opportunities to engage with
those positionings.
Degree of Support
Until this point the examination I present did not necessarily attend to subtle
differences within a positioning. Looking at seven different phases from four TGs, I was

68

more interested in the level of specificity that allowed me to make comparisons across the
phases and the TGs. Yet I acknowledge that subtle differences exist within a positioning. The
differences are due to variations in the range of support available from each TG, as
mentioned briefly earlier. In other words, TGs may impose the same set of duties on teachers,
but distinct variations exist in the degree of support those TGs individually provide to
teachers acting on that set. Here I present those cases with different degrees of support in
order to show that a positioning provided in two or more TGs does not mean that the teacherreaders will have the same experience with the positioning. Closer examination of this matter
might require a separate study.
Teachers have a duty to know vocabulary. Knowing vocabulary is the positioning
observed at an earlier stage of the chapter (i.e., IntCh) or the lesson (i.e., IntLe) of Pearson,
CMP, and Eureka. UCSMP presented the positioning in EnCh so that students could review
them before they work on the chapter assessment tasks. UCSMP offered the least support.
Providing the vocabulary list in the student version only, UCSMP asked teachers to have
students review the vocabulary. Pearson offered the most support. For each vocabulary word,
Pearson explains how teachers could introduce it to students. This positioning exemplifies
that although the same positioning is observable from the TGs, the degree of support for
teachers to act on the positioning varies.
Teachers have a duty to know potential student errors. Pearson consistently
attended to potential student errors. At the beginning of each chapter, the TG provided what
students might do. Possible student errors discussed here include invalid application of a
property, overgeneralization of linguistic features of mathematical sentences, steps students
might forget, potential place of confusion, and more. Some chapters provide how teachers
might address those errors by providing page numbers with potentially-helpful information or
showing an example of a valid application of a property. In MiLe, not regularly but

69

occasionally the TG provides a brief paragraph for error prevention. Unlike errors discussed
in IntCh, errors in MiLe were specific to the task. UCSMP and Eureka sometimes also
discussed potential student errors but not regularly. CMP was relatively less proactive than
the other three TGs in presenting student errors. IntCh of Pearson had three columns in the
Math Background page, each with purple headings named after mathematical activities of the
chapter (e.g., creating equivalent equations, solving proportions, and working with
percentages as proportions). Following the heading are general descriptions of strategies
students might apply when engaging with the mathematics activity. Often, TG presented
strategies using a simple mathematics task as an example. PROCESS of BeLe describes the
mathematically-valid process students might apply. Student strategies rarely were discussed
for tasks in MiLe. UCSMP, CMP, and Eureka presented a valid student approach when
needed, and are specific to the task, unlike IntCh of Pearson.
Teachers have a duty to know the pacing of the curriculum/chapter/lesson.
Support level varied also in a seemingly-straightforward positioning: teachers have a duty to
know the pacing of the curriculum/chapter/lesson. All four TGs presented how many days
are needed to cover the curriculum. UCSMP has a table with three different pacing options:
for an average group of students, for an advanced group of students, and for a block-schedule
class. For each option, the TG provided the number of days considered sufficient for students
to learn each lesson. Pearson and CMP, too, showed numbers of days allocated for each
lesson in both traditional and block schedule. Eureka is unique: in IntTG of Eureka, Pacing
and Preparation Guide provided the number of instructional days needed to teach the whole
curriculum; chapter-level pacing information is given in IntCh, but lesson-level pacing
information not. Presumably, each lesson was supposed to be covered in one instructional
day, but this was not communicated explicitly in the TG. In both IntTG and IntCh, Eureka
did not indicate whether the days are for the traditional or the block-schedule.

70

Examples provided here are not exhaustive. Other positionings, too, have subtle
differences in terms of the level of support they provide. My intention in providing these
examples is partially an effort to strengthen this study’s rigor. Acknowledging such subtlety,
I aimed to provide a base for nuanced reading of the results. In addition, I suggest possible
direction for future research by presenting examples.
Results for Research Question 2: Idiosyncratically Occurring Positionings
In this section, I share the positionings that idiosyncratically occurred in any of the
four TGs. From my investigation, I found two different types of idiosyncratically occurring
positionings: an idiosyncratic-only type and an idiosyncratic-regular type. I classified a
positioning as an idiosyncratic-only type when it occurred sporadically not regularly in a TG.
A positioning of idiosyncratic-regular type in a TG occurs regularly in certain phases and
sporadically in other phases. Idiosyncratic-only type of positionings inform with the
positionings that seemed absent from my investigation of the first research question. My
investigation with idiosyncratic-regular type of positionings showed the following: some of
the regularly occurred positionings were being reinforced by their idiosyncratic occurrences.
From my examination, I suggested that idiosyncratic positionings have different level of
presences and that idiosyncratic occurrence is what curriculum authors could use to
foreground the positionings deemed significant.
General Descriptions
In total, I identified 17 positionings seeming to appear sporadically. Some of these
were sporadic in some TGs but regularly observed in other TGs. No positionings were
idiosyncratic in all four TGs, which was expected from the design of this research as
explained in the Methods chapter. In the following, I discussed in turn the two types of
idiosyncratic positionings. First, I attended to positionings that appeared, in any of the four
TGs, idiosyncratically only. That is, I discuss the positioning teachers have a duty to know

71

potential student errors from UCSMP and Eureka (see Table 10). I name such positionings as
idiosyncratic-only type. Second, I discuss idiosyncratic positionings that also regularly were
observable. For example, I discuss the positioning in Table 10 from Pearson. I name these
positionings as idiosyncratic-regular type. I close by presenting pervasive positionings in
each TG when idiosyncratic ones were counted.
Table 10. Regularly and Idiosyncratically Occurring Positionings
Positionings
UCSMP
Pearson
CMP
Eureka
Teachers have a duty to know
IntCh
MiLe
MiLe
potential student errors.
MiLe
Notes. Green indicates phases where the positioning occurred regularly. Red indicates
phases where the positioning occurred idiosyncratically.
Idiosyncratic-Only Type
In Table 11, each number indicates the number of phases in which the positioning was
identified. The first column for each TG shows the number of phases where positioning
occurred regularly. The second column shows the number of phases where positioning
occurred idiosyncratically. Numbers with an underline are idiosyncratic-only types (i.e., the
number in the first column is 0). Among 17 idiosyncratically occurring positionings, nine
were of idiosyncratic-only type; four positionings in UCSMP, none in Pearson, one in CMP,
and seven in Eureka.

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Table 11. Idiosyncratic-Only Type Positionings
Positionings
Teachers have a duty to know
what electronic resources are
needed.
Teachers have a duty to know
how to support emergent
bilingual students.
Teachers have a duty to know
tasks/activities/questions for
opening a chapter/lesson.
Teachers have a duty to know
questions to ask.
Teachers have a duty to know
potential student errors.
Teachers have a duty to know
strategies students might use
when solving tasks.
Teachers have a duty to know in
general the mathematical
contents of the chapter at the
lesson level.
Teachers have a duty to know
mathematics for pedagogical
purposes.
Teachers have a duty to know to
consider students’ prior
mathematical knowledge.

UCSMP

Pearson

CMP

Eureka

2

0

5

0

6

1

0

1

0

1

3

0

1

0

0

0

1

0

1

0

2

0

0

1

0

0

5

0

1

2

0

2

0

1

1

1

1

1

0

1

0

1

2

0

0

3

0

1

1

0

1

0

1

0

0

1

1

1

1

1

2

0

0

1

0

1

1

0

1

0

1

0

The idiosyncratic-only types in UCSMP are connected to students. These positionings
address supporting emergent bilingual students, anticipating student responses (either
mathematically valid or invalid), and incorporating mathematical knowledge that students are
expected to know at the point of the lesson. Although these positionings are not built into the
design (e.g., do not appear with regularity), UCSMP still acknowledges these positionings to
be salient when teaching mathematics. These positionings were all placed in the phase of
MiLe, except one about prior knowledge, which is in the phase of IntLe.

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Pearson did not have idiosyncratic-only types. The six idiosyncratic positionings I
observed from Pearson are of the second type – idiosyncratic yet regularly observable. I
discuss these six later.
When regularly occurring positionings are considered, as in the first research question
of this study, CMP seems not to suggest anticipating student strategy as a duty for teachers.
My analysis for the second research question showed that this is a misunderstanding of the
TG. CMP was in fact suggesting the positioning that teachers have a duty to know strategies
students might use when solving tasks, idiosyncratically. I observed this positioning from
three phases, namely beginning of a lesson (BeLe), middle of a lesson (MiLe), and ending of
a lesson (EnLe). Such appearance of the positioning indicates that teachers using this TG do
have ample opportunity to engage in anticipating student responses.
Eureka is the TG with the highest number of idiosyncratic-only types. Similar to the
case of CMP, Eureka suggests more positionings than it seems from the list with regular
positionings only. The two positionings, teachers have a duty to know
tasks/activities/questions for opening a chapter/lesson, and teachers have a duty to know in
general the mathematical content of the chapter at the lesson level, might be ones suggesting
TG authors intentionally attend to the regularity of a positioning. Communication actions
associated with positionings like the above might contain information beneficial for teachers
in every lesson or chapter.
Idiosyncratic-Regular Type
Some communication actions associated with this positioning were embedded in
paragraphs and sentences, and others were in headings. In Table 12, the underlined numbers
indicate idiosyncratic-regular types. Similar to the idiosyncratic-only type table, numbers in
cells indicate the number of phases where positioning was identified. Among 17 idiosyncratic

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positionings, 12 were of this type; two positionings in UCSMP, six in Pearson, four in CMP,
and three in Eureka.
Table 12. Idiosyncratic-Regular Type Positionings
Positionings
Teachers have a duty to know
CCSS MP relevant to the content
of the TG.
Teachers have a duty to know
relevant CCSS content standards
at the chapter/ lesson level.
Teachers have a duty to know
what hardcopy resources and/or
materials are needed.
Teachers have a duty to know
what electronic resources are
needed.
Teachers have a duty to know
supplementary information to
make accommodations.
Teachers have a duty to know
tasks/projects that overarch a
chapter, to be revisited multiple
times.
Teachers have a duty to know
questions to ask.
Teachers have a duty to know
answers to tasks/questions.
Teachers have a duty to know
potential student errors.
Teachers have a duty to know how
the curriculum contributes to
students’ college and career
readiness.
Teachers have a duty to know
mathematics for pedagogical
purposes.
Teachers have a duty to know
supplementary information to
implement a task.

UCSMP

Pearson

CMP

Eureka

0

0

4

0

2

0

1

1

0

0

2

0

1

0

1

2

2

0

1

0

1

3

0

0

2

0

5

0

6

1

0

1

4

0

3

1

0

0

1

0

2

1

2

1

0

0

0

0

0

0

5

0

1

2

0

2

5

0

5

0

3

1

3

1

0

1

1

1

0

0

0

1

0

0

1

1

0

0

0

0

1

1

1

1

2

0

0

1

3

0

4

1

4

0

1

1

Within idiosyncratic-regular type of positionings, I identified two kinds of
idiosyncratic-regular type. One is that of extending, the other is that of disconnected. This
classification is based on the connection between communication actions associated with the
75

regular appearance of a positioning and communication actions associated with idiosyncratic
appearance of the positioning. When a positioning occurred idiosyncratically, the contexts of
those idiosyncratic occurrences either can align with, or extend on, the context of regular
occurrence or be different, or disconnected. For each TG, I analyzed which idiosyncraticregular positionings were in which category.
In UCSMP, the positioning that teachers have a duty to know tasks/projects that
overarch a chapter, to be revisited multiple times being of an idiosyncratic-regular type was
expected by its design. This is so because the TG introduced the overarching project at the
beginning of the chapter and summarized at the end of the chapter. In addition to this regular
introduction, the TG idiosyncratically reminded teachers of the projects in some of the
relevant lessons. Therefore, there was a coherency between the contexts of regular
occurrences and idiosyncratic occurrences of the positioning.
The positioning that teachers have a duty to know mathematics for pedagogical
purposes is without such coherence. UCSMP, in its IntLe phase, regularly provided
paragraphs for teachers to read about the mathematical content of the lesson. In the middle of
each lesson, the TG idiosyncratically provided relevant mathematical knowledge that could
support teachers in implementing the tasks of the lesson. These two kinds of communication
actions are interrelated because they deal with mathematical content of the same lesson, or
addressing the same positioning that teachers have a duty to know mathematics for
pedagogical purposes. Yet, the communication actions associated with the idiosyncratic
occurrences provided supportive information for a specific part of the lesson or a specific
task. In other words, these communication actions did not extend on the contexts that regular
occurrences are drawing on. Therefore, this positioning occurred regularly and was
reinforced idiosyncratically in multiple contexts.

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Pearson was dominated by those with disconnected contexts. All six idiosyncratic
type positionings were more of idiosyncratic-general type than of idiosyncratic-only type.
Five of these did not share contexts across regular and idiosyncratic occurrences. For
example, teachers have a duty to know potential student errors occurred regularly in the
phase of IntCh. At this phase, the TG discussed student errors with limited specificity so that
the discussion can cover all lessons of the chapter. The TG compensated this lack of
specificity by revisiting the positioning in the phase of MiLe. Here, Pearson described
potential errors students can make, probably when the TG authors thought such information
could be salient for teachers preparing their lessons. Positionings about knowing
supplementary information for making accommodations, college and career readiness, and
mathematics for pedagogical purposes are similar in that regular positionings were provided
at the general level, and specific aspects of the positionings are revisited in the middle of or at
the end of the lesson. The positioning that teachers have a duty to know supplementary
information to implement a task had the strongest presence among the six idiosyncratic
positionings. This positioning regularly appeared in four phases and idiosyncratically in the
phase of the middle of a lesson. Only one positioning, teachers have a duty to know
tasks/projects that overarch a chapter to be revisited multiple times, shared the context.
Among the four idiosyncratic-regular type of positionings in CMP, one positioning,
teachers have a duty to know what hardcopy resources and/or materials are needed, had
consistency across the contexts of regular and idiosyncratic occurrences. At the IntLe phase,
the TG provided a comprehensive list of resources teachers should prepare for the whole
lesson. In the BeLe, MiLe, or EnLe phase, the TG gave the name of the resource from the
comprehensive list when the resource is needed. This is clearly the case when the
idiosyncratic occurrences of a positioning extend on the context of regular occurrence. Such
occurrence of idiosyncratic positionings provide teachers with supports at specific level,

77

which a regular occurrence by itself could not achieve. The other three positionings had
disconnected contexts, meaning that the contexts of idiosyncratic occurrences and of regular
occurrences differed. Teachers have a duty to know what electronic resources are needed, is
a good example. In all phases except the IntTG, CMP regularly reminded teachers at the
upper margin to visit a website for additional resources. Main support here was the address of
the website. In BeLe phase, the TG idiosyncratically asked teachers to show a video. Those
lessons provided the online address of the video with a brief description of what the video is
about. The contexts on which the idiosyncratic occurrences drew were disconnected from the
context of the regular occurrence. Still, both cases support teachers via the use of electronic
resources.
In Eureka, both CCSS MP and CCSS content were revisited, regularly and
idiosyncratically. Regularly in the phase of IntCh, the TG identified the standards addressed
in the chapter. In the phases of MiLe and EnLe, the TG notified specific texts relevant to each
standard. That is, when it comes to the two positionings about the standards, Eureka provided
a general-level support at an earlier phase with a specific-level support at later phases. The
other two positionings are of disconnected contexts.
Closing Remarks
From the examination of idiosyncratic-only type of positionings, I showed that
UCSMP described what students know and ways to meet their needs, CMP did provide
possible student strategies, and Eureka provided a range of information including where to
find resources on possible student errors. Results from analysis of idiosyncratic-regular type
of positionings suggested that UCSMP strongly emphasized teachers’ duties of implementing
projects and of knowing mathematics for pedagogical purposes. For Pearson, the analysis
suggested that the TG reinforced the duties of knowing how to make accommodations,
implementing projects, knowing possible student errors, considering students’ college and

78

career, knowing mathematics for pedagogical purposes, and knowing supplementary
information to implement a task. In terms of CMP, the TG highlighted the hardcopy and
electronic resources needed to implement a lesson, knowing what questions to ask students,
and knowing answers to tasks or questions. Eureka emphasized standards, answers to tasks or
questions, and supplementary information to implement a task. Some of these idiosyncraticregular positionings shared contexts across regular and idiosyncratic occurrences. Other
positionings of this type did not share the contexts.
Idiosyncratic positionings are worth examining because these are the positionings the
TG authors provided by breaking the structure of the genre of the TG. From my examination
of idiosyncratic positionings, however, I claim that not all idiosyncratic occurrences are the
same. Idiosyncratic-only type of positionings had rather vague presence while others had a
much stronger presence, reinforced by regularity. In addition, among those with stronger
presence, some positionings were placed in multiple contexts while others in singular
context. Idiosyncratic-regular positionings with disconnected contexts might be those the TG
authors wanted to emphasize the most, because of the multiplicity of contexts and their
breaking of the TG’s genre. In addition, those could be positionings teacher-readers might
take up because of the support provided at both the general and specific levels in a variety of
contexts. Therefore, curriculum authors can maximize the opportunities for teacher-readers to
a certain positioning by placing it both regularly and idiosyncratically, and by drawing on
multiple contexts. Without explicit attention to this matter, the authors might unintentionally
overemphasize the positionings with mediocre importance.
Results for Research Question 3: Voices of the TGs
To understand the voice of the TGs, I examined the three following aspects: i) use of
pronoun, ii) modality, and iii) imperatives. Regarding the pronoun, I showed that all three
pronouns are used to acknowledge teacher-reader presence. Therefore, more pronoun use

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means higher tendency of speaking to teachers. When it comes to modality, I grouped
modalities into two: suggestive and assertive. With this grouping, I compared incidences of
suggestive cases versus assertive cases to examine the degree of teachers’ professional
judgment acknowledged in each TG. Last, I analyzed the use of imperatives. My analysis
showed that the TGs used imperatives directing teachers to follow TG suggestions rather than
critically examine those suggestions. From this, I concluded that more use of imperatives in
these four TGs indicates limited acknowledgement of teachers’ professional judgment, hence
closer to speaking through than speaking to. At the end of this section, I compared the TGs
based on the results from the examination of pronoun, modality, and imperatives.
General Description
Before sharing the findings I outlined above, I provide general findings in Table 13.
By total sentences directed at teachers, I mean the sum of sentences that include a pronoun
referring to teachers plus sentences that begin with an imperative. Most pronouns were
referring to teachers, either explicitly or implied. Only two sentences with the pronoun we
clearly excluded teachers and were referring to the authors. I did not count these two
sentences as referring to teachers. All imperative sentences are included because the
sentences are from TGs, which are written for teachers to read. By total incidences directed at
teachers, I mean the sum of sentences with pronoun directed at teachers and imperative
incidences. Imperative incidences is the number gained by multiple counting of sentences
with multiple imperatives (e.g., a sentence with two imperatives is counted twice, a sentence
with three is counted thrice). In other words, I counted the number of commands directed at
teachers.

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Table 13. General Findings

Sentences with Pronoun
Sentences with Pronoun
Referring to Teachers
Imperative Sentences
Imperative Incidences
Imperative Incidences per
Pronoun Referring to
Teachers
Total Sentences Directed at
Teachers
Total Incidences Directed at
Teachers (IDT)
Total Pages

UCSMP

Pearson

CMP

Eureka

70

17

45

13

68

17

45

13

135
137

219
223

38
38

110
114

2.01

13.12

0.84

8.77

203

236

83

123

205

240

83

127

49

82

20

48

Simple counts may be inappropriate for cross TG comparison. One way to address
this is by comparing the ratio of imperative incidences to the sentences with a pronoun
referring to teachers; the higher the ratio, the less the sense of human existence. Imperative
incidences do not use explicitly stated pronouns. Rather, the recipient of the message is
implied. Therefore, these incidences have less human presence than the sentences with
pronouns. Because this study’s focus is on the TGs use of voice in relationship to teachers, I
used the number counts of the sentences and incidences imposing duties on teachers. All
imperative incidences were imposing duties on teachers. A small number of sentences with
pronouns were exclusively referring to the curriculum authors or students. The number count
of the sentences with pronouns referring to teachers only is in the row Sentences With
Pronoun Referring to Teachers. The ratio in the row Imperative Incidences per Pronoun
Referring to Teachers shows that Pearson, with a ratio of 13.12, rarely used a pronoun
referring to teachers only rarely, compared to its use of imperatives. The ratio and the
dominant use of imperatives might suggest Pearson’s low personal involvement, hence the
TG is speaking through teachers rather than speaking to teachers (Herbel-Eisenmann, 2007;

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Remillard et al., 2011). CMP is the only TG that presented more sentences with pronouns
than it presented imperative sentences. The next highest was UCSMP but it still was much
lower than Eureka and Pearson, Eureka’s ratio being more than thrice that of UCSMP and
being slightly higher than half of Pearson. Below I discuss TGs’ use of pronoun, modality,
and imperatives in detail.
Pronoun: General Findings
In Table 14, I organized general findings regarding the use of pronoun.
Table 14. The Use of Pronoun: General

Total Referring to
Teachers (Explicit)
Total Referring to
Teachers (Explicit or
Implied)
Total Sentences with a
Pronoun.
Pronouns referring to
teachers per IDT
Pronouns referring to
teachers per page

UCSMP

Pearson

CMP

Eureka

26

15

28

3

68

17

45

13

70

17

45

13

0.33

0.07

0.54

0.10

1.39

0.21

2.25

0.27

With the exception of two sentences from UCSMP, all sentences with a pronoun
referred to teachers. Some sentences made explicit that the pronoun is directed at teachers.
Two examples include “You might write or project the following so that students can answer
these questions as they enter the classroom” (UCSMP) and “If you need to, show them or
have a student demonstrate the answer to this question” (Eureka). Sentences Implied are
those with pronouns open enough to refer to teachers and, at the same time, to others (e.g.,
students, curriculum authors). This often happened when the TG described mathematical
facts or processes. Consider the following example. “Point out that as you round off to more

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and more decimal places for your estimate, the estimate becomes more accurate.” (Pearson).
In this study, I counted this as a sentence with a pronoun implying teachers. The pronoun you
in the previously given example could include students – seeing the students as those who
were rounding the numbers and teachers were expected to almost read to the students the
sentence excluding “Point out that.” Yet, there is a possibility to include teachers in the
pronoun – imagine a teacher rounding off numbers showing students the estimate is
becoming more accurate. Two sentences from UCSMP were using the pronoun we to refer
exclusively to the authors. These are the two sentences: “In this book, we have chosen to
think of terms as added” (UCSMP, p. 16) and “We have purposely separated them in Lessons
1-1 and 1-2 so that students will see the associative properties as switching order of
operations, while the commutative properties involve switching the order of addends (in
addition) or factors (in multiplication)” (UCSMP, p. 17). Here, the pronoun “we” refers to the
authors, with a clear purpose of sharing their design principle with teacher readers. Therefore,
these are the incidences where the TG is speaking to teachers.
In the rate of sentences with pronouns per total incidences directing at teachers, CMP
was the highest, followed by UCSMP, Eureka, and Pearson. This order remained the same
when the ratio was examined via pages examined. This might suggest that CMP is the
curriculum speaking to teacher readers, while Pearson is speaking through them.
Pronoun You
Table 15 is a summary of my findings regarding the TGs use of the pronoun you.

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Table 15. The Use of Pronoun You

You

Teachers (Explicit)
Teachers (Implied)
Not Referring to
Teachers
Total Referring to
Teachers
Total Referring to
Teachers per Total
Sentences with a
Pronoun

UCSMP
26
13

Pearson
15
2

CMP
19
4

Eureka
3
0

0

0

0

0

39

17

23

3

0.56

1.00

0.51

0.23

All sentences with the pronoun you were referring to teachers. With such direct
addressivity, more sentences were explicit than implying, which means the pronoun was open
enough to refer to others in addition to teachers. In UCSMP and CMP, slightly more than half
the sentences with a pronoun used you. Pearson had no sentence with a pronoun other than
you. About a fifth of Eureka sentences with a pronoun used you. The table immediately above
indicates that, across the four TGs, the pronoun you was used to communicate with teachers.
This data indicates that all four TGs are acknowledging the teacher-reader presence, although
with varied degree. The TGs more often explicitly referred to teachers. In addition, even
when the sentences were not explicitly referring to teachers, they implied teacher presence.
No use of the pronoun you excluded teacher presence. Drawing on my improvisation of
speaking to versus speaking through (as explained in Chapter 3), this acknowledgement of
teacher-reader presence indicated that the TGs are speaking to them. This result, however,
does not guarantee that all TGs present teacher-reader with high visibility. Their use of other
pronouns, modalities, and imperatives, which are discussed below, support this point.
Considering that the TGs are written for teachers to read, all the sentences with the you
pronoun referring to teachers is more of a natural phenomenon than anything else.

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Pronoun We
I organized the TGs’ use of the pronoun we in the table below.
Table 16. The Use of Pronoun We

We

Teachers (Explicit)
Teachers (Implied)
Not Referring to
Teachers
Total Referring to
Teachers
Total Referring to
Teachers per Total
Sentences with a
Pronoun

UCSMP
0
29

Pearson
0
0

CMP
0
7

Eureka
0
10

2

0

0

0

29

0

7

10

0.39

0.00

0.16

0.77

The TG with the highest use of the pronoun we is UCSMP, albeit that Eureka has the
highest percentage of we pronoun sentences. CMP used we in less than a fifth of its sentences
with pronouns directed at teachers; no sentence using we is directed explicitly at teachers;
instead, the pronoun is used in describing mathematical activity in the context the authors
assume is to be shared among teachers, students, and the textbook. Another use of we is when
describing general mathematical facts. The exception was UCSMP, which twice used we to
make the authors visible (e.g., “We have purposely separated them in Lessons 1-1 and 1-2 so
that students will see the associative properties as switching order of operations” (UCSMP, p.
17).). Making authors visible is indeed a way to have the TG speak to teachers by
acknowledging their presence. I observed such use of we from UCSMP only. Other TGs’ use
of we was to acknowledge the teacher-reader presence by referring to them.
Pronoun I
In addition to the pronoun we, I also examined how TGs are using the pronoun I.
Table 17 is a summary of my findings.

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Table 17. The Use of Pronoun I

I

Teachers (Explicit)
Teachers (Implied)
Not Referring to
Teachers
Total Referring to
Teachers
Total Referring to
Teachers per Total
Sentences with a
Pronoun

UCSMP
0
0

Pearson
0
0

CMP
9
6

Eureka
0
0

0

0

0

0

0

0

15

0

0.00

0.00

0.33

0.00

Only in CMP is the I pronoun used. The explicit I pronoun is in questions on which
teachers should or may reflect, such as “How will I use this to plan for tomorrow?” (CMP, p.
46). In terms of implied I pronoun sentences, CMP placed those sentences immediately after
providing suggested questions to ask students. Typically in CMP, what comes after suggested
questions are intended answers or pedagogical information for teachers. The intended
answers are where CMP used I. For example, in the sentence “I could do more chores around
the house to increase my allowance” (CMP, p. 42), the TG used the pronoun I, which seems
to refer to students for the most part. In other lessons, the TG gave pedagogical information
without using a pronoun. In the sentence “Students should notice that the rate of change for
the quadratic function is different from that for linear or exponential,” (CMP, p. 52) the TG is
making clear that the sentence is more for teachers than students. This brings complexity.
The TG placed at least two different types of sentences (i.e., intended answers and
pedagogical information) at the same location (i.e., after the suggested questions) across
different lessons. Taking this into consideration, I interpreted the I pronoun as open enough
to imply teachers in addition to students.
With or without counting the implied cases, CMP is the only TG to place itself as the
teacher-reader. This proactive level of communication appears in one TG and in a third of the

86

total sentences with a pronoun. That is, the examination with I pronoun shows that CMP is
most actively speaking to teachers while other TGs are not.
So far I examined three pronouns in the TGs. From examining you, I found all four
TGs were foregrounding teacher-reader presence with the pronoun. Regarding the pronoun
we, Eureka used it most frequently to refer to teachers. Particularly interesting was UCSMP’s
use of the pronoun we. UCSMP is the only TG that used the pronoun to refer to themselves as
authors to explicitly discuss their design principles. With the pronoun I, CMP is the only TG
which used it. All in all, these findings suggest that each TG has their own way to highlight
teacher-reader presence, hence speak to teachers in various ways. Because most of the
sentences with pronouns were acknowledging teacher presence, what becomes salient is how
often the TGs used these three pronouns. For example, Pearson used the pronoun you to refer
always to teachers. Focusing on this particular finding, it suggests that the TG is speaking to
teachers. What if, however, only a few sentences in the TG had pronouns? Were this the case,
it would be difficult to consider the TG as actually speaking to teachers. Therefore, the ratio
of sentences with a pronoun to total sentences is worth examining. I presented results from
such examination toward the end of this chapter.
Modality
To understand the use of modality, I examined sentences with pronouns referring to
teachers. In other words, among the total sentences examined in this study, I excluded the
sentences without pronouns, or imperatives. Table 18 shows the number of sentences per
each modality used, explicitly or implicitly referring to teachers. [do] indicates sentences
with no modality but a verb asking teachers to perform certain action. T indicates explicitly
directed at teachers and (t) indicates implicitly directed at teachers. All modal verbs I found
were positive, except for one case from Eureka that used should not. I count this as should,
following Halliday and Matthiessen’s (2004) classification.

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Table 18. Modality per Explicit and Implying

can
could
may
might
will
would
should
need
[do]
total

UCSMP
T
(t)
3
3
1
3
1
1
14
2
0
0
0
0
2
1
1
3
4
29
26
42

Pearson
T
(t)
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
14
2
15
2

CMP
T
5
1
8
0
7
0
0
0
7
28

Eureka
T
(t)
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
7
3
10

(t)
4
3
0
0
2
0
0
0
8
17

Halliday and Matthiessen (2004) classified modal operators as of low-, median-, or
high-value. Table 19 below shows which modal verbs are in which group.
Table 19. Excerpts from Halliday and Matthiessen’s (2014, p. 116) Table for Finite Verbal
Operators
Modal operators:
low
positive
can, may, could, might,
(dare)
negative needn't, doesn’t/didn’t
+ need to, have to

median
will, would, should,
is/was to
won't, wouldn’t,
shouldn’t (isn’t/wasn’t
to)

high
must, ought to, need,
has/had to
mustn't, oughtn’t to, can’t,
couldn’t, (mayn’t,
mightn’t, hasn’t/hadn’t to)

In addition to modal verbs in Halliday and Matthiessen’s work. I paid attention to
bald assertions, i.e., sentences with no modality (Herbel-Eisenmann, Kristmanson, &
Wagner, 2011), or root modality (Rowland, 2005). Having no modality, bald assertions give
no room for negotiation but rather present a sentence as a fact that does not reflect the
speaker’s stance (Herbel-Eisenmann et al., 2011; Rowland, 2005).
Table 20 presents the sum of the number of sentences for each modality.

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Table 20. Modality with Explicit and Implying Combined

can
could
may
might
will
would
should
need
[do]
total

UCSMP
6
4
2
16
0
0
3
4
33
68

Pearson
0
0
1
0
0
0
0
0
16
17

CMP
9
4
8
0
9
0
0
0
15
45

Eureka
0
1
0
1
1
0
1
0
9
13

In my analysis, I combined the modality with low and median values as suggestive
(can, could, may, might, will, would, should), and high value and bald assertions as assertive
(need, [do]). By so doing, I sought to compare the degree of obligation TGs are imposing on
teachers. Table 20 presents the number counts of the sentences with suggestive voice versus
those with assertive voice. Some modalities from Halliday and Matthiessen’s (2004) work are
not assigned to either group because none of the four TGs used them. Some of the
imperatives I had under suggestive may seem stronger than suggestive. My rationale for such
grouping is that I wanted to be conservative with my coding in order to highlight when the
TGs strongly impose duties on teachers. Table 21 shows that despite the decision to
conservatively code the TGs, three of the four TGs were using a more assertive voice than
suggestive.

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Table 21. Modality by Suggestive and Assertive

Suggestive
(can, could, may, might, will, would,
should)
Assertive (need, [do])
Suggestive per Total Modality
Sentences
Assertive per Total Modality
Sentences
Suggestive per IDT
Assertive per IDT
Suggestive per page
Assertive per page

UCSMP

Pearson

CMP

Eureka

31

1

30

4

37

16

15

9

0.46

0.06

0.67

0.31

0.54

0.94

0.33

0.69

0.15
0.18
0.63
0.76

0.00
0.07
0.01
0.20

0.36
0.18
1.5
0.75

0.03
0.07
0.08
0.19

In UCSMP, suggestive and assertive voices are used with similar frequency. Pearson
and Eureka used assertive voice more often than suggestive voice. CMP is the only TG using
voice more suggestive than assertive. Suggestive voice in CMP appears about twice as often
as the assertive voice in it. This result suggests that CMP is the TG most highly appreciative
of teachers’ ability to make professional judgment, followed by UCSMP, Eureka, and
Pearson.
The ratio with IDT and page shows how frequently the two voices are used in the
whole data set. In addition, the ratios make possible the comparison across TGs. Ratio per
total incidences shows that overall modality is used rarely in Pearson and Eureka. Ratio per
pages examined reinforces that CMP uses suggestive voice much more often than do other
TGs, and that Pearson and Eureka rarely use modalities. That is, CMP is not only the TG that
used more suggestive voice than assertive voice, but also the TG that used suggestive voice
with the highest ratio – 36% – among the four TGs. The limited use of modality, combined
with more frequent use of assertive than of suggestive, indicates that such TG might be
forcefully imposing teaching duties on teachers, rather than communicating with teachers.
The duty seems highly obligatory in such TG.
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Imperatives
To find sentences with imperatives, I reviewed all sentences in the four TGs. In sum, I
found in UCSMP 135, in Pearson 219, in CMP 38, and in Eureka 110. Some sentences had
two or more imperatives, so my count is based on the imperatives used. For example, the
sentence “Collect these papers, mix them up, and pass one out to each student” (Pearson, p.
28A), is counted as one imperative sentence and three imperative incidences. In Table 22, I
organized number counts and ratios of imperatives.
Table 22. Imperatives: General Results

Total Sentences w/ Imperatives
Total Incidences w/ Imperatives
Incidences w/ Imperatives per IDT
Incidences w/ Imperatives per
page

UCSMP
135
137
0.67

Pearson
219
223
0.93

CMP
38
38
0.46

Eureka
110
114
0.88

2.80

2.72

1.90

2.38

Table 22 shows that Pearson and Eureka are quite heavy with imperative sentences.
Although the per-page ratio of incidences with imperatives is higher in UCSMP than in
Pearson, imperative sentences in UCSMP are lower than those of Pearson and Eureka when
compared to the total incidences directed at teachers. CMP’s ratio is the lowest in both per
incidences directed at teachers and per-page. If all imperatives direct teachers in what to do
and do not acknowledge teachers’ professional judgment, which I unpack in the latter part of
this subsection, the high number count and the high ratio indicates low degree of room for
professional judgment. Pearson is the most obligatory among the four TGs, both in terms of
its number counts and the ratio. The number count shows that UCSMP used more
imperatives than Eureka. When the ratios are considered, Eureka is in fact using more
imperatives than UCSMP. Slightly below half of all incidences in CMP were using
imperatives. Therefore, if my assumption is reasonable – that all imperatives limit teachers’

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professional judgment – Table 22 suggests that CMP is the most speaking to TG and Pearson
is the most speaking through one.
Table 22 by itself does not present enough information about the degree of teachers’
professional judgment acknowledged by the TGs. This is so because the number counts or the
ratio is not a direct reflection of degree of obligation imposed on teachers. Rotman (1988)
distinguished imperatives as exclusive or inclusive. Exclusive imperatives strongly impose
duties on the readers. Inclusive imperatives acknowledge the judgment the readers have.
Therefore, understanding which types of imperatives are dominant in which TG is important.
In the following, I show that exclusive imperatives dominated inclusive ones in all four TGs.
To understand the type of imperatives each TG is using, I analyzed the kinds of
imperatives. Ninety-seven imperative verbs appeared in at least one of the four TGs. UCSMP
used 32 imperative verbs. Pearson used 45, CMP used 38, and Eureka used 48. Not all
imperative verbs appeared with similar frequency. Table 23 presents the range, mean, median
and mode of the imperatives.
Table 23. Range, Mean, Median, Mode of the Frequency of Imperative Incidences

Range
Mean
Median
Mode

UCSMP
39
4.28
2
1

Pearson
53
4.85
1
1

CMP
5
1.9
1
1

Eureka
21
2.38
1
1

As Table 23 above shows, the common feature across the four TGs is that they used
most of the imperatives once or twice. In UCSMP, the two most-used imperatives were have
(39 x) and ask (35 x). Excluding those two, the frequency range becomes 9, which indicates a
relatively low frequency of the 37 imperatives. In Pearson, use (53 x) and have (46 x) were
the two most dominant imperatives; without those two, the frequency range becomes 19.
Sentences in CMP used ask (5 x) and tell (5 x); again, not counting those two imperatives, the

92

frequency range is 3. Eureka used have (21 x) and ask (17 x) the most; not counting those
two, the frequency range is 5. Overall the four TGs, the three most-used imperatives are have
(107 x), ask (67 x) and use (60 x); excluding those three, the range is 19. Imperatives such as
have, ask, use, and tell all direct teachers to perform such action, hence exclusive. This
results shows that all TGs used more exclusive imperatives than inclusive ones. Therefore,
the numbers and ratios I present in Table 22 is a reflection of the degree of obligation each
TG is imposing on teachers.
Conclusion from the Three Results
In the subsections on pronouns, I argued that all pronoun use can be interpreted as
cases of speaking to, based on my improvisation of Remillard’s (2000) original definition. I
showed that the use of assertive modality and imperatives are the cases of speaking through.
In Table 24, I presented results combining the findings from pronoun, modality, and
imperative. Based on the combined results, I discussed the degree of obligation imposed on
teachers from each TG.
Table 24. Aggregated Table

Total Sentences with a
Pronoun Referring to Teachers
Suggestive
Modality
Assertive
Imperatives
Pronouns Referring to
Teachers per IDT
Suggestive per IDT
Assertive & Imperatives per
IDT
Suggestive per page
Assertive & Imperatives per
page
IDT per page

UCSMP

Pearson

CMP

Eureka

68

17

45

13

31
37
137

1
16
223

30
15
38

4
9
114

0.33

0.07

0.54

0.10

0.15

0.00

0.36

0.08

0.85

1.00

0.64

0.97

0.63

0.01

1.5

0.08

3.55

2.91

2.65

2.56

4.18

2.93

4.15

2.65

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Considering the ratio of assertive voice and imperatives combined to the incidences
directed at teachers shows that Pearson always use language with high obligation of duties
(1.00). Eureka is second-highest at 0.97. CMP is lowest at 0.64. That order matches the IDT
ratio for pronoun use. Based on numbers in the table, UCSMP and CMP actively
communicate with teachers (IDT per page), being more open than directive than the other
two. Accordingly, the degree of obligation to follow the TGs suggestions is higher in Pearson
and Eureka than in UCSMP and CMP. From this aggregated result, I suggest that CMP and
UCSMP are closer to the speaking to end of the spectrum while Pearson and Eureka are
closer to the speaking through end, due to the different level of teacher professional
judgement each TG is allowing. Yet, the per-page ratios show that teachers are likely to read
sentences limiting their use of professional judgment more often than the sentences
acknowledging it.

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CHAPTER 5: DISCUSSION
In this chapter, I first revisit each of the three research questions in order to locate my
findings in the literature. Then, in the section titled Looking Backward, I discuss what I
learned from conducting and writing this dissertation study. I ended this chapter with the
section Looking Forward to offer suggestions for practitioners and researchers.
Returning to the Research Questions
Research Question 1
Narrow list of positionings. In the Results chapter, I addressed RQ1 in four ways: i)
by comparing the list of positionings to the literature; ii) by presenting positionings
commonly observed across the four TGs; iii) by examining positionings revisited in more
than three phases for each TG; and iv) by drawing attention to varied degrees of support.
Following the classification by Ball, Thames, and Phelps (2008), I found that TGs
regularly presented three subdomains of what teaching mathematics entails: i) common
content knowledge, ii) specialized content knowledge, and iii) knowledge of content and
curriculum. Three TGs – UCSMP, Pearson, and CMP – regularly addressed knowledge of
content and teaching. This subdomain was present in Eureka, although idiosyncratically.
Knowledge of content and students was regularly attended in Pearson; the other three TGs
did it idiosyncratically. No TG suggested horizontal knowledge as what teachers should
know, although UCSMP and Pearson explained the place of the algebra curriculum within
the context of secondary-school mathematics curriculum. This shows that each TG
constructed teaching mathematics as entailing more than common content knowledge.
Instead, mathematics teachers are asked to have knowledge in multiple subdomains.
The literature about knowledge base emphasized that knowledge required for teaching
is well beyond common content knowledge (Shulman, 1986;1987) and that making visible
various subdomains of knowledge contributes to understanding teaching as a full profession

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(Ball, Thames, & Phelps, 2008). Considering this, having TGs pay attention to multiple
subdomains is to be welcomed and encouraged. My findings suggest that while the research
field’s effort to redefine subdomains (e.g., Speer, King, & Howell, 2014; Tatto et al., 2008)
are important contributions, the field also needs to examine the praxis of the subdomains.
Curriculum materials, including TGs, are powerful sources with the potential to bring largescale difference at the classroom-instruction level (Stein & Kim, 2009). More literature on
using multiple knowledge bases as a design principle for TGs not only could contribute to
enhancing the practicality of the subdomains, but also could support development of
teachers’ sense of professional self through developing their knowledge. This becomes even
more significant to the teachers who had primarily learned mathematics procedurally. TG
could provide opportunities for those teachers to develop a broader range of understanding of
mathematics.
Comparison of the list of positionings to the other five aspects from the literature
suggests that TGs could diversify their construction of teaching mathematics. Regarding
teacher research, its most visible feature was, at the end of a lesson or a chapter and focused
on collecting data from students about their learning. Teacher research was addressed in all
four TGs with three or four positionings. This is encouraging because of the importance of
teacher research (Cochran-Smith & Lytle, 2006). In addition, in all TGs the data collection is
constructed as what could be done with verbal interaction or activities, in addition to a more
traditional way of handing a set of mathematical tasks. UCSMP and CMP went a step further,
inviting teachers to make notes in the TG. Yet in all TGs it is unclear how teachers might
utilize data they collect. Further, data collection happens mostly at the end of a lesson or
chapter. Teachers can conduct a teacher research through written assessment as well as
journaling, writing essays, oral inquiries, and classroom studies (Cochran-Smith & Lytle,
1990). Literature emphasized the importance of teacher research because teachers such a

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process can enhance their understanding of the local context in which they are teaching.
Considering that curriculum authors design their TGs to a wider audience than [who?],
teacher research is an important professional skill for teachers to render the lessons relevant
to their students. My finding suggests that despite the importance of teacher research
(Cochran-Smith & Lytle, 1990; Cochran-Smith & Lytle, 2006; Sales, Traver, & García,
2011), the TGs rarely presented sufficient support for teachers on this matter.
Results from my analysis on the aspects of interaction with colleagues and utilizing
knowledge supports the aforementioned point. UCSMP was the only TG to address this
aspect, although by no means extensively. From my review of literature about colleagueship,
I found the research mostly to be done with a focus on teachers’ spoken interactions (Crespo,
2006; Males, Otten, & Herbel-Eisenmann, 2010; L. Shulman & J. Shulman, 2004). Lack of
attention to interaction with colleagues in TGs might indicate the need for closer
investigation in the research field regarding the colleagueship built between teachers who
contributed in the writing of a TG and teachers who are reading the TG.
Pearson and CMP were the TGs that addressed utilizing students’ knowledge. Again,
those two TGs could have made explicit what it would mean to utilize the knowledge
students bring in. The literature has discussed ethical reasons with practical suggestions and
evidence of effectiveness of utilizing students’ knowledge (Aguirre et al., 2013; Civil &
Andrade, 2002; Gutiérrez, 2002; Ladson-Billings, 1998; Turner, Domínguez, Empson, &
Maldonado, 2013). Given this, curriculum authors need to add into their curriculum practical
suggestions for teachers to utilize the knowledge emergent bilingual students bring in.
As to acknowledging uncertainty, TGs emphasized that uncertainty derives from
pedagogical situations more than from other types of uncertainty. Except for CMP, all TGs
regularly addressed pedagogical uncertainty (Meister & Nolan, 2001; Midthassel, 2006;
Wheatley, 2002; 2005). Yet, similar to the two aspects above, TGs could have introduced

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various other aspects of uncertainty, including, for example, those derived from mathematics
itself and student traits or school culture (Friedman, 1997; Labaree, 2003; Roeser, Skinner,
Beers, & Jennings, 2012; Villaume, 2000). Moreover, TGs could go a step deeper to present
how teachers proactively could use situations with uncertainty as opportunities to refine their
practice. Curriculum materials of quality help teachers build knowledge, both specific to the
scene of instruction, and general enough to be applied to multiple situations (Davis &
Krajcik, 2005). Making uncertainty visible, the TGs can achieve the latter.
Commonly-observed positionings. I selected four TGs with consideration of varied
design approach. Despite their differences, I identified seven positionings observable in all
four. The positionings were attending to general information (e.g., available supplementary
resources, and numbers of days to cover portions of the curriculum), specifics of the content
(e.g., vocabulary, supplementary information to implement a task, and answers to the tasks
and questions), and assessment (e.g., questions, activities, or tasks to assess students’
learning) of each TG. Given the literature’s suggestion that curriculum materials can impact
classroom practice on a large scale (Ball & Cohen, 1996; Collopy, 2003; Stein & Kim, 2009),
these seven positionings likely would be valuable in shedding light on what teacher
positionings the curriculum materials have reinforced and/or have neglected, regardless
enormous effort and time spent to raise awareness of the positionings.
Pervasive positionings from each TG. With the positionings I observed, I sorted
those, which occurred regularly from more than three phases of each TG. Notable from this
examination is that in all TGs, the positioning that teachers have a duty to know answers to
the tasks/questions (not solution strategies) was pervasive. In addition, except for Eureka, the
positioning that teachers have a duty to know supplementary information to implement a task
was observable from at least three phases of the TGs. In the Results chapter, I interpreted this
as a possible widespread narrow understanding of teaching mathematics: teaching

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mathematics is about solving tasks to find correct answers. In addition to these two
positionings, UCSMP positioned teachers as having a duty to know supplementary
information to make accommodations. This positioning was pervasive in Pearson also.
Pearson had eight pervasive positionings. Teachers using Pearson are exposed consistently to
a number of positionings yet, in some cases, communication actions associated with a
positioning were inconsistent across different phases. I question whether implementing a task
and knowing the correct answer are the only aspects the authors would want to emphasize. If
this is not the case, authors might want to consider the positionings they wish to emphasize,
then seed those in relevant phases because being frequently exposed to a positioning could
cause teachers to assume the positioning is important (Rindfleisch & Inman, 1998).
Degree of support. When a positioning is observable in TGs, this means that teacher
readers have an opportunity to engage with the aspect of teaching addressed by the
positioning. Whether a teacher enacts it, however, is that teachers’ decision. Yet, if TGs do
not provide enough support for teachers, they might refute the positioning in their practice,
not because they disagree with it but because they do not know to try it in their classroom. In
the Results chapter, I presented subtle differences within three positionings across TGs in
terms of the level of support. Examination of the level of support requires careful inspection
of communication actions associated with a positioning from each TG. The varied degree of
support appears in all TGs, meaning that no TG always provides limited or ample support.
Although I did not conduct such analyses, this is a topic worth examining because the degree
of support of a positioning could positively impact the likelihood of teachers’ enactment of
the positioning. In addition, because prospective teachers are more likely to follow the
suggestions from curriculum materials (Drake, Land, & Tyminski, 2014), providing
sufficient support to the positionings deemed important could encourage teachers at an earlier
stage to develop productive sense of professional self.

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Summary. Attending to regular positionings, I found that all TGs construct teaching
mathematics as more than having mathematical knowledge. Still, the construction could be
refined by attending to other aspects (i.e., teacher research, interaction between colleagues,
utilizing knowledge, and acknowledging uncertainty) with higher frequency and deeper
connection. In addition, TGs might have been reflecting and strengthening the construction of
teaching mathematics as solving tasks with correct answers. The four TGs showed
differences across the areas I examined. There is, however, neither consistency nor patterns
in the differences. In other words, no TG was superior or inferior to any other in many areas.
This indicates that at least the selected TGs are considering numerous aspects as to what
teaching mathematics entails, but not widely or deeply enough regarding the five aspects I
reviewed from the literature. Curriculum authors might want to evaluate the positionings they
use based on their ideally constructed model of teaching mathematics, and use such an
evaluation to decide on the kinds and levels of supports they wish to provide in their TGs.
Research Question 2
Examining the second research question, which attended to idiosyncratic positionings,
I found two types of idiosyncratically occurring positionings, namely idiosyncratic-only type
and idiosyncratic-regular type. I again grouped the idiosyncratic-regular type positionings
into two: those with consistency of contexts across regular and idiosyncratic occurrences, and
those without consistency of contexts.
Idiosyncratic-only type. Pearson had no idiosyncratic-only type of positionings.
Most positionings of this type in UCSMP were about students and appeared in the MiLe
phase. CMP idiosyncratically presented anticipating student strategy as to what teaching
mathematics entails. Eureka had as many as seven idiosyncratic-only type positionings.
Among those, two positionings seemed to better support teachers when provided regularly
rather than idiosyncratically. For example, teachers might benefit more from reading a

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general description of mathematical contents of a lesson in each lesson, not in some selected
lesson. All the idiosyncratic-only type positionings I identified appeared in one or two phases
of the TGs, except one positioning in CMP that appeared in three different phases. This
suggests that teachers are likely to have low exposure to the idiosyncratic-only type
positionings due to their idiosyncratic and infrequent occurrence. Considering that repetition
can thicken a positioning (Gresalfi, 2009; Polman & Miller, 2010), curriculum authors need
to be careful not to have the positionings they deem as important to be that of idiosyncraticonly type.
Idiosyncratic-regular. Idiosyncratic-regular type positionings with coherency in the
contexts are these: i) teachers have a duty to know CCSS MP relevant to the content of the
TG; ii) teachers have a duty to know relevant CCSS content standards at the chapter/lesson
level; iii) teachers have a duty to know what hardcopy resources and/or materials are
needed; and iv) teachers have a duty to know tasks/projects that overarch a chapter. These
positionings are revisited multiple times, both regularly and idiosyncratically, within the
same context. The positionings with no coherency in the contexts are as follows: i) teachers
have a duty to know what electronic resources are needed (CMP); ii) teachers have a duty to
know supplementary information to make accommodations (Pearson); iii) teachers have a
duty to know questions to ask (CMP); iv) teachers have a duty to know answers to
tasks/questions (CMP; Eureka); v) teachers have a duty to know potential student errors
(Pearson); vi) teachers have a duty to know how the curriculum contributes to students’
college and career readiness (Pearson); vii) teachers have a duty to know mathematics for
pedagogical purposes (UCSMP; Pearson); and viii) teachers have a duty to know
supplementary information to implement a task (Pearson; Eureka). The TGs presented these
positionings both regularly and irregularly in multiple contexts. Literature suggests that
repeated exposure to a positioning affects teachers’ sense of professional self, and that the

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multiplicity of contexts increases the strengths of influence (Baker, 2006; Gresalfi, 2009;
Hansson, 2015; Parks, 2010; Parks & Wager, 2015). That is, idiosyncratic-regular type
positionings with disconnected contexts could be most powerful among different types of
positionings. When choosing among the four selected TGs, teachers might want to consider if
the positionings listed above are those that align with their sense of professional self.
Similarly, curriculum authors intentionally can place the positionings they deem important
both regularly and idiosyncratically, drawing on multiple contexts.
I do not have access to the authors’ intentions for choosing some positionings to be
regular and others idiosyncratic. I even wonder if those choices were more unintentional than
carefully designed, as many language choices tend to be. Yet the substance of idiosyncratic
positionings cannot to be disregarded, because communication actions associated with the
idiosyncratic positionings are crafted enough that the actions well address specifics of the
TGs’ contents. Contrarily, not all general positionings provide supports with high specificity.
In some cases, communication actions are identical across lessons or chapters, suggesting
that texts regularly are cut and pasted into multiple places in the TG. In addition to the
specificity of the support, to be idiosyncratic a positioning means the authors provided it even
when it is not required. The positioning is there because the author wanted to provide such
support to teacher readers. A regularly occurring positioning, however, because of its
regularity, has to appear at a certain part of the TG, even when there is no support to provide.
For example, CMP has the heading Vocabulary at the beginning of each lesson. Some lessons
listed vocabularies but some other lessons said there is no vocabulary to introduce. An
examination of idiosyncratically occurring positionings showed that idiosyncrasy supports
teachers by suggesting a positioning when it is highly relevant. Regularity of a positioning
guarantees stable support from the TG to the positioning. Irregularity of a positioning
provides focused support addressing specific parts of the TG. As I discussed in chapter 2,

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well-designed curricula provide teachers with both specific and general support for teaching
(Davis & Krajcik, 2005). By carefully designing which positionings to provide regularly or
idiosyncratically, curriculum authors can maximize teacher-readers’ opportunity to learn
from curricula materials.
Research Question 3
To answer the third research question, which focused on teacher professional
judgment as acknowledged by each TG, I examined sentences directed at teachers. Among
these sentences, I analyzed those with pronouns to examine TGs’ use of pronoun and
modality. Then, I analyzed the rest of the sentences (i.e., sentences without pronouns) to
examine TGs’ use of imperatives. When analyzing the sentences, I drew on the notion of
speaking to and speaking through (2011). Curriculum materials speak through teachers when
they guide teachers’ actions, offer steps to follow, and give pre-designed questions to ask
students. Materials speak to teachers when they give rationales, assumptions, or agendas
supporting them. What I see to be central from this work is acknowledgement of teachers’
professional judgment by making explicit the presence of teacher-readers. I attended to this
particular aspect of speaking through versus speaking to dichotomy, instead of following the
original. By focusing on uses of pronoun, modality, and imperatives, I sought to understand
the space available for teachers to enact their professional judgment.
Analysis suggests that, in general, the voices of UCSMP and CMP acknowledged
teacher presence and their professional judgment more than did the voices of Pearson and
Eureka. In other words, UCSMP and CMP spoke more to teachers than did Pearson and
Eureka. In pronoun use, all but two were referring to teachers across the four TGs, either
explicitly or implied. The two pronouns not referring to teachers were from UCSMP,
referring to authors. Although these two incidences did not include teachers, by making
explicit the UCSMP author’s intentions, in fact, were speaking to teachers. For the purpose of

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cross-TG comparison, I calculated two ratios: i) pronouns referring to teachers divided by
total incidences directed at teachers (IDT), and ii) by total pages. Both ratios showed the
same result that CMP is the TG that most-proactively used pronouns (0.54 and 2.25,
respectively), followed by UCSMP (0.33 and 1.39), Eureka (0.10 and 0.27), and Pearson
(0.07 and 0.21), Eureka and Pearson being close to each other. Although Morgan (1998)
argued that the use of first-person pronouns of I and we could broaden the distance between
the authors and the readers, my analysis showed that the first-person pronouns contributed to
the acknowledgement of teachers’ professional judgment. In particular, the pronoun we in a
mathematical textbook places the author as an authority of mathematics or assumes
agreement from the readers (Herbel-Eisenmann, 2007; Rowland, 1999), but this was not the
case with the TGs.
To understand TGs’ use of modality, I reexamined the sentences with pronouns. To
understand the degree of obligation each TG was imposing on teachers, I classified the
modalities and bald assertions as either suggestive or assertive. The result from the analysis
supported that UCSMP and CMP spoke to teachers by using less assertive voice than that of
the other two TGs. Regarding the ratio with IDT, CMP used twice-more suggestive
modalities than assertive (0.36 and 0.18, respectively). UCSMP used more assertive voices
than suggestive (0.18 and 0.15, respectively). The gap between suggestive modalities per IDT
and assertive voice per IDT was smaller in Pearson (0.00 and 0.07, respectively) and Eureka
(0.03 and 0.07, respectively) than in UCSMP and CMP, but this was because of the
generally-low count in sentences with pronouns in Pearson and Eureka. CMP is the only TG
with higher use of suggestive modalities than of assertive voice. Regarding ratio per page,
CMP is still the only TG with higher use of suggestive modalities than assertive voice (1.5
and 0.75, respectively). In UCSMP more assertive voice was observed than suggestive
modalities (0.76 and 0.63, respectively) and Eureka (0.19 and 0.08, respectively). Pearson’s

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use of assertive voice is twentyfold more than suggestive modalities (0.20 and 0.01,
respectively). The high frequency of assertive voice to suggestive modalities is not to be
overlooked. This is so because I conservatively defined assertive voice by grouping median
modalities together with low modalities (Halliday & Matthiessen, 2014). Despite the
conservative grouping, the result shows that three of the four TGs used assertive voice more
often than suggestive modalities. Assertive voice could potentially restrict teacher-readers’
enacting their professional judgment by suggesting that the content of the TG was true and
not up for negotiation (see Herbel-Eisenmann, Kristmanson, & Wagner, 2011).
For analysis of the use of imperatives, I focused on the sentences without pronouns.
From the use of imperatives, I confirmed that CMP most proactively acknowledged teachers’
professional judgment. Results for UCSMP, Pearson and Eureka, on the other hand, were
mixed. Frequent use of imperatives itself might not be sufficiently-strong evidence to show
whether the TG is speaking to or speaking through teachers. This was so because although
those sentences did not use pronouns, some imperatives, such as consider, are inclusive. The
pattern I observed in all four TGs, however, showed that exclusive imperatives such as have,
ask, and use were more dominant than inclusive imperatives. Accordingly, more use of
imperatives suggested a higher degree of speaking through teachers. Compared to IDT, CMP
was the lowest in its use of imperatives (0.46), followed by UCSMP (0.67), Eureka (0.88),
and Pearson (0.93). In its use per page, CMP was the lowest (1.90), then Eureka (2.38),
Pearson (2.72), and UCSMP (2.80). If the use of exclusive imperatives places authority on
the authors only (Martin & Rose, 2007; Rotman, 1988), this frequent use of imperatives in
the TGs implied low authority placed on the teacher-readers, hence limited opportunity for
teachers to practice their professional judgment.
Comparing the use of suggestive modality versus the use of assertive voice and
imperatives combined, CMP had the highest rate of incidences with suggestive voice (0.36

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for suggestive and 0.64 for assertive or imperatives), followed by UCSMP (0.15 and 0.85,
respectively), Eureka (0.03 and 0.97, respectively), and Pearson (0.00 and 1.00, respectively).
This combined result with the other results discussed until now (i.e., examination of voice
with TGs’ use of pronoun, modality, and imperative) support that, in general, the voice of
UCSMP and CMP were more open than the other TGs. In other words, these TGs
acknowledge teacher professional judgment more pervasively than do the other two. Such use
of language indicates that when compared to Pearson and Eureka, UCSMP and CMP were
closer to the speaking to side of the spectrum than to the speaking through side. Attending to
the high IDT per page ratio of CMP and UCSMP, an interesting topic for future study might
be examining the relationship between talkativeness of a TG and the tendency of speaking
to/through.
All in all, I found no extreme differences across TGs in their construction of what
teaching mathematics entails. Subtle differences existed, but, in general, they place at the
center solving mathematical tasks. Regarding less-conventional positionings, such as that
about making notes from UCSMP and CMP or supporting emergent bilingual students from
Pearson and CMP, TGs could have provided more support in their communication actions
than they now do. The voice TGs use differs. UCSMP and CMP consistently invite teachers
to use their professional judgment. In other words, these two TGs acknowledge that teachers
could choose to refute positionings imposed on them by the TG based on their knowledge
and experience.
Looking Backward
In writing this dissertation, I learned several things about conducting research. First, I
learned to find proper grounding of the study. Initially when searching the literature I was
hoping to find laid-out, essential knowledge or central practices all teachers – either in
mathematics or in general – should have. In such literature, I hoped for an initial list of

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positionings I could or should expect from the TGs. Unexpectedly, though, my literature
search led me to explore a much broader range of topics than I originally had expected and,
although different from my expectation, nonetheless provided my groundings.
In addition, I had the opportunity to develop deeper understanding of positioning
theory. In this dissertation, I used that theory to examine the moment when TGs were being
read. My reading of the literature on positioning theory indicated that more research has been
done on spoken interaction than on written interaction. Exploration of rights and duties, the
terms frequently used to define positioning, also led me to a more-precise understanding of
the theory than before.
Regarding data, I have learned to find the balance between the amount of data and the
amount of detail for the analysis. Because I wanted to compare the four TGs, I had to
maintain a certain generosity to make the comparison possible. Because of the vastness of
data, I had to choose to attend to the headings rather than to every minute detail in the texts
below those headings. Were the focus of the study narrower than it now is, I could have
provided results with denser description and lesser data. But from the data analysis process, I
learned to make decisions so that the results best could address the research questions.
Looking Forward
Implications for Curriculum Authors
Each TG provides similar yet different sets of positionings with which teachers could
engage. When curriculum authors decide the content to include, they might first seriously
consider beginning the TG writing process with generating a list of positionings they wish
teachers to take up. In doing so, one productive approach is to make explicit the storylines
they want to enact or the values and the beliefs they have about teachers – their primary
audience for TGs. The list itself and the comparison of the list to their storylines and beliefs
could inspire the authors during the curriculum design and writing, including what headings

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to use and what content to present at which phases. For example, authors might decide to
consistently present tips for supporting emergent bilingual students in MiLe so that teachers
are repeatedly positioned to address emergent bilingual student needs via TG supports closely
connected to classroom interaction. Alternatively, authors could decide to provide general
support via tips in IntCh or IntLe. In addition, this study’s results showed that some
positionings have a strong presence by being addressed in multiple phases. To go a step
further, authors could make the positioning more visible by assigning a heading pinpointing
the positioning. By carefully attending to their desired positionings, authors efficiently can
use curriculum space to convey content they want, to control that content’s visibility, and to
position teachers in the ways they hope to do. Curriculum authors might consider using
pronoun, modality, and imperatives as tools for regulating the voice of the TG. By using
more suggestive modalities, fewer imperatives, and pronouns making visible their presence
(i.e., the authors’), they can speak to teachers.
Implications for Teachers and Teacher Educators
This study’s findings suggest to teachers that they could consider teacher positionings
as factors to consider when choosing a curriculum. If positionings embedded in the
curriculum rarely align with the teacher’s sense of professional self, it could be wise not to
pick that curriculum because the curriculum does not offer the kind of information the
teacher considers to be relevant to her teaching. A teacher who are interested in expanding
her perspective on teaching might benefit from the extreme mismatch between the
positionings suggested by a curriculum and a teacher’s sense of professional self. This,
however, is not the case when the teacher is looking for a material that she could rely on to
save planning time. From the very construct of positioning theory, and from my deliberate
choice of “teachers have a duty to know” statement, instead of “teachers have a duty to do”

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or “teachers have a duty to enact,” I wanted to stress that teachers can decide to accept or
reject the positioning the TG is imposing.
Teachers fully could reject the positioning by ignoring texts conveying that
positioning. Alternatively, teachers have the option to accept the positioning only partially,
by modifications when enacting the curriculum. If, however, a TG with more positionings for
teachers to accept than reject or make modifications, this might indicate that the TG has more
information useful to their teaching context than the TGs with positionings that do not align
with their self-positioning. Teacher educators could design an activity for teachers to
recognize the positionings suggested by TGs. In addition to recognizing the kinds of
positionings, attending to the voice of the TG could permit teachers to see the degree of
obligation the TGs are imposing on them.
I hope teachers can raise awareness of the limitations of positionings in the TGs, can
proactively demystify embedded positionings, and can refute positionings with which they
cannot agree based on their own experiences as teachers. Women’s voices too often have
been regarded as less than a full opinion. Considering that teaching is a female-dominant
occupation, teachers’ active and critical engagement in discussion of teacher positionings is
important in ensuring their voice is heard and that their professionalism is acknowledged by
others including curriculum authors. Teacher educators might support teachers by
encouraging their participation in the discussion space of teacher positionings.
Implications for Future Research
Several ideas for future research were discussed earlier in this dissertation. First, the
field could benefit from much closer examination of some of the positionings provided in this
study. Because this study looked at seven phases from four TGs, the observations could not
be too specific. Additional examination of a phase or a positioning across the TGs could
result in a much more nuanced understanding of this matter, in particular with the degree of

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support TGs provide for teachers to act out the positioning. The positioning that teachers
have a duty to know supplementary information to implement a task is an example of such
case. I had to use language as vague as supplementary information because the kind of
support provided in that part of the text was inconsistent – possible student errors, possible
strategies, factual information of the real-world context of the task, mathematical knowledge
from previous lessons, ways to support visual learners, etcetera. The range of information
covered varies across the TGs. For example, from chapters examined for this study, Pearson
did not elaborate on the factual information of the real-world context but UCSMP did. What
this study can tell is that, at least from the four selected TGs, it is challenging to pinpoint the
major duty involved in task-implementation, besides that teachers have a duty to know the
answer to the task. Considering that this positioning is observed regularly from three phases
of UCSMP, four of Pearson, four of CMP, and one of Eureka, supplementary information
could be unpacked based on much more careful examination of this positioning in and of
itself. Another example is the positioning of knowing vocabulary: such positioning was
observable from the four selected TGs, with varying level of support, as scarce as simply
asking teachers to have students review the vocabulary, or as sufficient as providing
suggestions on each vocabulary how teachers could introduce it to students. For example,
TGs could ask teachers to assign students a community-based research project about
mathematical terminologies (Staats, 2009). This level of specificity was not addressed in this
study, as it is outside the scope of this dissertation. Investigations at a smaller grain size than
that of this study will result in insightful findings and discussions.
Another area for further research concerns TG features. Increasingly, scholars are
paying attention to visual images in mathematics (Lemke, 2003; 2017; O'Halloran, 2003;
2005). Examining visual images is as important as examining language use in mathematics
because meaning emerges also from visual images, both mathematical and in everyday

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contexts. Not only visual images, but also layout designs might impact differently on the
degree of emphasis of positionings. Related to layout, a possible extension of this study is
analyzing electronic versions of TGs. In this dissertation, I used three hardcopy TGs and one
electronic TG formatted as print-ready. Becoming more popular are electronic versions of
curriculum materials with features ranging from as close to printed materials as pdf files, to
as far from printed materials as interactive links or embedded videos. This has possible
complications, in that features available only on electronic versions might bring teacher
positionings difficult to observe from printed materials.
Last, I want to suggest examining teachers’ engagement with their TGs. The
motivation of this study was that of respecting teachers’ professional judgement. As a teacher
education researcher, I often heard prospective and practicing teachers be receptive to
external positionings that see teaching as, at most, a non-profession or a para-profession. I
expect the perspective and analysis from this study to encourage teachers with
acknowledging teaching as a full profession and advocating such status of teaching. Casting
alternative storylines might be an effective strategy, as positioning theory suggests.
Therefore, a possible extension of this study is: When teachers engage with TGs, what
positionings do teachers accept and refute and under which storylines?

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APPENDICES

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APPENDIX A
LIST OF THE REGULARLLY APPEARING HEADINGS
Table 25. Headings Examined from the Phase of IntTG
Phase
IntTG

UCSMP
• UCSMP
Program
Organization
4 UCSMP
Program
Overview
4 Teaching
Modes and
Strategies
([Suggestions
from teachers];
An Articulated
Curriculum
Across All
Grades)
4 UCSMP
Research
Results
4 UCSMP
INSTRUCTIO
NAL
PLANNING
AND
SUPPORT
(Hardcover
Student
Edition;
Teachers’
Edition)

Pearson
CMP
Eureka
• A New Way to
• [Not Applicable] • Pacing and
Experience Math
Preparation
Guide
• Problem Solving
• Preparing to
• Solving Rich
Teach a Module
Problems
•
Preparing to
• Visual Learning
Teach a Lesson
• Big Ideas
• Interactive
Learning
• Differentiated
Instruction
• Assessment
• Big Ideas and the
Common Core
• Efficacy
Research
• Standards for
Mathematical
Practice
• Pearson Algebra
1 Common Core
• What is STEM
Education?
• College and
Career Readiness
• Teaching
Resources
• Common Core
State Standards
for Mathematical
Content
• Algebra 1 Pacing
Guide

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Table 26. Headings Examined from the Phase of IntCh
Phase
IntCh

UCSMP
Pearson
CMP
Eureka
• Chapter #
• Get Ready!
• Unit Planning
• Module #
overview
4 [the table
4 Unit
4 OVERVIEW
4 Chapter
with lesson
Overview
4 Focus
Overview
and skill]
(Unit
Standards
4 Differentiated
4 Why Students
Description;
4 Foundational
Options
Need These
Summary of
Standards
4 Objectives
Skills
Investigation
4 Focus
4 Technology
4 Looking
s; Unit
Standards for
Resources
Ahead
Vocabulary;
Mathematical
4 Chapter
Vocabulary
Planning
Practice
Resource
Charts;
4 Terminology
• Chapter #
Masters
Block
(New or
Overview
Pacing;
Recently
4 BIG idea
• Chapter # opener
Parent
Introduced
4 Pacing
4 Content
Letter; Goals
Terms;
4 Chapter #
Standards
and
Familiar
Projects
4 Overview of
Standards)
Terms and
4 Chapter #
the
Symbols
Overview
Performance • Mathematics
4 Suggested
4 Notes
Task
Background
Tools and
4 Introducing
• Unit
Representatithe
Introduction
ons
Performance
4 Using the
4 Preparing to
Task
Unit Opener
Teach a
4 PARCC
4 Using the
Module
CLAIMS
Mathematic4
Preparing to
4 SBAC
al Highlights
Teach a
CLAIMS
• Investigation
Lesson
• PowerAlgebra.co
Overview
4 Assessment
m
4 Investigation
Summary
• Chapter# Math
Description
•
Topic
@
Background
4 Investigation
4
Focus
4 Math concept
Vocabulary
Standards
(BIG idea;
4 Mathematics
4 Instructional
ESSENTIAL
Background
Days
UNDERST4 Planning
4 [A
ANDING;
Chart
description]
Common
4 Goals and
Errors With
Standards
[Math
(Goals;
Concept];
Common
Mathematical
Core Content
Practices)
Standards;
Facilitating
• Pacing and
the
Assignment
MathematicGuide
al Practices)
• Resources
114

Table 27. Headings Examined from the Phase of IntLe
Phase
IntLe

UCSMP
Pearson
CMP
Eureka
• GOAL
• #-# Preparing to • Problem
• Student
Teach
Overview
Outcomes
• SPUR Objects
4
BIG
idea
4
Focus
• Materials/Resour
4 ESSENTIAL
Question
ces
UNDERSTA
4 Problem
• HOMEWORK
NDINGS
Description
• Local Standards
4
Math
4
Problem
• Background
Background
Implementat4 Mathematical
ion
Practice
(Materials)
4 Vocabulary
4 Mathematics
Background
4 At a Glance
Lesson Plan

Table 28. Headings Examined from the Phase of BeLe
Phase
BeLe

UCSMP
• 1 Warm-Up

Pearson
CMP
• 1 Interactive
• Launch
Learning
4 Connecting
4 Solve It!
to Prior
(PURPOSE;
Knowledge
PROCESS;
4 Presenting
FACILITAthe
TE;
Challenge
ANSWER;
CONNECT
THE MATH)
• PowerAlgebra.co
m

115

Eureka
• [Not applicable]

Table 29. Headings Examined from the Phase of MiLe
Phase
MiLe

UCSMP
Pearson
CMP
Eureka
• 2 Teaching
• 2 Guided
• Explore
• Classwork
4 Notes on the
Instruction
4 Providing for
(Example/Exerci
Lesson/Activ
4 Problem #
Individual
se)
ity
4 Got It?
Needs
4 Additional
4 Additional
4 Planning for
Examples
Problems
the Summary
4 Accommoda- • PowerAlgebra.co
ting the
m
Learner

116

Table 30. Headings Examined from the Phase of EnLe
Phase
EnLe

UCSMP
Pearson
CMP
• 3 Assignment
• 3 Lesson Check • Summarize
4 Recommende
4 Do you
4 Orchestrating
d Assignment
Know HOW?
the
4 Notes on the
4 Do you
Discussion
Questions
UNDERST(Suggested
AND?
Questions)
• 4 Wrap-Up
4 Close
4 Reflecting on
4 Ongoing
Student
Assessment
• 4 Practice
Learning
4 ASSIGNME
4 ACE
NT GUIDE
Assignment
4 Mathematical
Guide
Practices
4 Applications
4 EXERCISE #
4 HOMEWORK QUICK
CHECK
• #-# Lesson
Resources
4 Additional
Instructional
Support
(Algebra 1
Companion;
ELL Support;
4 5 Assess &
Remediate
(Lesson Quiz;
PRESCRIPTION FOR
REMEDIATION)
4 Differentiated
Remediation
• PowerAlgebra.co
m

117

Eureka
• Closing
• Exit Ticket
• Exit Ticket
Sample Solutions
• Problem Set
Sample Solutions

Table 31. Headings Examined from the Phase of EnCh
Phase
EnCh

UCSMP
• Projects
4 Project
Rubric
4 [a table
presenting
Project # and
associated
lesson #]
4 [# Project
Title]
4 Notes
• Summary and
Vocabulary
• Chapter # SelfTest
• Chapter #
Review
4 Chapter
Review
4 Resources
4 Technology
Resources
4 Assessment
(Evaluation;
Feedback)

Pearson
CMP
• # Pull It All
• Mathematics
Together
Reflections
(Completing the
4 Possible
Performance
Answers to
Task;
Mathematic[Questions];
al
FOSTERING
Reflections
MATHEMATI4 Possible
CAL
Answers to
DISCOURSE;
MathematicANSWERS; On
al Practices
Your Own)
Reflections
• # Chapter
Review
4 Essential
Questions
(BIG idea;
ESSENTIAL
QUESTION)
4 Summative
Questions
• Chapter Test
• Common Core
Cumulative
Standards
Review
• PowerAlgebra.co
m

118

Eureka
• Mid-Module
Assessment Task
4 [the tasks]
4 A
Progression
Toward
Mastery
4 [answer to
the tasks]
• End-of-Module
Assessment Task

APPENDIX B
TABLES OF REGULAR AND IDIOSYNCRATIC POSITIONINGS
The observed positionings presented below are grouped into eight topics: Standards
and goals, resources, accommodation, tasks, assessment, general information: features and
structures of the TG, general information: mathematics, and additional features. This
grouping is for the purpose of breaking the results into smaller pieces to avoid bulkiness.
That is, the grouping should not be understood as representing the significant themes that
emerged from the data. Green indicates regular positionings or the heading coded once. Light
blue indicates regular positionings with the heading coded multiple times, and hence
appeared at least twice across the six tables. Red indicates phases with idiosyncratic
positionings.
Table 32. Standards and Goals
Positionings

UCSMP

Pearson

Teachers have a duty to know
CCSS MP relevant to the
content of the TG.

IntTG
IntCh
(Math
Background)
IntLe
EnLe

Teachers have a duty to know
relevant CCSS content
standards at the chapter/
lesson level.

IntTG
(Big Ideas
and the
Common
Core;
Common
Core State
Standards for
Mathematical
Content;
Algebra 1
Pacing
Guide)
IntCh

119

CMP
IntCh
EnCh
(Possible
Answers to
Mathematical
Practices
Reflections)

IntCh

Eureka

IntCh
MiLe

IntCh
(OVERVIEW)
MiLe
EnLe

Table 32 (cont’d)
Teachers have a duty to know
to identify local standards
relevant to each lesson.

IntLe

Teachers have a duty to know
SPUR standards addressed in
the chapter/lesson.

IntCh
(Chapter
Overview;
Objectives)
IntLe
IntTG
(Big Ideas
and the
Common
Core; BIG
ideas)
IntCh
(Chapter #
Overview;
Math
Background)
IntLe
(BIG idea;
ESSENTIAL
UNDERSTANDINGS)
EnCh
(Essential
Questions)

Teachers have a duty to know
Big Ideas and essential
questions/understandings.

Teachers have a duty to know
the aim of the chapter/lesson

IntCh
IntLe

IntLe

Teachers have a duty to know
claims and skills relevant to
the task.

IntTG
(Algebra1
Pacing
Guide)
IntCh

Teachers have a duty to know
why students need the skills
introduced in the chapter.

IntCh

120

IntCh
(OVERVIEW)
IntLe

Table 33. Resources
Positionings
Teachers have a duty to know,
in general, supplementary
resources available.

UCSMP
IntCh

Teachers have a duty to know
what hardcopy resources
and/or materials are needed.

IntLe
EnCh

Teachers have a duty to know
what electronic resources are
needed.

IntCh
EnCh

121

Pearson
IntTG
(Teaching
Resources)
IntCh
(Resources)
EnLe
(EXERCISE
#; Additional
Instructional
Support;
Differentiated
Remediation)
IntCh
BeLe
MiLe
EnLe
EnCh

CMP

Eureka

IntCh
(Planning
Charts)

IntCh

IntLe
BeLe
MiLe
EnLe

IntChEnCh*
IntLe

MiLe

Table 34. Accommodation
Positionings

UCSMP

Teachers have a duty to know
supplementary information to
make accommodations.

IntCh
IntLe
MiLe
EnLe

Teachers have a duty to know
how to support emergent
bilingual students.

Pearson
IntTG
(Teaching
Resources)
IntCh
(Get Ready!;
Pacing and
Assignment
Guide)
EnLe
(ASSIGNME
NT GUIDE;
Differentiated
Remediation)
MiLe
IntTG
(Teaching
Resources)
IntCh
(Resources)
EnLe
(ELL
Support;
Differentiated
Remediation)

MiLe

CMP

Eureka

IntTG

IntCh
(Parent
Letter)

Table 35. Tasks
Positionings
Teachers have a duty to know
tasks/activities/questions for
opening a chapter/lesson.
Teachers have a duty to know
additional tasks that are not in
the student version.
Teachers have a duty to know
how to extend tasks.

UCSMP
BeLe
(1 WarmUp)

Pearson
BeLe
(FACILITATE)
MiLe
MiLe
(Problem #)

MiLe

122

CMP

Eureka

IntCh
BeLe

MiLe
EnLe
(Exit Ticket)
EnCh

Table 35 (cont’d)

Teachers have a duty to know
tasks/projects that overarch a
chapter, to be revisited
multiple times.

IntCh
(Overview
of the
Performance
Task;
Introducing
the
Performance
Task)
EnCh
(Completing
the
Performance
Task)
EnLe
IntCh
(Introducing
the
Performance
Task)
BeLe
(FACILITATE)
MiLe
(Problem #)
EnLe
EnCh
(Completing
the
Performance
Task)

IntCh
EnCh
EnLe

Teachers have a duty to know
questions to ask.

Teachers have a duty to know
answers to tasks/questions.

IntTG
BeLe
(1 WarmUp)
MiLe
EnLe
EnCh

IntCh
BeLe
MiLe
(Problem #;
Answers;
Additional
Problems)
EnLe
EnCh

Teachers have a duty to know
potential student errors.

MiLe

IntCh
MiLe
123

BeLe
MiLe
EnLe
(Suggested
Questions)

MiLe
EnLe

BeLe
MiLe
(Providing
for
Individual
Needs)
EnLe
(Suggested
Questions)
EnCh
(Possible
Answers to
Mathematic
al Practices
Reflections)

BeLe
MiLe
(Classwork)
EnLe
(Closing;
Exit Ticket
Sample
Solutions;
Problem Set
Sample
Solutions)
EnCh
MiLe

Table 35 (cont’d)
Teachers have a duty to know
strategies students might use
when solving tasks.

IntCh
(Math
Background)

MiLe

BeLe

BeLe
MiLe
EnLe

MiLe

CMP

Eureka

Table 36. Assessment.
Positionings
Teachers have a duty to know
for each assessment type, when
to administer, its format, and
the standards.
Teachers have a duty to know
to selectively review tasks.
Teachers have a duty to know
where students are at from
student performance on the
task/project/question/quiz
using a rubric.

Teachers have a duty to know
questions and/or activities for
students, to assess their
learning of the lesson/chapter.

Teachers have a duty to know
tasks for students, to assess
their learning of the chapter.

UCSMP

Pearson

IntCh
EnCh

EnLe

EnCh

EnLe
(Lesson
Quiz)

EnLe
(Lesson
Quiz)
EnCh
(Essential
Questions;
Summative
Questions)

EnLe

EnCh

EnCh
EnCh
(Possible
Answers to
Mathematical
Reflections;
Possible
Answers to
Mathematic
al Practice
Reflections)

EnLe
(Closing;
Exit Ticket)

EnLe

EnCh
(End-ofModule
Assessment
Task)

CMP

Eureka

EnCh

Table 37. General Information: Features and Structures of the TG
Positionings
Teachers have a duty to know
the merits and significant
features of the curriculum.
Teachers have a duty to know
information of mathematical
topics in addition to algebra.

UCSMP

Pearson

IntTG

IntTG

IntTG

IntTG
(BIG ideas)

124

Table 37 (cont’d)
Teachers have a duty to know
the excellence of the
curriculum proved by
research.
Teachers have a duty to know
how the curriculum contributes
to students’ college and career
readiness.

IntTG

IntTG

IntTG
EnLe
IntTG
(Preparing
to Teach a
Module;
Preparing to
Teach a
Lesson)

Teachers have a duty to know
steps to follow when preparing
to teach a chapter and a
lesson.
Teachers have a duty to know
the Lesson Structure of each
lesson.
Teachers have a duty to know
general structure of the lessons
in the curriculum, both student
and teacher versions.
Teachers have a duty to know
the pacing of the
curriculum/chapter/lesson.

IntCh

IntTG

IntTG

IntCh
(Chapter
Overview)

IntCh
(Pacing and
Assignment
Guide)

125

IntCh
(Planning
Charts;
Block
Pacing)

IntTG
IntCh

Table 38. General Information: Mathematics
Positionings
Teachers have a duty to
know in general the
mathematical contents of
the chapter at the lesson
level.
Teachers have a duty to
know mathematics for
pedagogical purposes.
Teachers have a duty to
know vocabulary.
Teachers have a duty to
know to consider students’
prior mathematical
knowledge.

UCSMP

Pearson

CMP

Eureka

IntCh

IntCh
(Math Background)

IntCh

IntCh

IntLe
MiLe

IntLe
MiLe

IntCh
IntLe

MiLe

EnCh

IntCh
(Math Background)

IntCh
IntLe

IntCh

IntLe

IntCh
(Get Ready!)

BeLe

IntCh

MiLe
EnLe
EnCh
([#
Project
Title])
Teachers have a duty to
know supplementary
information to implement a
task.

IntCh
IntLe
MiLe
(Overview of the
MiLe
(Classwork)
Performance Task;
(Providing
EnLe
Introducing the
for
Performance Task)
Individual
BeLe
Needs)
(FACILITATE)
EnLe
EnLe
EnCh
EnCh
(Possible
(Completing the
Answers to
Performance Task; Mathematical
FOSTERING
Reflections)
MATHEMATICAL
DISCOURSE; On
Your Own)
MiLe

126

Table 39. Additional Features
Positionings
Teachers have a duty to know
what to consider when
reflecting on their teaching to
plan next stage of the lesson
accordingly.

UCSMP

Pearson

MiLe
EnLe
IntCh
(Using the
Mathematical
Highlights;
Parent
Letter)

Teachers have a duty to know
that they communicate with
households.
Teachers have a duty to know
tips from other teachers who
have experience with using the
curriculum.
Teachers have a duty to know
they can make notes as
needed.
Teachers have a duty to know
which tasks are addressing
CCSS MP Modeling.

CMP

IntTG
IntCh
EnCh

IntCh
EnCh
EnLe

127

Eureka

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128

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