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Noticing identity: a critically reflective cycle to leverage student mathematical funds of knowledge and identity

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Noticing identity: a critically reflective cycle to leverage student mathematical funds of knowledge and identity

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Content Noticing Identity:
A Critically Reflective Cycle to Leverage
Student Mathematical Funds of Knowledge and Identity
By
Katherine Risbrough
Rossier School of Education
University of Southern California
A dissertation submitted to the faculty
in partial fulfillment of the requirements for the degree of
Doctor of Education
December 2023

© Copyright by Katherine Risbrough 2023
All Rights Reserved

The Committee for Katherine Risbrough certifies the approval of this Dissertation
Yasemin Copur-Gencturk
John Pascarella
Julie Slayton, Committee Chair
Rossier School of Education
University of Southern California
2023

iv
Abstract
This study examines my leadership enactment as an adult learning facilitator within my
role as Mathematics Instructional Coordinator at PS 103. To provide a comprehensive structure
of my leadership enactment, I deconstruct my use of andragogy and (critical) reflection with the
math department teachers. My action research question was: Within my role of Instructional
Coordinator, how did I (a) develop myself as an adult learning facilitator and (b) assist
participants in using a (critically) reflective cycle to see, describe, and analyze how their identity
impacted the ways they noticed student funds of knowledge in their math classrooms? This
action research will ultimately move me towards my long-term goal of supporting teachers in (a)
noticing alternative forms of mathematical success as student funds of knowledge and identity
and (b) leveraging those funds to provide Black and Latine students with math learning
opportunities that are connected to their home learning contexts. I collected audio recordings,
transcriptions, (critical) reflections, and documents developed in my role as adult learning
facilitator. In this study, I found that I was able to move my participants from infrequent,
unstructured descriptive reflection to consistent reflection-on-action and increased the amount of
trust in our space to support more vulnerable, identity-conscious conversation. These serve as a
foundation for future growth toward noticing and leveraging student funds of knowledge and
identity. Additionally, I found ways in which I supported and hindered participant learning, as
well as my own, throughout the study.

v
Dedication
To Maddy. For supporting me through every tear and celebration along the way.
To Emily. For teaching me the beauty of alternative perspectives.
To Mom. For modeling what it looks like to selflessly love and work for the next generation.
To Dad. For showing me how to Fight On in the smallest, biggest and most joyful ways.
To my family and my friends. For helping me to form my favorite parts of my identity.
To my fellow educators. For inspiring me to stay passionate, show up, create joy, confront
weaknesses, and celebrate strengths.
And to my students. For being the most wonderful reason for it all.

vi
Acknowledgements
To my committee chair: Dr. Julie Slayton. Thank you for teaching me not to hope, but to
expect. You will forever be the voice in my head pushing me to seek alternative perspectives,
reflect critically, and learn deeply.
To my committee members: Dr. John Pascarella and Dr. Yasemin Copur-Gencturk.
Thank you for challenging my thinking, sharing your time and expertise, and for being role
models in this work. I am forever grateful for you both.
To my USC Rossier professors. Thank you for supporting me, challenging me, and
encouraging me, and for the work that you have done to pave the way for me and other
educators.
To my USC EdD colleagues. Thank you for being my forever critical friends. I am better
for knowing you and learning alongside you, and am so grateful to be able to do this work with
you.

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Table of Contents
Abstract iv
Dedication v
Acknowledgements vi
Table of Contents vii
List of Figures ix
List of Tables x
My Experience With Learning 2
Historically Entrenched Inequity 15
Context 23
Role 30
Conceptual Framework 36
Funds of Knowledge and Identity 41
Rodgers’s Reflective Cycle 44
Andragogy 49
Critical Reflection 64
Research Methods 67
Participants and Settings 69
Actions 76
Data Collection 80
Data Analysis 82

viii
Limitations and Delimitations 84
Credibility and Trustworthiness 87
Ethics 89
Findings 89
Increasing Trust in the Learning Environment 90
Forms of Assistance to Promote (Critical) Reflection-on-Action 116
My Growth 163
Afterword 184
Continuing Development as an Adult Learning Facilitator 185
Continuing Toward Critical Reflection 190
References 192

ix
List of Figures
Figure 1: Conceptual Framework Page 38

x
List of Tables
Table 1: Planned Actions with Teachers Page 76

1
Noticing Identity:
A Critically Reflective Cycle to Leverage Student Mathematical
Funds of Knowledge and Identity
The intention of this study was to learn to notice funds of knowledge and identity in
places it was often ignored; very specifically, within mathematics learning in my setting. I aimed
to notice the ways in which my own White identity had perpetuated the historical harm done to
students of color via White-dominant teacher development, instruction, and curricula. I did so
with the intent of disrupting the perpetuation of these systems in PS 103 by growing my capacity
as an adult learning facilitator within my role as Math Instructional Coordinator.
In the remainder of this section, I examine the ways in which my math identity was
developed both at home and at school, as well as how my White identity impacted the ways that
I was noticed by teachers in my math classrooms. I then reflect on the moments of disorientation
that led me to deeper learning about the role of race and identity in learning and teaching. Next, I
consider the historical context surrounding the marginalization of Black and Latine students in
math education, as well as the ways in which my professional context and role contributed to
said marginalization. Finally, I present an action research study that focused on disrupting said
marginalization by considering the ways in which we, as teachers and adult learning facilitators,
could use a (critically) reflective cycle to leverage students’ funds of math knowledge and
identity, thus, in the longer term, creating more equitable and affirming math classroom
experiences for Black and Latine students.

2
My Experience With Learning
The first memory I have about learning is that when I learned something new, I was
applauded. Looking back, I understood learning at this phase to be acquiring new skills and
knowledge. I vividly remember being publicly praised, via clapping and exclamation, each time I
demonstrated a new skill or shared a new fact. These loud, joyful, frequent forms of positive
reinforcement signaled to me at a young age that if I did something new, I was celebrated. The
more I demonstrated, the more I was praised. I related this positive experience to learning, and in
doing so learned that my family displayed excitement when I learned new skills; therefore, they
must have valued learning.
The next thing I understood about learning was that learning was something to be shared.
My parents modeled learning by asking each other questions about their days, engaging in
discussions about politics, world events, and culture, and seeking understanding within authentic
experiences like travel and social gatherings. I was expected to learn by discovery each day,
modeled to me by the way that my parents started my sisters’ and my days with “Go play
together” and ended it with “What did you learn today?” From this I learned that in order to learn
I was to go play, and that each day was an expected opportunity for new learning. When I
returned, I was asked to share what I had discovered. My parents asked me and my sisters openended questions at the dinner table about what we had discovered during our day, what we
thought about those discoveries, and, informally, why we came to the understanding we did.
From this I learned that the world was full of information to be found, and now recognize that I
learned via the contextual experiences found in playing. I was trusted to control my own learning
or co-construct it with my sisters during this playtime, and internalized the idea that learning was

3
collaborative and enjoyable. I now recognize that learning in my own home followed a pattern,
typically taking the form of collaborative discovery followed by sharing new knowledge.
The questioning posed by my parents also created a space of collaborative learning. In
asking us questions together, often around the dinner table, my parents modeled sharing their
experiences and prompting us to share our own, asking questions to better understand, and
listening to each other’s experiences. I was then frequently prompted to carry my learning on in
applied ways; most often this was in the form of “Tell your sister what you found!” or “I think
your sister would love that; help her do it,” which taught me that learning was a thing to be
shared, and that as I had learned it first, I was now responsible for passing that learning along via
modeling or direct teaching. As the three of us were so close in age, this sharing of knowledge
happened frequently and multilaterally—although as I was oldest, it was frequent that I was
expected to do the sharing. In this way, my parents modeled learning as a type of inquiry cycle
that emphasized personal experience, questioning, and application. When that application was in
helping others to learn what I had, I was praised as a helper. This helped me to gain self-efficacy
in informal teaching and motivated me to continue this behavior with my sisters and eventually
with other peers. This informal inquiry cycle instilled in me a desire to continue discovering new
things, something that I continue to find joy in in my adult life.
In addition to the modeling, questioning, and collaborative, contextual learning I
experienced, I was socialized into a school-setting before I arrived at kindergarten. Both of my
parents are highly educated—mom as a teacher, dad as a lawyer. College was framed as an
expectation rather than a goal, demonstrated to me via the numerous times my parents told their
own college stories, took me on trips to campus starting as early as 1-month old, and used
“when” rather than “if” when they talked about my eventual turn at an elite university. My

4
parents valued reading and modeled the expectation that we would read also, both directly—via
bedtime stories and trips to the bookstore as rewards for good behavior—and indirectly in the
way that I could frequently find either of them reading a new book of their own. The
combination of the positive-reinforcement around learning, the informal inquiry cycle described
above, the collaborative learning I experienced with my sisters, and my socialization into an
informal school-setting all led me early on to identify as someone who liked learning and was
good at it as I moved into formal education. Prior to events of disorientation that I will describe
later, discovering new skills or facts was my definition of learning, and I therefore classified
myself as someone who was a “learner.” Looking back, I recognize that the real learning
occurring was actually using these new skills, knowledge, and the modeled behaviors that I
absorbed from my parents, other family members, and interactions in my community to construct
my understanding of my home context; this was the fund of knowledge that I would take with
me into formal schooling, and the foundation that my identity and implicit biases were based on.
My experience is reflective of Vygotsky’s sociocultural learning theory, in which the social
environment operates as a facilitator of learning, and where cultural-historical context cannot be
separated from the ways in which children create their understanding (Schunk, 2012); this theory
continues to inform many of the ways in which I learn and teach to this day.
I came into formal school with these funds of knowledge and identity and a current
understanding of the way the world worked in my home context. Unlike many children, I was
immediately validated for that knowledge in the ways that I saw teachers, peers, and the
curriculum mirror my home experiences. Now, I recognize that I attended a public school in a
majority-White, upper-middle-class neighborhood, composed of majority White students and all
White teachers. This leads me to believe that my funds of knowledge and identity were most

5
likely valued because they were similar to the experiences of my White teachers. My teachers
noticed and validated my thinking because, I assume, it was what they expected; the
representations I used and experiences that I shared were similar to their own, and so their
relation to what I shared made it natural for them to validate my thinking—they were essentially
validating what they already knew, from their own experience, to be true. This instilled in me a
sense of belonging, and I was frequently able to use what I already knew to provide correct
answers. This gave me an early sense of school self-efficacy, and my confidence as a learner
continued to grow.
In addition to seeing connections between learning at home and inside my classroom, I
witnessed very visible connections in other ways. My mom was the president of the ParentTeacher-Association, my dad read to my classroom every Friday morning, we frequently had
dinner with the principal and his family at our home, and my kindergarten teacher lived across
the street and picked me up to take me to McDonalds. All of this was evidence to me that my
family held an important place in the school, and I therefore belonged. Their involvement
showed me that we, as a family, valued formal education (which, at the time, I equated with
valuing learning), and that because we valued it, it was our responsibility to help others attain it
and enjoy it. I clearly saw the connection between my home and my school and understood my
place in it both as a learner and helper. At the time, I did not recognize that this experience was
different for many students; now, I recognize that it is particularly different for students from
historically marginalized communities.
My parents had mainly taught me to learn through discovery and play; but of course,
there were many skills that they directly modeled for me to imitate. In some classes, particularly
in early elementary, discovery-through-play continued, but as I grew older, I remember

6
instruction becoming more focused on direct modeling of skills, particularly in math. Although
this was different from the inquiry process that my parents had modeled, I was used to watching
White adults model behaviors and then mimicking them. This, in the math classroom, became
something that I could continue to do to learn new skills. I was used to being asked questions
about my learning, and so, again, I was typically able to respond to posed questions in the same
way I was used to at home. My teachers responded to me showing off skills and knowledge by
referring to me as “smart” and a “quick learner,” and encouraged me to use my knowledge to
help other students. I again was seeing what I had internalized at home: if I learned new things, I
was praised and asked to help others. I was often named some form of peer-teacher as a result,
which taught me that if I was smart and helpful, I could become a teacher. For the majority of
my childhood and K–12 education, becoming a classroom teacher was my career goal.
Early on I earned a reputation for being “good at math”—which to me at the time, meant
that I could solve problems quickly, without errors, in the same way that my teachers did. This
was reflected by my high grades and comments on my report cards that again praised me for
being a “quick learner” and a strong “helper” or “classmate.” Although my parents praised me as
smart from a young age, my success in math surprised them; they both disliked math, and as I
continued to succeed in math classes I frequently heard my parents say, “I don’t know where you
got it from,” or “It must have been from your great-grandfather—he was an engineer.” As early
as third grade my parents made comments like “I can’t help you with math anymore. You’ll have
to ask someone else.” This signaled to me that despite their own lack of math self-efficacy, I was
still capable of having high self-efficacy in math if I found others to model and peers to learn
with. Teachers continued to model what my parents had; when I learned a new math skill I was
praised, and then I was asked to help my peers. In fifth grade I, along with three other students,

7
was sent out into the hallway with a textbook and told that we were to teach ourselves sixth
grade math. And we did learn the skills, as evidenced by my class and state-test scores, positive
praise from teachers, and my continued success as I moved into Algebra 1 two-years before the
majority of students take the course. I continued to gain confidence and because I was
experiencing success, I continued to have high mathematical self-efficacy and therefore began to
identify as a “math person.” When my teachers didn’t model in the way I needed, I turned to my
peers to learn in the same way that I had learned alongside my sisters—socially—by asking
questions, co-exploring, and coming to decisions together. This meant that I was frequently
chastised for talking with my peers rather than watching the teacher model. Instead of being
disciplined, however, my reputation for helpfulness and mathematical success meant that I was
instead sent out with a small group of others to complete advanced work in the hallway or asked
to become a peer-tutor. Rather than being punished for my excessive talking, I felt trusted and
validated by my teachers. This continued to add to my math self-efficacy and the notion that the
funds of math knowledge I had to contribute were valuable. I again recognize now that this was
an example of the privilege I held as a White student in a White environment; my talking in class
was viewed as leadership to be praised, rather than a disruption to be punished. As will be
explained in later sections, this is not the same experience that I have seen my Black and Latine
students have throughout their math educations.
My school and home experiences were similar enough that, as I moved through middle
and the beginning of high school, I didn’t experience dissonance between how and what I
learned in my two main contexts—school and home. The first time that I can recall experiencing
disorientation was as a junior in AP US History class. Many of my family members were
passionate about United States history and had told numerous stories about the ways in which

8
my family was involved in major historical events. I entered the room excited to take the course.
I expected to be able to share these experiences—and I was, but I was also asked to consider
history from multiple points of view. Similar to most of my classrooms, my teacher was White
and the majority of my classmates were White, with a small Asian and Latine minority. My
teacher brought in texts and artifacts in order to include more voices of color, relied on frequent
debates to hear all voices and model what disagreement looked like, and pushed all of us,
particularly White students, to examine the version of history that we had internalized thus far.
He pushed me to actively listen to others’ thoughts and to slow down my own thinking by asking
probing questions and by modeling what it looked like to consider events from multiple
viewpoints. I was no longer immediately validated as right. In this classroom, learning did not
seem to be about gaining and sharing knowledge or learning skills. Instead, it seemed to mean
deep thought around what counted as fact, by whom, and why. Looking back, I recognize a
specific set of moments that led me to experience a racial disorienting dilemma (although I did
not know what to call it at the time). This started during a debate about attacking Japan with
nuclear weapons at the end of World War II. During the debate I operated from my own
perspective; my great-grandfather fought in WWII and as my family’s narrative went, after the
bombs fell, he was able to come home. Therefore, the bombs were to be celebrated. When I
heard other students speak to the immediate and lingering effects on Japanese families, I
remember feeling ashamed that, prior to this debate, I had not considered or cared about
alternative perspectives to my own. Looking back now, I recognize that this was the first
moment in which I was beginning to be aware of the ways I held biases due to my colorblind
upbringing and my family’s cultural history (again, although I could not name that at the time).

9
A few weeks later, we engaged in a similar debate about the Vietnam war. In viewing the
event from my own perspective, I again dismissed the deaths of thousands of Vietnamese men
and women and minimized their lives as less than. My teacher pushed me to consider other
perspectives and I was embarrassed; when my Vietnamese friend told me that I had personally
hurt her by my comments, I was mortified. It was the first time I remember recognizing White
and American as titles that represented centuries of harm and oppression, rather than simply
being the color of my skin and my nationality, and I realized that my Whiteness and White ways
of thinking could be actively harming those around me. It wouldn’t be until years later that I
could recognize this moment as anything other than one of embarrassment, but for the first time I
recall actively pausing to consider other points of view and recognizing that mine was limited by
the experiences that I had been exposed to. Now, I recognize that this moment was an experience
of deep learning (Wergin, 2019), in which the learner experiences a “feeling of arousal brought
about by a perceived disconnect between the current and a desired state” (p. 27). This course
showed me that learning is more than acquisition of facts; it involves challenging identity-based
biases, valuing alternative perspectives, and shifting mindsets. Wergin also states that this
disconnect must come with “a sense of efficacy that one is capable of dealing with that
disconnect” (2019, p. 27), and, because my teachers and peers continued to involve me in
discussions and push me to reconsider mindsets, I continued to stay engaged. This teacher
became one I wanted to emulate. I will return to the power of this moment later, when I reflect
on my own instructional decisions as a teacher.
As I applied for college, I chose to become a doctor. Although I had been praised as a
strong math student, I didn’t envision myself in a math-related career. Medicine seemed to be a
way that I could again prove myself to be “smart,” gain the praise and admiration of those

10
around me, and acquire more knowledge with the intent to help others—all of which I valued due
to the majority of my educational experiences thus far. In addition, I chose to minor in history
because of the power I found in my AP US history class. Once enrolled, I found the pre-med
track to be isolating and more about memorizing than learning (a distinction I did not make at the
time, but that I recognize now). In contrast, in my history classes I found myself constantly
questioning what I had previously held to be true. These courses were not majority-White and
were taught by professors of color, and I was able to view previously held facts from their
different perspectives. More and more, I began to redefine my idea of learning—although again,
I did not know how to name it at the time. At the same time, I was volunteering at a low-income,
predominantly Black and Latine middle school in South Los Angeles. I found that I loved
convincing students that they could be successful in math, because I was there to help them. I
still possessed the high math self-efficacy that I had internalized in K–12 and found that I could
successfully teach skills, and often did so by modeling my own thought process and asking
probing questions (again, something that I recognize now). I ultimately was torn between
becoming a doctor and a teacher, and so I chose to enter Teach for America (TFA) for 2 years to
help me decide which path was the right one to take. As much as I would love to say that I was
driven by the mission of equitable education, I was not. I had heard during my volunteer
experience that many schools, particularly in low-income communities, lacked qualified
teachers. Again, at the time I believed that learning math required someone who understood
content to model, and then praise, students. I felt confident that I could be that person, and was
looking to find where I could be successful and use that success to help. I considered myself to
be the highly-educated math expert who could deliver knowledge to those who needed it; the
exact mindset that this study aimed to work against.

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Once accepted to TFA, I moved to Memphis, Tennessee to attend a two-month “Summer
Institute,” which included courses in Diversity, Equity and Inclusion (DEI) and math pedagogy,
as well as a student teaching experience. TFA was, at the time, one of few teacher preparation
programs that considered DEI classes to be an essential part of teaching students of color. These
courses were my first introduction to many of the concepts discussed in the next section, and the
first time that I was expected to consider how my Whiteness and racial biases impacted the ways
that I made decisions. For the first time, I was asked to critically reflect (although at the time, it
was not named as such). I experienced extreme discomfort in these classes, as did many of my
White peers. I can admit now that for the majority of that experience, I participated in the
activities because I had to; the deep learning described above did not occur until experiences that
I will describe later in this section.
Although TFA did push us to consider our racial identities and the impacts that they
would have on our students, the majority of our professional development still focused on
classroom management and direct instruction. Both in this two-month institute and in the
professional development that I later received at my first school, I was trained to always consider
behavior management before learning. In prioritizing management over meaningful learning
experiences, I contributed to lost learning time in the classroom and imposed what Whiteness
defines as “managed” onto students of color. This messaging is common in teacher prep
programs and is typically unquestioned; it is therefore a hegemonic assumption in that it is
accepted as in students’ best interests, when really it is working against students of color
(Brookfield, 2010). In alignment with this hegemonic way of prioritizing management, other
teachers warned me that if the students in my classroom were not compliant, I would be fired. I
was told that students “couldn’t work in groups” and that, if I wasn’t consistently “redirecting”

12
them toward accomplishing tasks, students would not learn because they did not want to. We
spoke of educational equity and closing the achievement gap, but looking back even this was
messaged with low expectations—students were low because they lacked fundamental math
skills, we needed to catch them up, and to do so we had to cover material quickly. For quick
skills acquisition to happen, students had to be attentive every minute of the class period and we
had to cover multiple years of content in one year. I internalized this as a silent classroom in
which students were quickly absorbing information delivered by the teacher—again, a
hegemonic White supremacist approach that devalues student learning and emphasizes
management and compliance.
Following Summer Institute, I was assigned to teach Algebra 2 at a community charter
school in a low-income neighborhood in Memphis, Tennessee. Ninety-eight percent of my
students were Black and the other 2% were Latine; already, my new classroom would be
different from the environment I had grown up in. However, I was coming from a background
that, for the most part, didn’t acknowledge race. Despite my training in TFA, I continued to
believe that the right thing to do was to ignore race and to treat my students the way I had been
treated. My personal success in math and my self-efficacy around helping others learn made me
hold the strong conviction that any student was capable of learning math; this was a colorblind
approach that I at the time confused with TFA’s mission of all students receiving equitable
educations. I believed that, regardless of race, identity and experiences, students just needed the
right helpers around them. What I didn’t recognize at the time was that, in doing so, I was
ignoring the racial and cultural funds of knowledge and identity that my students were bringing
into the classroom. I viewed myself as the expert responsible for modeling “correct math.” In not
slowing down to reflect on what they were contributing to the classroom, I was refusing to notice

13
their funds of knowledge and identity, and therefore the multiple ways in which they knew how
to represent their mathematical thinking. In doing so, I was perpetuating an educational model
that was designed to empower White students and to oppress students of color.
As I approached my second year of teaching, my class looked like a lot of direct
instruction, and I remember feeling like I was as bored (as the teacher) as I had been in my premed courses (as a student). I began using more questioning and collaboration, which more
mimicked the learning I had done at home and my experiences in my history classes, and began
to build stronger relationships with my students as the culture of my classroom became more
student-focused. However, at the time, I did not understand the difference between procedural,
conceptual, and application math standards or know any math pedagogy. My own lack of
conceptual math understanding made it difficult for me to understand students’ alternative
representations, and my White educational experience and own Whiteness made my way of
noticing student thinking White-centered.
After my first two years of teaching in Memphis, two experiences made me understand
that I was teaching in a way that was further harming my Black and Latine students. First, I
applied to and was accepted as a Hollyhock fellow at Stanford’s Center to Support Excellence in
Teaching (CSET). This was a two-year program that brought together 100 educators across the
country, all from low-income schools with historically minoritized populations. Their mission is
to develop teachers in low-income communities to increase retention and the quality of education
for students who typically experience high teacher turnover and inexperienced teachers. Along
with three teachers from my school, I spent 4 weeks over 2 summers in intensive sessions split
between discussion-based mathematical practices and building equitable learning experiences.
Over 2 years with my students, I had started to reflect upon and recognize some of the implicit

14
biases that TFA had initially attempted to expose; I was therefore more receptive to speaking
about race, hegemony, and the impact that Whiteness had on students of color. This time, when I
was explicitly told how harmful traditional White teaching can be to students of color, I was able
to engage. I learned the term “funds of knowledge” and critically reflected upon the ways that I
had been completely invalidating my students’ funds. In this program, I realized that I had been
treating my students as ‘empty vessels’ who came to me below grade-level and I saw it as my
responsibility to model and fill them with as much as I could. I was depriving them of the chance
to use their brains and the funds of cultural and historical math reasoning, knowledge and skills
that they had from their own contextual experiences. Although I thought that I was validating
them via praise and support in class, I was actively invalidating the idea that they had any math
reasoning or skill beyond me. When I returned to my school for my third year, I began using
open-ended tasks and question stems that encouraged students to demonstrate what they already
understood, discuss their ideas, and use multiple representations to demonstrate their thinking.
As a result of Hollyhock, I was more aware of my Whiteness and was implementing structures
that attempted to honor my students’ cultural funds of knowledge; however, due to my continued
lack of conceptual math knowledge I was still mainly asking them to apply the procedures that I
had taught students based on my own experience and then validating them.
In my fourth year in Memphis, I became an instructional coach for students K–12 in the
same charter network that I had been teaching in. This is where I was forced to confront the fact
that my math conceptual understanding was not strong. Although I had always succeeded in
math, I came to learn that I had just been extremely proficient in learning procedural skills. I
lacked the understanding needed to draw connections between skills, understand the concepts
behind the procedures, or see and vertical alignment between skills learned previously and new

15
skills learned. Our school was transitioning to EngageNY, a curriculum designed to build
conceptual understanding based on the Common Core standards, and I attended numerous
trainings so as to better support the elementary school teachers. I was shocked to find that there
were multiple ways to represent mathematical thinking and that many had roots in other cultures.
When I returned to Los Angeles for my fifth through ninth years of teaching, I continued
to push myself to grow in my conceptual understanding and to increase discussion in my
classroom. I returned full-time to the classroom at a charter school in South Los Angeles, and
worked to build an equitable learning experience that honored my Latine students’ funds of
knowledge and identity in Los Angeles. Each of the experiences described in this section
ultimately forced me to recognize that I had much more to learn if I wanted to disrupt the
inequity I was seeing in education. I recognized that I needed to learn more in order to do so, and
that I wanted to do so with educators who felt equally passionate; this led me to this doctoral
program and served as the personal motivation for this study.
Historically Entrenched Inequity
My personal experience is representative of ways that White teachers come into lowincome schools and do harm to Black and Latine students. For the purposes of this study, I
examine how this harm stems from hegemonic deficit ways of thought, is perpetuated in teacher
professional development, and plays out in classroom instruction. As I do so, I focus in particular
on the ways that educators treat Black and Latine students as ‘empty vessels’ by failing to
leverage the funds of historical and cultural math knowledge, skills, and reasoning that they
bring into our math classrooms. In doing so, we fail to support their development as
mathematicians, problem solvers, and deep learners.

16
White supremacy ideology has historically labeled Black and Latine communities as less
intelligent than their White counterparts to keep people of color from holding positions of power
(Utt & Tochluk, 2020). This dominant ideology labels Black and Latine students as “less than”
and blames low performance on individual students rather than the biased system that
perpetuates this deficit narrative (Solórzano & Yosso, 2002). This ideology has been internalized
by teachers, parents, and administrators, all of whom make decisions surrounding their students’
educations without attending specifically to the biases they carry. According to research from the
National Council of Teaching Mathematics (NCTM): 
In too many schools, unproductive mindsets and practices have harmed many students
and particularly marginalized students such as Black, Latine, and Indigenous students;
students who are economically disadvantaged; students who are learning the English
language; and students with special needs and disabilities (2021, p. 5).
This deficit labeling is particularly true in math education, where Black students are
described as “behind” White students even before they enter the classroom (Martin et al., 2019),
and where educators hold deficit views of Latine students’ home languages and cultures
(Franquiz et al., 2022). These deficit mindsets perpetuate the idea that students are ‘empty
vessels’ to be filled with content, rather than whole beings coming to school with lived
experiences and funds of knowledge and identity to contribute. As Martin et al. (2019) states,
Largely absent in studies of Black students in pre-school settings are attempts to explore
and document these children’s mathematical development in naturalistic everyday
settings and the ways in which they engage the world in mathematical ways … nor are
there attempts to determine how their mathematical sense-making in these naturalistic
settings is supported by their cultural experiences … This has helped to reify a persistent

17
and violent narrative that Black children enter school with little or no mathematical
knowledge in relation to other children (p. 44).
This is just one example of how White supremacist ideology sets students up for failure
in schools before they enter, as researchers neglect funds of knowledge and thereby perpetuate
the narrative that Black and Latine students lack cultural and mathematical sense-making
abilities. This ‘empty vessel’ view of students’ lack of mathematical knowledge aligns with the
White supremacist tenet paternalism. Jones and Okun (2001) describe paternalism as “those with
power often [not thinking] it is important or necessary to understand the viewpoint or experience
of those for whom they are making decisions” (p. 4); in ignoring students’ previous experiences
and problem-solving strategies, the education system labels Black and Latine students as deficit
and makes the decisions for what and how they should learn. Mathematics education also
perpetuates the White supremacist tenet of perfectionism, which Jones and Okun (2001) describe
as “the tendency to identify what is wrong; little ability to identify, name, and appreciate what is
right” (p. 1); this is also linked to the idea of students as ‘empty vessels’ that must be filled with
content, as students are seen only as lacking knowledge rather than being appreciated for the
naturalistic math skills that can be leveraged.
In addition to what is described above, the perfectionist tendency of “identifying what is
wrong” is a consistent narrative in research and published statistics. The discrepancy in
standardized-math-test performance between Black and White and Latine and White students is
commonly known as the achievement gap (Ladson-Billings, 2006). However, Ladson-Billings
(2006) warns that referring to this as a gap focuses on short-term solutions that “fill” the gap,
rather than recognizing the causes of the gap. She therefore recommends using the term
“education debt” that Americans, and I argue particularly White Americans, owe Black and

18
Latine students. This language emphasizes what we as a nation owe, rather than focusing on the
difference between White and Black and Latine performances.
Published math data consistently shows that White or Asian students are more frequently
enrolled in higher-placement math courses and outperform Black or Latine students on
standardized tests (CA Department of Education, 2021; TNTP, 2021). For example, in 2018 the
average score on the AP Calculus AB exam was a 3.76 for White students, while the average
score was a 2.11 for Black students and 3.17 for Latine students (Jaschik, 2018). A score of 3 is
considered passing, which means that a lower percentage of Black and Latine students receive
college credit for the advanced math courses that they are taking. This therefore places them
behind White and Asian students in college STEM majors, even before entering college.
Research has shown that students with low interest or self-efficacy in a subject, and consequently
with higher anxiety around that subject, are more likely to disengage with that subject at an
earlier age (Allen & Schnell, 2016; Stoet et al., 2016). It therefore stands to reason that students
who do not experience themselves as successful in mathematics are less likely to pursue more
advanced math classes in high school, or STEM majors or careers post-high school; often,
success is tied to the standardized test scores shared above.
Many companies and researchers are attempting to rectify the achievement gap
(Ladson-Billings, 2006). However, some argue that the push to improve math education in the
United States has been primarily motivated by the international economic consequences of a
weak STEM workforce, which has meant that reform has been primarily focused on contentacquisition to raise math achievement statistics (Gutiérrez, 2008). This data is frequently shared
in relation to the United States’ competitiveness with the international STEM sector, and recent
pushes to increase representation are typically tied to the negative effects that a lack of engineers

19
and scientists will have on the United States’ economic well-being as our country continues to
become more diverse (Lowell & Salzman, 2007). However, Martin et al. (2019) argues that this
emphasis on representation and finance is ultimately another commodification of Black bodies
and that data is once again being used to cast Black and Latine students and workers as inferior.
According to Teo (2010), epistemological violence occurs when “when theoretical
interpretations regarding empirical results implicitly or explicitly construct the Other as inferior
or problematic, despite the fact that alternative interpretations, equally viable based on the data,
are available” (p. 298); in this case, merely looking at the data could place blame on Black and
Latine students for being underprepared or unwilling to pursue STEM careers, rather than
looking at the racist schooling practices that ignore Black and Latine funds of knowledge and
identity from a young age (Martin et al., 2019; McCarthey, 1997; Moll et al., 1992).
Long-term, this disparity continues to add to the wealth-gap between White communities
and Black and Latine communities, as White and Asian workers have always held the greatest
percentage of high-paying STEM jobs (US News & World Report, 2022). Although Latine
employees make up 17% of the overall work force in the United States, they hold only 8% of
STEM jobs (Fry et al., 2021), and Black employees make up 11% of total employment compared
to 9% of STEM jobs. These statistics show that there is a large underrepresentation of Black and
Latine workers employed in STEM jobs compared to the total workforce, and therefore a large
amount of wealth that is not available to their communities. This is a tangible financial example
of the educational debt that our country owes to our Black and Latine students (Ladson-Billings,
2006).
Teacher development also perpetuates the White supremacist tenets of perfectionism and
paternalism described previously. In many low-income, Black and Latine schools, professional

20
development is frequently designed as atomic units that lack context (Webster-Wright, 2009),
and often in ways that ask teachers to use formal research or practice, taught outside of their
context, in their own applied settings, with no further modeling or support (Cochran-Smith &
Lytle, 1999). This atomic, skills-based approach is referred to as knowledge-for-practice
learning, where teaching is “understood primarily as a process of applying received knowledge
to a practical situation” (Cochran-Smith & Lytle, 1999, p. 257). These development sessions
often focus on “closing the achievement gap” via a set of strategies meant to improve test scores,
many of which focus on behavior management (Ladson-Billings, 2006). The harm in this is
twofold: first, it perpetuates the deficit mindset that prioritizes student compliance over student
learning and second, it treats teachers in the same way. In this model, both students and teachers
are expected to obtain knowledge from an expert and apply it, rather than use their experience,
knowledge, and problem-solving skills to reflect and learn. This deficit mindset treats teachers as
‘empty vessels’ in the same way that educators treat students; experts are called in to fill teachers
with strategies, rather than build on their experiences and understandings. Teachers are provided
with strategies that, as I experienced in my own training and early years of teaching, create
classrooms that are quiet, orderly, and on-task, rather than that seek to use student culture to
build stronger learning environments. This model of teacher development perpetuates the
paternalism described previously, as those in power (i.e., districts, school boards, administrators,
coaches) choose which knowledge to provide to teachers and how to assist them in implementing
that knowledge.
Utt and Tochluk (2020) emphasize the importance of teachers understanding their own
identity as they work to notice student identities. While they speak to the importance of
particularly White teachers “taking up nuanced considerations of their racial identity” (p. 126),

21
other researchers call on all urban teachers to attend to their beliefs around culture, race and
identity and the ways in which they impact instruction (Brookfield, 2017; Howard & Milner,
2014). However, in knowledge-for-practice development, context does not matter; therefore,
teacher and student identities are not considered. This form of professional development
therefore fails to acknowledge racial identity and the impact that it has on instruction (CochranSmith & Lytle, 1999; Utt & Tochluk, 2020). Teachers are therefore “developed” in a way that
does not value their funds of knowledge and identity, as they are seen as “knowledge-users, not
generators” (Cochran-Smith & Lytle, 1999, p. 257), and are not asked to consider their own
identities during these sessions. This then impacts classroom instruction, and the ways that
students view their own math identities.
In math classrooms, most efforts to change instruction focus primarily on content
acquisition over conceptual problem-solving (Gholson & Robinson, 2019), with little regard for
alternative ways that students may have encountered problem solving in their homes. Math
instruction in low-income schools often follows the dominant White cultural way of solving,
which ignores multiple representations of cultural and historical mathematical thinking and
teaches students that there is one right way to solve problems (NCTM, 2021). In this traditional
style of math teaching, the “right” way is the way that was modeled by the teacher; this idea of
the teacher always being right is an example of paternalism. In contrast, research shows that,
similar to my personal experience, White students experience more activities in the classroom
that ask them to draw connections between home and school, whereas students of color see the
two contexts as separate; this then fails to provide students of color with learning that is relevant
to their lives (McCarthey, 1997) and fails to draw on their funds of knowledge and identity

22
(Franquiz et al., 2021). According to Gholson and Robinson (2019), this is due to several
reasons, often connected to course offerings and curriculum:
Remedial courses seek to address inadequate instruction and inquiry- and project-based
learning have emerged as curricular frames to make mathematics classrooms more
dynamic, more productive, and more positive (Flores, Phelps, & Jansen, 2017; Hassi &
Laursen, 2015). However, such efforts fail to address the racialized nature of students’
experiences with mathematics (Martin, 2003) and the relational harms. (p. 350)
Although dynamic, productive, and positive classrooms could push toward a more
culturally responsive environment, these curricula are colorblind and ignore the years of harm
that Black and Latine students have encountered during their time in school. Students who have
been taught for years that they do not have anything to contribute are now being asked to
problem-solve collaboratively, without recognizing that previous math experiences have cast
Black and Latine students as inferior before even entering math classrooms (Martin, 2003). The
call for students to freely share their current math understandings runs counter to the years of
previous experience that has taught them that silent compliance is rewarded and that quick
acquisition of skills to “close previous gaps” and excel on standardized tests is the goal. And
while inquiry-based learning is now being pushed by NCTM and highly ranked curricula, Black
and Latine students have experienced years of adultification. School administrators and teachers
who ask students to “be mature,” “have grit,” “work quietly,” and “grow up” have taught
students that the childhood play and socialization needed for successful inquiry will result in
discipline. They are also told that they are behind-grade level and are working to “catch-up,”
which ignores the mathematical reasoning that students have learned outside of the classroom
setting from families, community members, and exploration (Moll et al., 2014; NCTM,

23
2021). Alternatively, “as students see themselves as doers of mathematics, they build confidence
and develop mathematical agency” (NCTM, 2021, p. 7). It is therefore each school’s
responsibility to build math programs that affirm students’ identities as doers of mathematics, not
regardless of their racial identity and past mathematical experiences, but because of them.
Context
PS 103 was a public-charter network in South Los Angeles (South LA), California,
serving approximately 1300 students over one elementary, one middle, and one high school. The
network was founded by three doctoral students from the University of Southern California in
2004, beginning with the elementary school and expanding to a middle and high school in 2008
and 2011, with the intention of creating a community school in South LA that provided a strong
STEM education to students of color. For the purposes of this study, I focused on the middleschool campus. I begin by sharing statistics that I believe contextualize the types of learners and
teachers that composed our community; I then address the systems that were in place for teacher
development, instruction, course design, and curriculum implementation.
I share this data for two reasons: first, as context for the identities that I believe my
students and teachers held; second, to show that many of the teachers I worked with were the
same race as our students, and that, overall, they came from diverse backgrounds and were all
racially different than I was; and third, to provide standardized achievement data that situates our
school in the greater historical context. At the time of the study, at the middle school, 98% of the
480 students were Latine and the other 2% were Black. Ninety-nine percent were eligible for
free-or-reduced lunch (National Center for Education Statistics, 2022). At the high school, 553
out of 557 of our students qualified for free-or-reduced lunch. Five-hundred and fifty-two were
Latine, with the other five students identifying as Black or American Indian/Alaska Native

24
(National Center for Education Statistics, 2022). In 2019, 27.88% of our 6–8 students and
26.96% of our 11th grade students scored proficient or advanced in the California Smarter
Balanced Assessment (SBAC) in math, compared to 39.73% of California and 39.11% of Los
Angeles residents (CA Department of Education, 2021). Our school’s averages showed
outperformance of other Latine populations (CA Department of Education, 2021), which calls
more attention to the huge disservice that our school and others were doing to our students of
color. 
The middle and high school math teachers identified as Latine (4/8), Asian (2/8), Biracial
Black and Latine (1/8) and Middle Eastern (1/8); I taught one course and was the only White
member of the department. This was not typical of most schools; nationally, 89% of teachers
were White (Schaeffer, 2021), making our school teaching staff much more racially diverse than
most public schools. At the time of this study, one of our teachers was in his first year of
teaching and using an emergency teaching credential; previously, he was an instructional
assistant in science courses at the high school for a year and a school alumnus. The remainder
had been teaching for 2 or more years, all of whom earned their credentials from 4-year
universities. One was pursuing her master’s degree and one held an administrative credential.
Our charter network stated teacher development was a priority, and provided
opportunities via individual coaching, site-wide department meetings, and outside opportunities.
All this development was intended to be an opportunity for teachers to reflect on their current
practice and determine ways to enhance student learning, both in alignment with our
instructional vision and mission. At the time of this study our instructional vision was being
rewritten, but the existing version emphasized a holistic approach to education, shared best
practices, collective accountability, and empowering students to be the next generation of

25
problem solvers. Each form of development was loosely intended to achieve this vision;
however, they were designed independently of each other and there was no cohesive scope and
sequence or set of learning objectives that we, as a network, were working toward. Instructional
Coordinator expectations were that each teacher was observed by and engaged in a coaching
meeting weekly with their assigned Instructional Coordinator. All teachers received
approximately 90 minutes of 1:1 observation and coaching per week. These coaching meetings
were intended to support teachers in working toward individual goals set by themselves,
Instructional Coordinators, and administrators, and meeting agendas and activities were designed
completely by each Instructional Coordinator. As this was a key function of my role, I explain in
more detail in the following sections how these goals were chosen. In addition to individual
coaching, teachers attended 2 hours of school-designed department meetings or staff meetings
each week. Furthermore, teachers were occasionally given opportunities to participate in paid
further learning opportunities in the form of conferences, fellowships, and school-developed
summer learning sessions. One of these development opportunities was UnboundEd’s Standards
Institute, a week-long conference for teachers that emphasized the importance of Grade-Level,
Engaging, Affirming, Meaningful (GLEAM) instruction as a tool for repaying the education debt
owed to Black and brown students in the United States (UnboundEd, 2021). For the 22–23
school year, the leadership team collectively decided that our instructional focus—both in
individual and collective professional development, evaluation, and feedback—centered on
GLEAM instruction. This will be further explained when I describe my role in the next section.
As mentioned above, at the time of this study our network was currently in the process of
redesigning our instructional vision. Historically, instructional practices were left to teacherchoice, with some influence by coordinators and administrators in the form of development

26
offered. No instructional practices were mandated. Despite this, there was some uniformity in the
way that teachers are teaching. Following network-wide walk-throughs in the Fall of 2021, the
Instructional Leadership Team (ILT) noticed a lack of student voice in classrooms. By this, we
meant that in the majority of classes, teachers were doing the majority of the speaking and doing
the majority of the cognitive lift. This is related to the historically entrenched inequity described
above; teachers were attempting to provide students with skills, rather than stopping to notice the
understanding that was already in their classrooms. Latine funds of knowledge were therefore
being devalued. At PS 103, this was especially apparent to me in the seventh and eighth grade
math classrooms. In these classes students sat facing the instructor as the instructor modeled and
were rarely asked to contribute their own understanding.
PS 103 was created with a STEM emphasis, which was most clear in our partnership with
Project Lead the Way (PLTW) at the high school. PLTW was a national nonprofit that aimed to
supplement STEM education in public schools by offering pathways that included Intro to
Engineering, Engineering Principles, Human Body Systems, Engineering Essentials and
Principles of Biomedical Science as elective courses that students could take during the school
day. The partnership served to provide students with exposure to potential STEM careers and to
add more advanced science experiences to student resumes, thus increasing student interest in
pursuing STEM careers and making them more competitive for college admission. However,
beyond PLTW the organization fell short of providing a strong catalog of STEM course
offerings. The only AP STEM courses offered were AP Calculus and AP Physics and the school
did not have an IB or Honors program. Prior to the pandemic, counselors chose middle school
students to take Algebra I in eighth grade based on standardized test scores and course grades,
thus putting them on the track to take AP Calculus by their senior year. During the pandemic this

27
option was removed, leaving students responsible for taking Pre-Calculus during the summer or
skipping Pre-Calculus to take AP Calculus. While students were still recommended by
counselors, they were required to use their own and their families’ time and resources to receive
the educational experience that was previously made available within the structure of the school
year. Additionally, the high school enrolled students scoring a level 1, out of a possible 4 on the
SBAC test, in a remedial math course, which they took concurrently with Algebra I during their
ninth-grade year. While remedial math courses are meant to provide extra time to fill gaps,
research has shown that acceleration, the act of teaching grade-level material and only pausing to
support pre-requisite skills, when necessary, is more powerful than remediation for increasing
student learning (Levin & Hopfenberg, 1991; TNTP, 2021). In fact, TNTP’s report states that
remediation can actually “exacerbate racial inequities” (2021, p. 1) by taking time away from
grade-level learning and eliminating opportunities for Black and Latine students to engage in the
same content as their White peers. Finally, students were only given options for math courses in
12th grade, when they could elect to take AP Calculus, a college-prep math course, or opt out of
math courses entirely. This lack of choice could also have led to lower motivation and may have
been a reason that students choose not to take a fourth year of math, thus making it much less
likely that they would pursue STEM careers post-high school.
Curriculum also affects students’ learning experiences. As mentioned above, Black and
Latine students have historically been deprived of inquiry-based, grade-level learning. The 2010
Common Core shifts valued focus, coherence, rigor, and the mathematical practices, each of
which was meant to focus instruction on grade-level content in ways that are meaningful and
relevant for students. As attention to equitable education grew, numerous companies developed
programs that emphasized inquiry-based conceptual math learning. UnboundEd, among other

28
learning institutions, stressed the importance of curriculum aligned to these shifts as an equitable
move to provide meaningful learning for historically marginalized populations (Baldwin et al.,
2021). Prior to the 2022-23 school year, the middle school used the Mathlinks curriculum. This
curriculum was rated at 11/14 for Focus & Coherence and 14/18 for Rigor & Mathematical
Practices by EdReports, an independent, educator-led nonprofit organization with a mission to
identify high-quality materials for students and teachers (EdReports, 2022). This was a low
rating compared to other curricula, and two of our PS 103 teachers who supported conceptual
inquiry-based learning argued that the curriculum did not provide students opportunities to
grapple with deep math understanding. They therefore spent hours revising the curriculum to
include speaking, writing, and exploration, when they could have been using that time to analyze
student work, deepen their own conceptual understanding, or collaborate with colleagues. The
other teacher used Mathlinks consistently, and his classroom learning experiences therefore
aligned with traditional direct instruction that lacked opportunities for students to explore. This
traditional instruction model typically valued White cultural discussion agreements including
“urgency, quantity over quality and only one right way” (Baldwin et al., 2021, p. 5), which
thereby valued White discussion agreements over Black and Latine language and behaviors. In
the Spring of 2022, our math department asked for and gained approval to adopt a new
curriculum, Illustrative Mathematics, which was an open-source curriculum endorsed by
EdReports. In 2022–23, teachers at PS 103 were focused on internalizing and implementing the
new curriculum. Additionally, we decided to adopt the accelerated version of the curriculum, in
which students learned the 6–8 standards throughout sixth and seventh grades, preparing them to
take Algebra I in eighth grade and college preparatory math courses in high school. This track
was typical in White schools, setting White students up for advantages as early as sixth grade.

29
This new curriculum attempted to ameliorate this by providing our Latine students with the same
opportunity. 
Although the high school used College Preparatory Mathematics (CPM), which was rated
at 15/18 and 16/16 respectively, curricula itself was not enough to ensure unbiased teaching.
Teachers who did not use the curricula in the way it was designed might have been removing the
intentional beneficial alignment. I believe this was the case at the high school. At the time of this
study, four of the five teachers using CPM had not received formal training for using the
curriculum and the fourth used CPM only virtually for most of her career. All five expressed
hesitation in using the curriculum to me during department meetings and 1:1 coaching meetings
and admitted that they frequently edited or dropped pieces of the curriculum in favor of more
procedural, traditional learning. This was also evident in my weekly observations and review of
lesson plans. While all teachers planned with and used the problems from CPM in class, shiftaligned discourse structures like team roles, collaborative problem solving, and learning logs
were consistently absent from my weekly visits and reviews. When pushed to explain their
hesitance, responses were typically that students did not work well in groups, students were too
far behind to access the grade-level work independently, or that there just wasn’t time to let
students struggle. These concerns came with the intent of supporting students, but they
perpetuated the deficit mindset that labeled Black and Latine students as not capable of
succeeding in grade-level, conceptual math. The impact was that Black and Latine students were
again not being allowed to explore via curricula that support deeper math understanding,
transferable problem-solving skills, and strong collaborative learning.

30
Role
At the time of the study, I held two roles at the network level. My primary role was as
Math Instructional Coordinator, serving both the middle and high school math team staff. The
overall intention of this role was to strengthen math instruction at both sites; this was typically
measured by student standardized test results and administrator observations. In my role as Math
Instructional Coordinator, I was consistently given the opportunity to make important decisions
that directly impacted instruction in the math department. These choices included the goals that
teachers set, the feedback they received, the development they engaged in, the instructional
moves that they were suggested to use, and the curriculum and courses that schools offered. Each
choice that I made was impacted by my identity; most relevantly to this study, by my Whiteness,
my epistemological beliefs developed from my own learning experience described above, and by
the positional power involved in my role. If I was to disrupt the deficit mindsets around Latine
mathematical funds of knowledge and identity, described above, to improve student learning
experiences, I had to consider the aspects of my identity that made me an outsider; most notably,
race and power. To do this, I used (critical) reflection, described in greater detail in future
sections, to uncover my biases, consider the impact of my identity on marginalized communities,
and take subsequent co-conspiratorial action. I place critical in parentheses intentionally, as
reflection was not always critical, although that was the intent. This (critical) reflection
continued throughout the course of this study. For the purposes of the study, I categorize my role
into four major responsibilities: instructional coaching, designing collaborative professional
development, supporting course design and curriculum implementation, and teaching. Each of
these will be described in greater detail, and for each category I will examine the ways in which

31
this category was contributing to the historically entrenched inequities described above. In
addition, I will speak to how the responsibilities of each role affected my study.
Most of my role was spent providing 1:1 coaching to nine different math teachers,
ranging in experience from 1–8 years and teaching courses from sixth grade math to PreCalculus, along with a remedial math course and a college preparatory math course. This
involved approximately 90-minutes of support per teacher per week, which entailed a
combination of goal-setting, lesson-observation, observation-feedback, lesson-reflection,
pedagogical modeling or research, and/or lesson-planning with exact timing of each dependent
on teacher goals. Goals were co-constructed by the teacher, the assistant principal, and me during
week 5 of the academic year. These were based on a combination of teacher-choice and
observer-feedback; in the year of the study, they were all aligned to the GLEAM framework
mentioned previously.
For my instructional coaching responsibility, I collected qualitative and quantitative data
and interpreted the data with the goal of improving instruction and student learning. Robinson
and Leonard (2018) remind us that “through the very act of collecting and analyzing information
from and about others, researchers hold power and privilege” (p. 70), which could also be true of
my coaching role as I observed, interpreted, and ultimately provided feedback. All feedback was
given from my own lens and with my own biases, and while I tried to critically reflect and frame
my feedback in ways that supported student learning, ultimately that feedback was my own
opinion. As this feedback informed not only yearly-goals, as described above, but smaller
weekly action-items that lead to the overall yearly-goal, my feedback impacted the direction that
teachers moved their instruction throughout the course of the year. I therefore impacted student
learning through this feedback. If I gave feedback that encouraged teachers to teach from a

32
White perspective, I would continue to harm our Latine students and devalue the funds of
knowledge and identity that they brought to the classroom. As a result of this study, the way in
which I meet this responsibility has shifted; this is discussed in more detail in the afterword.
Most of my time with teachers was spent during our individual meetings each week.
During these meetings we reflected on their weeks, discussed challenges that they were facing,
planned instruction for following weeks, and assessed movement toward their overall goal. Part
of my role in disrupting inequity was to monitor what assumptions I was carrying into our
conversations in the form of what I said. However, if I was to truly disrupt systemic deficit
mindsets in order to value student funds of knowledge and identity, I had to also actively
consider the teachers I worked with as adult learners and create a space in which their own biases
were noticed and challenged. This required that I create learning conditions in which teachers
felt safe to learn but challenged to confront their own thinking. This was the setting in which the
majority of my study took place, and the andragogical moves included in my theory of change to
assist them in (critical) reflection-on-action are further described in the conceptual framework
section of this study. As a result of this study, I became more aware of how the way in which I
was enacting my role as Instructional Coordinator was similar to the knowledge-for-practice
approach spoken of previously (Cochran-Smith & Lytle, 1999); my movement from this
approach toward that of an adult learning facilitator is explored at length throughout the
remainder of this study. For the purpose of this study, I distinctly separate “Instructional
Coordinator” from “adult learning facilitator.” I refer to myself as “Instructional Coordinator”
when I am speaking to my specific title at PS 103 and all of the responsibilities and positional
power that the title holds; when I refer to myself as “adult learning facilitator,” I am specifically

33
speaking to my broader responsibility and goal of supporting teacher learning, both at PS 103
and beyond.
In addition to attending to bias, I attended to the power dynamic in the coach-teacher
relationship. I was seen as an authority figure (even though evaluation was not a part of my role).
While my simultaneous role as a part-time-teacher (described below) could be viewed as a
balance of power between me and the teachers I worked with, I had to keep in mind that my role
was often viewed as a “teacher of teachers,” and that often teachers had internalized the same
message that I was fighting against; that they were relying on my modeling in order to learn. I
therefore attended to the types of learners that I believed the teachers I worked with to be, based
on a year’s worth of informal evidence, and used forms of assistance to help them experience the
constructive disorientation that supported them in reflecting on their practice in ways that
considered funds of knowledge and identity. These terms are further defined in my conceptual
framework.
In addition to providing adult learning experiences via individual coaching, I was also
responsible for planning and facilitating adult learning experiences within math department
meetings. These mandatory school-based meetings occurred every other week for 2 hours.
Content was determined by my own assessment of learning needs based on observed schoolwide trends, and occasionally based on universal network needs determined by the Instructional
Leadership Team (ILT). At the time of the study, the focus was on teacher pedagogical moves,
rather than on student contributions; I was therefore perpetuating the idea that student learning
was solely dependent on the actions of the teacher, as well as the knowledge-for-practice
approach to teacher development (Cochran-Smith & Lytle, 1999). Although I attempted to create
a space that included sharing of experiences and collective problem-solving, our collaborative

34
space did not acknowledge the role that identity played in our work and only descriptive levels of
reflection. Our space was safe, rather than brave, which Arao and Clemens (2013) warn is often
conflated with comfort; teachers feel comfortable because they are not being challenged to
confront their practice in meaningful ways. To disrupt this narrative, my goal was to assist the
teachers I worked with in creating more opportunities to notice and leverage student funds of
knowledge and identity in their classrooms. Research has shown that noticing student thinking
can continue learning for teachers after formal professional development ends (Jacobs et al.,
2010), and research around math identity has shown that students’ positive math identity
increases when student voice is prioritized and mathematical success is redefined (Aguirre et al.,
2013; Allen & Schnell, 2016). The reflective cycle depends on collaborative viewing of events
(Rodgers, 2002), and so I intended to use collective department meeting space as an opportunity
to bring multiple perspectives into the reflective process. In our collaborations we worked toward
noticing student thinking, describing the thinking as mathematical understanding, analyzing the
ways in which our identity impacted our noticing and describing, and then ultimately leveraging
the student funds of knowledge and identity in classrooms. This process required learning
conditions that foster a brave space in which critical reflection can occur; the ways in which I
worked toward fostering these conditions are addressed in my conceptual framework.
In considering course design and support, I had to think critically about the difference
between my identity and the identity of teachers and students. Were my decisions creating
instruction that imitates the way that I was taught, or the ways that our community wanted to
learn? Were our course offerings providing opportunities for our students, or preventing them for
further access? One of the biggest decisions that I had made in this role was adopting the
Illustrative Mathematics curriculum at the middle school, thus replacing the Mathlinks

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curriculum described previously. I was motivated to look for a new curriculum based on teacher
complaints about Mathlinks. After consulting all three middle-school teachers, together we
decided to adopt the Illustrative Mathematics curriculum endorsed by UnboundEd and
EdReports. When we discovered that there was an option for an accelerated sixth and seventh
grade curriculum that provided a pathway to Algebra I in middle school (and therefore advanced
math in high school), we made the decision to change our courses at PS 103 to entirely
accelerated sixth grade, accelerated seventh grade, and Algebra I. In advocating for this change
to the principal and with teachers, I believed that I provided our students access to further
opportunities via course offerings and set high expectations for their math abilities. However, it
is possible that I perpetuated inequities by asking teachers to adopt curriculum quickly and with
little support, again treating them like “knowledge-users rather than knowledge-generators” as
teaching-for-practice suggests (Cochran-Smith & Lytle, 1999).
Most of this study was conducted from the lens of my coordinator role; however, I also
taught one course of AP Calculus, which affected the ways that I interacted with participants and
is explored in later sections of this work. At the time of this study, I had one year of experience
in my coordinator role, compared to nine as a teacher; I therefore instinctively thought of myself
as a teacher first and a coach second. When coaching, I primarily used my teacher identity to
build trust and relatedness with the teachers I coached. My role in this study was as a researcherparticipant, and so I engaged in the reflective cycle alongside teachers. In my findings, I examine
how much I embraced my teacher identity versus my coaching identity and reflected on the ways
that both roles interacted with my action-research goal of becoming an adult learning facilitator.
As demonstrated above, at the time of this study I had begun to examine the ways that my
own Whiteness and biases affected my work at PS 103. I therefore informed my study design

36
and conceptual framework in what I had already uncovered; I additionally revised these
following the study because of the ways in which my research informed my current theory of
change. This study uses Rodgers’s Reflective cycle, as well as several andragogical moves, to
assist teachers as learners on the path to leveraging Latine students’ funds of knowledge and
identity in their math classrooms. In the next section I describe the revised conceptual framework
that both guided and resulted from this study; I will continue to use and revise this framework as
I progress as an adult learning facilitator. In this framework, I define in depth some of the terms
already mentioned previously: funds of knowledge and identity, Rodgers’s reflective cycle,
andragogy, and critical reflection. Following my conceptual framework, I detail the methods that
I used to conduct research around the following questions: How can I, in my role as Instructional
Coordinator at PS 103 (a) develop myself as an adult learning facilitator and (b) assist
participants in using a (critically) reflective cycle to see, describe, and analyze how their identity
impacts the ways they notice student funds of knowledge in their math classrooms?
Conceptual Framework
Maxwell (2013) contends that a conceptual framework is “a visual or written product,
one that explains, either graphically or in narrative form, the main things to be studied—the key
factors, concepts, or variables—and the presumed relationships among them” (p. 39). My
conceptual framework for this study, shown below in figure 1, is a revised framework based on
what I learned from my experiences both in the field and because of my analysis. It demonstrates
the relationships between several concepts that, because of my research and time in the field,
comprise my current theory of change. My long-term goal is to use the concepts set forth in this
theory of change to support teachers in: (a) noticing alternative forms of mathematical success as
student funds of knowledge and identity and (b) leveraging those funds to provide Black and

37
Latine students with math learning opportunities that are connected to their home learning
contexts. In doing so, students will be affirmed as mathematical thinkers and acquire strong
conceptual knowledge and skills that they can apply to whatever future context they choose.
While in the field, we did not fully reach either part of this long-term goal. However, we did
make progress towards both of my short-term action research goals; these were to (a) develop
myself as an adult learning facilitator and (b) to assist participants in using a (critically)
reflective cycle to see, describe, and analyze how their identity impacts the ways they notice
student funds of knowledge and identity in their math classrooms. I will continue to use this
framework beyond the scope of the study in order to work towards these short- and long-term
goals, and will continue to revise it based on data and my increasingly critical reflections.

38
Figure 1
Conceptual Framework
This revised conceptual framework serves as the theory of change for how I, as an adult
learning facilitator, will work within my school context to support teachers in leveraging
students’ funds of knowledge and identity into their lessons, thereby affirming students as
mathematical thinkers. This theory of change seeks to combat the ways in which current teacher
professional development structures and math instructional practices perpetuate White
supremacist tenets and deficit mindsets in math education for Black and Latine students. In doing
this work, both in this study and beyond, I acknowledge my own role in perpetuating hegemonic
structures within my school context and commit to using and revising this theory to be a more
critically conscious educator, adult learning facilitator, and community member.

39
My conceptual framework begins with arguing that a funds of knowledge and identity
mindset can be used to combat the tenets of White Supremacy mentioned in my context
statement, perfectionism and paternalism in teacher professional development and mathematics
instruction. I ground this work in my school and community context, as described previously.
Within that school context, I sought to create a learning environment that supported the
consistent (critical) reflection-on-action necessary for adopting new mindsets; again, I place
critical in parentheses intentionally, as reflection was typically descriptive with the goal of
eventually becoming consistently critical. As we began this work, I intended for the teachers and
me to collaboratively engage in descriptive reflection repetitively, cycling towards increased
criticality as we evolved in our abilities to name our biases and consider alternative perspectives.
I follow my conception of funds of knowledge and identity with my adaptation of the
Rodgers cycle (2002), which I believe should be used as a cognitive structure to help teachers
and me slow down and notice student funds of knowledge and identity, as well as our own
identities. I include “identity” in our reflective cycle analysis, as it is only when we consider the
impacts of our identities and our students’ identities on our instruction that we can begin to
authentically work toward dismantling deficit views in math education. Once we notice
alternative forms of mathematical success as students’ funds of knowledge and identity, we can
work toward experimenting with leveraging those funds of knowledge and identity long-term
and affirming Black and Latine students as mathematical thinkers, thereby breaking down deficit
views. Additionally, this study informed the way that I now think about leveraging teacher funds
of knowledge and identity in my own work; I therefore revised this conceptual framework to
include teachers bringing their own personal and professional experience into the cycle and
intend to continue to do so in my role as adult learning facilitator.

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For teachers to adopt this belief system and ultimately provide Black and Latine students
with more equitable and affirming math learning opportunities, the learning environment must be
one where teachers are supported in recognizing alternative perspectives and critically reflecting
upon their role in current systems; I therefore provide a more detailed explanation of the type of
learning environment that this level of critical reflection requires, as well as the moves that I
believe foster that environment. I follow the Rodgers cycle (2002) with a description of
andragogical tools and theories that I, as adult learning facilitator, depend on to honor teachers as
learners as they progress in their capacity to reflect-on-action. My theory of andragogy includes:
movement towards a knowledge-of-practice approach that treats teachers as learners (CochranSmith & Lytle, 1999); creating a brave learning environment in which teachers can experience
constructive disorientation (Arao & Clemens, 2013; Wergin, 2019) around the ways that their
identities inform their practice; and using forms of assistance (Tharp & Gallimore, 1991) to
support individual learners toward reaching our long-term objective of leveraging student funds
of knowledge in math instruction. It is my goal to consistently be assessing the effect of my
andragogical moves on teacher learning, perpetually working toward using an increasingly
critical lens. Finally, although neither my participants nor I achieved critical reflection during
this study, I assert that critical reflection remains an essential component of my theory of change
if we are to ultimately notice and leverage student identities in our classrooms and defy deficit
views of Black and Latine mathematical thinking. As a result of this study, I have come to
recognize the necessity of critical reflection in my own growth as well as the growth of my
learners; I therefore end my conceptual framework with a description of types of reflection, with
the intention of reaching critical reflection. Additionally, I will address this further in my
findings and in the afterword, as this conceptual framework will continue to be the theory of

41
change that I use to drive my future growth as an educator fighting for a more equitable system
of math education.
Funds of Knowledge and Identity
As stated previously, both traditional math education and general schooling systems are
rooted in White Supremacy ideology and oppress Black and Latine students by labeling them as
“less-than,” “behind,” and “low-achieving.” In contrast, a funds of knowledge approach “defies
deficit views of subjugated languages, communities, families and students” (Franquiz et al.,
2021, p. 405) and seeks to recognize “all students as creative multilingual and multidialectical
languagers, critically aware of the relationship between language and (social) power”
(Mckinney, 2017, p. 139, as cited in Franqiz et al., 2021, p. 406); this approach honors the
knowledge that students bring from their home cultures, actively fighting the idea of “less-than.”
Moll et al. (1992) defines funds of knowledge as “historically accumulated and culturally
developed bodies of knowledge and skills essential for household and individual functioning and
well-being” (p. 133). Additionally, Moll et al. (1992) speak to the importance of knowing the
student not just as a student, but as a whole child, as well as recognizing the learning that is done
in the home via trusted adults. I draw on this definition as a contrast to paternalism; teachers
must recognize that students learn mathematical reasoning first from the trusted adults in their
lives, and that teachers are not the only source of mathematical teaching that students encounter.
Research has expanded the original funds of knowledge approach to include the funds of identity
approach (Esteban-Guitart, 2016), which additionally recognizes the “accumulated set of
historically and culturally developed tools essential for constructing one’s identity and defining
individuality,” and includes “linguistic, cultural, literacy, and experiential resources” that
students both bring from home and absorb into their identities as they interact with family

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members and peers (Franqiz et al., 2021, p. 406). Together, the concepts of funds of knowledge
and funds of identity honor Black and Latine students and can therefore serve as a belief
framework for fighting White Supremacy ideology and deficit thinking in the classroom. I adapt
Moll et al.’s (1992) and Esteban-Guitart’s (2016) definitions to define funds of knowledge and
identity as the historically accumulated and culturally developed bodies of math reasoning,
knowledge, and tools that students use to construct their mathematical identities. However, in
this study I only used the term “funds of knowledge” with participants, as that phrase was a part
of their prior knowledge. In future work towards my long-term goal, I intend to include “and
identity” transparently. For the remainder of this study, I will use the term “funds of knowledge”
when referencing participant experience, and “funds of knowledge and identity” when speaking
to my long-term goal and future work.
Because of my research, I have recognized additional ways that both math education and
teacher professional development are currently upholding the more specific White supremacist
tenets of perfectionism and paternalism (Jones & Okun, 2001). Jones and Okun detail multiple
attributes of perfectionism; in addition to what I mentioned previously, I assert that, in the math
classroom, this “tendency to identify what is wrong; little ability to identify, name, and
appreciate what is right” (p. 1) can look like teachers focusing on a final numerical value rather
than identifying the correct conceptual thinking behind the numerical value, or seeing a different
representation of student understanding as wrong rather than another correct representation. This
then messages to students that they are wrong when they are expressing their understanding in
alternative ways, and can therefore lead to a diminished sense of mathematical self-efficacy. In
using a funds of knowledge and identity approach, teachers seek to identify, name, and
appreciate what is right; in doing so, they affirm students’ understanding and defy deficit views.

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Similarly, traditional teacher professional development and instructional coaching place
emphasis on areas for growth and missing skill sets (what is wrong) and ignore teacher
experience and knowledge (what is right). In applying the funds of knowledge and identity
approach to teachers as well as students, adult learning facilitators can move towards a
knowledge-of-practice approach that honors teachers’ personal experiences alongside theory and
inquiry (Cochran-Smith & Lytle, 1999); this will be discussed at greater length in the next
section.
In addition to perfectionism, both the math classroom and teacher development are
marked by paternalism, defined by Jones and Okun (2001) as the way “those with power often
don’t think it is important or necessary to understand the viewpoint or experience of those for
whom they are making decisions” (p. 4). This manifests in the hierarchical relationships between
instructional coaches, teachers, and students. In these relationships, coaches act as “expert”
teachers who provide advice and problem-solving methods to teachers, just as teachers do for
students. In both cases, the educator views themselves as the keeper of knowledge, where they
decide which skills their learners need, deserve, or are ready to learn rather than focusing on
creating learning experiences that honor learner identities, knowledge, and motivations.
This revised conceptual framework argues that a funds of knowledge and identity belief
structure can be used to combat the White Supremacist tenets of perfectionism and paternalism
that are often found in math classrooms. However, to support teachers in adopting this belief
structure and adapting their own teaching accordingly, teacher professional development spaces
must first be spaces that combine teacher knowledge, personal experiences, inquiry, and theory
(Cochran-Smith & Lytle, 1999); as well as possess the level of trust necessary for adults to risk
judgment and seek alternative perspectives (Arao & Clemens, 2013; Rodgers, 2002; Spikes,

44
2018). This requires that teachers engage in consistent reflection-on-action. In this study, I call
on Rodgers’s reflective cycle (2002) as an organizing structure to promote consistent reflectionon-action. Initially, I expect reflection-on-action to be descriptive; eventually, reflection will
move towards comparative (Jay & Johnson, 2002) and critical (Brookfield, 2017; Jay &
Johnson, 2002) as we include alternative perspectives. In this section, I discuss how Rodgers’s
reflective cycle promotes consistent descriptive reflection. Comparative and critical reflection
will be discussed in the final section of my conceptual framework, as I did not intend for
participants to reach them in this study but include them in my long-term goal.
Rodgers’s Reflective Cycle
To provide a cognitive structure that assists learners, including me, to engage in
consistent reflection-on-action, I call on Rodgers’s reflective cycle (2002). This cycle serves as
an organizing framework that assists teachers in slowing down to notice student thinking. This
iterative process includes seeing, describing, analyzing, and experimenting in which, at each
phase, participants are collaboratively engaging in reflection-on-action. In this study, I used
participant video to serve as the focus artifact for our (critical) reflection; in the future, I will
continue to do so, as well as consider other artifacts (e.g., student work or narrative recounting of
events) and their potential uses. Due to the time constraints of this study, we only engaged in the
first three phases of Rodgers’s reflective cycle; however, my long-term goal of leveraging
student funds of knowledge and identity requires that teachers also engage in the experiment
phase of the cycle. I therefore describe the see, describe, and analyze phases in greater detail
below, as well as briefly explain how I see the experiment phase supporting my long-term goal.
Within the cognitive structure of the reflective cycle, I use andragogical tools to support learners
in considering their identities in the analysis phase; this supports recognizing and defying deficit

45
views. This would move us toward Brookfield’s critical reflection (2017); all of this, including
the progress that we did make within the scope of the study, will be expanded upon in later
sections.
This cycle supports teachers through (critical) reflection on-action. In this study, we used
it to view video moments of practice in pairs and in larger collaborative groups, as Rodgers
(2002) emphasizes using the cycle collaboratively as a tool for exposing multiple perceptions of
a given moment of practice. At the onset of each cycle session, we engaged in the see phase
separately as we watched the video. The intent of this phase is to gain insight into what each
individual participant in the cycle instinctively notices. In the next phase, participants describe or
generate as many details as possible; this may be done multiple times, to unearth sights
previously overlooked. Together, these serve as a foundation for descriptive reflection, which
typically includes facts about what is happening, and interpretations based on observer
experience and feeling (Jay & Johnson, 2002). During the analyze phase, we consider alternative
views; this is the phase in which we will start to consider the ways our identities are affecting
what we saw and the ways that we describe. In the scope of this study, we intended to move
towards comparative reflection, where participants consider alternative views of what is
happening, research around the matter, and consider who is served from different interpretations
(Jay & Johnson, 2002). This will enable us to notice multiple different understandings of the
ways that students are demonstrating their conceptual math understanding, pushing beyond our
original interpretation of events, and recognizing previously overlooked funds of knowledge and
identity exhibited by students. As we ultimately grow towards critical reflection, we will utilize
colleagues and counter stories to consider power, race, hegemony, and implications of alternative
perspectives to reach a renewed perspective (Brookfield, 2017, Jay & Johnson, 2002). Although

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critical reflection was not reached during this study, I ultimately intend to use the cycle as a
critically reflective one to explore the dissonance between what teachers expect students to
contribute and what they are contributing, so that, moving forward, we can leverage that
understanding as a fund of knowledge in future moments of practice to deny deficit views and
affirm students as mathematical thinkers.
See
I define seeing for the purpose of this framework as the teacher’s intentional presence
and attention to their practice; this includes both student and teacher actions. Rodgers explains
seeing as the “ability to be present.” She says, “The more a teacher is present, the more she can
perceive; the more she perceives, the greater the potential for an intelligent response” (Rodgers,
2002, p. 236). Rodgers’s reflective cycle is meant to reflect on one’s own action and does not
specifically expand upon what the teacher should be seeing. Multiple other studies do explore
how teachers can choose what they are seeing, often referred to as attending or noticing. To more
specifically pursue my long-term goal of noticing and leveraging student funds of knowledge, I
draw on studies in which teachers attend specifically to student thinking. Goodwin’s (1994)
notion of professional vision, along with Sherin and van Es’s (2009) expansion in the math
classroom context, emphasize the importance of selecting where to pay attention and then
attending to the details of that instance. To do so, I used questioning, described in greater detail
in later sections, which included: “What do you see? Who is speaking? Who is responding?
What does that person look like? What are they doing?” Jacobs et al.’s (2010) idea of
professional noticing of children’s mathematical thinking expands upon this, adding in
intentionality as a necessary component of noticing. A limitation of these studies is that the
majority are colorblind in their attending to student thinking, and do not take the critical stance

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of self-noticing. Meanwhile, this study helped teachers attend to not just student thinking, but to
their own thinking. While viewing their practice, they saw the opportunities they created for
students to share their thinking, or lack thereof, as well as their responses to the knowledge that
students shared. This prepared us to consider what they recognized as mathematical knowledge
in the analyze phase.
Describe
During the describe phase, participants worked “through collaboration, to dig up as many
details as possible, from as many different angles as possible, so that one is not limited to the
sum of one’s own perceptions” (Rodgers, 2002, p. 238). This phase began collaboration;
participants shared their “sights” and listened to their colleagues. In this phase, Rodgers
emphasizes the difference between description, “what one sees,” and interpretation, “ascribing
meaning to what one sees” (2002, p. 238). The first is intended to be neutral, while the second is
affected by participant experiences, identity, biases, and ways of knowing. Although I did not
make this distinction clear within the timeframe of this study, we did emphasize “factual” sights;
in the future, I intend to make this distinction clear so as to recognize and name when our biases
are impacting our (critical) reflection. Additionally, this bias is attended to explicitly in the
analyze phase.
Analyze
Rodgers defines analysis as generating multiple explanations for what is occurring, and
then coming to a consensus about how one will act moving forward (Lampert & Ball, 1998;
Rodgers, 2002). I use her definition, which includes three parts: grounding analysis in the text of
experience, developing a common analytical language, and unearthing assumptions. This study
also pursued all three, with the attempt at a critical lens; the criticality will be expanded upon in a

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future section. In this study, analysis is grounded in the text of experience in the form of cowatching a video of a participant’s practice. When speaking of a common analytical language,
Rodgers states “teachers and facilitators need to assume the responsibility of asking each other to
define what they mean by words or terms that we assume are commonly understood” (p. 247). I
assumed that responsibility by sharing definitions of the major concepts included in this
framework; most notably, funds of knowledge. As mentioned before, I chose not to share “funds
of knowledge and identity” as participants were already aware of funds of knowledge, and I did
not want to immediately overwhelm teachers with too much new information. I therefore intend
to add to their current understanding as I continue to work with them beyond the scope of this
study. Any additional terms that we encounter in future work will be “forged by the group” (p.
247). Finally, Rodgers speaks to unearthing assumptions as an essential piece of the analysis
phase but does not speak to how our assumptions are often grounded in race, class, and other
pieces of our positionalities. In this study, the “analyze” phase of the Rodgers cycle is defined as
generating multiple cultural and epistemological explanations for what is occurring. Although
we did not reach this level of unearthing assumptions in this study, in the future I intend to use
the concept of counter stories to operationalize this, defined by Solórzano and Yosso (2002) as
“a method of telling the stories of those people whose experiences are not often told” (p. 32). In
my ongoing work, I will ground these collaborative discussions in critical questions such as:
“What is the impact of race on my beliefs?” “How do I situate and negotiate the students’
knowledge, experiences, expertise, and race with my own?” and “How do I, as a teacher, situate
myself in the education of others, and how do I negotiate the power structure in my class to
allow students to feel a sense of worth?” (Milner, 2003, p. 205). These probing question stems
will help me and participants to consider alternative ways that our students are demonstrating

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their funds of math knowledge, and how we as instructors are noticing and leveraging them in
our classrooms. As an entry point to this work, in this study we investigated Allen and Schnell’s
(2016) Multiple Ways to Redefine Mathematical Success in our final collaborative session and
discussed the representations of mathematical success that we are drawn to based on our own
strengths. Moving forward, we will attend to mathematical successes that we may ignore and use
them to inform what we look for as we engage in the reflective cycle.
Experiment
The final phase of the critically reflective cycle is experimentation, and for this definition
I adapt Rodgers’s call for “ideas for intelligent action” to instead be calls for ideas for identityconscious action. This phase emphasizes offering potential strategies in the form of “What would
happen if you tried …” versus giving direct “you should” advice, but the critical version will add
in a “How would this action notice and leverage student funds of knowledge?” Although I did
not get here during the span of this study, in the future I intend for participants to begin to
imagine ways that they might change their instructional practices after the learning that occurs in
this study, which would then signify that the learning was indeed deep. Additionally, I will
continue to meet with participants as a part of my typical role requirements and intend to
continue this work with teachers who are interested in the experimentation phase. I will continue
to use the andragogy moves, described in the next section, to support their learning.
Andragogy
Mezirow (1991) defines andragogy as an “organized and sustained effort to assist adults
to learn in a way that enhances their ability to function as self-directed learners” (p. 199). As a
result of this study, I use this definition of andragogy to pursue not only adult self-directed
learning, but a deeper degree of learning that supports adult learners in pursuing the funds of

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knowledge and identity belief system described above. For this, I depend on Wergin’s concept of
deep learning, in which learners’ “existing beliefs are challenged, but only within the limits of a
person’s perceived ability to handle the challenge” (2019, p. 35). For participants to experience
deep learning, the disorientation that they are feeling must be within what Heifetz et al. (2009)
refer to as the productive zone of disequilibrium. Wergin (2019) refers to this as constructive
disorientation; participants must feel that the disorientation that they are experiencing is enough
to encourage learning and not so uncomfortable as to make them shut down. Adult learning
facilitators must foster a learning environment in which participants have a deep enough level of
trust to take risks, seek alternative perspectives, and grow their practice (Spikes, 2018) without
shutting down. In this study, I used some of Arao and Clemens’s (2013) brave space discussion
agreements to set expectations for this type of learning environment, as well as displayed
vulnerability to increase trust. I used forms of assistance (Tharp & Galimore, 1991) to support
teachers in adopting a funds of knowledge and identity approach to instruction in their math
classrooms. The first of these forms was cognitive structuring, which supported learners with a
framework for thinking and acting (Tharp & Gallimore, 1991). The second was questioning
(Sahin & Kulm, 2008; Tharp & Gallimore, 1989), which I used in conjunction with cognitive
structuring to assist participants and myself in turning toward practice and moving toward
critical reflection. All these andragogical moves pushed our learning experience toward the
knowledge-of-practice approach mentioned previously.
Teachers as Learners
As a result of this study, I revised my conceptual framework to place teachers more
firmly in the role of learners and me in the role of adult learning facilitator. As explained above,
I define learning not as simply acquiring knowledge, but rather in alignment with Wergin’s

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(2019) definition of deep learning, which emphasizes lasting mindset shifts over skill or
knowledge acquisition. My field-experience, analysis and (critical) reflection helped recognize
the relationship between perfectionism, paternalism, and Cochran-Smith and Lytle’s (1999)
concept of knowledge-for-practice, in which teaching is “understood primarily as a process of
applying received knowledge to a practical situation” and teachers are regarded as “knowledgeusers, not generators” (p. 257). Professional development is often looked at as an atomic single
event that can provide a quick fix (Webster-Wright, 2009) rather than a deep learning
experience. To work against this, I argue that, just as “teachers must work to broaden students’
understanding of what it means to be good at math so they, too, can find their place in the
mathematics classroom” (Horn & Campbell, 2015, p. 169), adult learning facilitators must push
away from a knowledge-for-practice approach and toward a knowledge-of-practice approach. A
knowledge-of-practice approach supports teachers in engaging in “inquiry, connecting their work
in schools to larger issues, and taking a critical perspective on the theory and research of others”
(Cochran-Smith & Lytle, 1999); this is more aligned with the deep learning required for adult
learners to alter current belief systems. This additionally aligns with Webster-Wright’s (2009)
concept of authentic professional learning, which she states is “the lived experience of
continuing to learn as a professional” (p. 715). Together, the ideas of constructive disorientation,
knowledge-of-practice, authentic professional learning place the emphasis on learning rather
than on training, which aligns with the lasting mindset-shift required of deep learning.
Wergin argues that for disorientation to be constructive, learners must experience
autonomy, efficacy and relatedness. In this study, I focused on relatedness, or feeling socially
connected, cared for, and significant among others (Wergin, 2019); this is discussed more in the

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next section as a way to build trust. Here, I also include descriptions of autonomy and efficacy,
as I still deem them important components of my ongoing theory of change.
Wergin defines autonomy in the professional context as “the freedom to contribute to the
common good” (2019, p. 64). In this case, I argue that the common good is approaching math
education with a funds of knowledge and identity approach, to fight against deficit mindsets of
Black and Latine students’ math abilities. However, I admit that this is the good that I, as a
White researcher and adult learning facilitator, am pushing toward. As Mezirow states, the
learner has to determine what the learner wants to learn (1991). In the scope of this study, I did
not involve learners in determining what they wanted to learn; in the future, this is something
that I intend to spend more time on. Instead, in this study I leaned on vulnerability and shared
why I believed that this reflective cycle would help me get to my personal educator goal of
leveraging student funds of knowledge. Wergin also emphasizes the importance of a “clear but
manageable challenge,” which I provided in the form of session learning objectives and the
broader scope of how those learning objectives worked toward achieving our ultimate goal. This
is all described in the actions section of this study.
Efficacy can be built when a learner is given tasks within their proximal zone of
development and is a crucial element of motivation (Heifetz et al., 2009; Rueda, 2011; Wergin,
2019). Participants who have high self-efficacy will believe that their work can have an effect in
their context (Bandura, 1977; Wergin, 2019). In this case, I needed participants to believe that,
by participating in this study and engaging in the critically reflective cycle, they would be able to
notice and leverage student funds of knowledge in order to affirm students’ mathematical
thinking. Although we did not get to enactment, participants did work toward internalizing the
reflective cycle as a tool that they can use toward future enactment. To add to the intentionality

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of our work, we created a setting for “deep work,” as free from distractions as possible. Our
sessions occurred in private settings away from students and, when possible, away from other
distractions such as email, grading, or other meeting interruptions. I modeled this by refraining
from checking my own phone or email during our space together and will hold our time together
as a top priority in my schedule, as well as relating this professional discussion agreement back
to our brave space discussion agreement of respect. Other ways in which we strengthened our
learning environment are described in the next section.
Learning Environment
According to Wergin (2019), deep learning occurs when there is constructive
disorientation, defined as a “feeling of arousal brought about by a perceived disconnect between
the current and a desired state, accompanied by a sense of efficacy that one is capable of dealing
with that disconnect” (2019, p. 27). To keep disorientation constructive, as we moved toward a
funds of knowledge approach, I used andragogical moves to build a learning environment that
deepened trust, moved toward a brave space, and treated teachers as learners; these strategies are
described in detail below.
Deepening Trust. For us to take the risks necessary to experience disorientation, our
learning environment required a deeper level of trust than was present at the beginning of our
work together. According to Spikes (2018), I, as a learning facilitator, can deepen the trust
necessary for (critical) reflection and growth by modeling my own vulnerability. I therefore
include this in my theory of change to demonstrate my trust in participants, as well as to build
relatedness, which refers to feeling socially connected, cared for, and significant among others
(Wergin, 2019). Some of this was already in place prior to the study; our department already met
twice a week and had positive professional relationships, as evidenced by choosing to eat lunch

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or sit together at grade-level meetings, emailing each other for advice, offering suggestions, and
covering classes for one another in emergency situations. In our coaching meetings each teacher
had told me individually that they feel appreciated by me and can trust me with their challenges.
During the scope of this study, we used this foundation to increase vulnerability. Additionally,
trust and vulnerability are required for participants to publicly name and confront their biases,
which is a necessary component of critical reflection (Brookfield, 2017). As the adult learning
facilitator, it is my responsibility to model this vulnerable work, and I therefore demonstrated
each activity that I asked participants to do during this study and modeled my own (critical)
reflection throughout.
I also called on Horn and Little’s (2010) concept of normalizing to build relatedness.
Horn and Little (2010) offer normalizing as a move that provides learners with reassurance and
solidarity, by defining problems as common, normal experiences in all classrooms. However,
Horn and Little also warn that too much reassurance can lead to turning away from practice; in
this study, I anticipated that this could look like blaming systems, rather than looking inward
toward ways in which their identities are impacting their classrooms. As normalizing was already
something that occurred in our department meetings, I did not prompt this practice. Instead, I
attended to it during analysis to determine how I responded to it as an adult learning facilitator to
turn toward practice.
Building a Brave Space. To create disorientation, adult learning facilitators must assist
learners in considering alternative views; doing so challenges existing mental frameworks and
allows for the possibility of deep learning (Wergin, 2019). In this study, the funds of knowledge
and identity approach was intended to challenge current hegemonic ways of thinking, and I
worked toward building the brave space necessary to engage in these social justice discussions.

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Arao and Clemens (2013) define a brave space as in contrast to a safe one, as “authentic learning
about social justice often requires the very qualities of risk, difficulty and controversy that are
defined as incompatible with safety” (p. 169). At the outset of the study, our space was a safe
one. As explained in my context statement, our department had previously worked together
toward shared goals and were already comfortable with one another. However, few risks had
been taken in this space. My theory of change therefore depends on guiding and probing
questions as a form of assistance to push participants to consider their racial, ethnic, and gender
identities in their responses. This includes asking participants to consider the ways in which their
internalized biases affect the ways that they see and describe students, with the intention that
doing so will change future ways of noticing and leveraging student funds of knowledge and
identity to affirm student mathematical thinking. Arao and Clemens (2013) assert that just using
the term brave space at the onset has a positive impact; however, I did not include that in this
study, as I decided that providing learners with three new theoretical ideas (funds of knowledge
and identity, the Rodgers cycle, and brave space) would be asking participants to simultaneously
grapple with multiple new concepts and that too large of a disorientation could be
unconstructive. However, I still include this statement in my theory of change, as I intend
ultimately to transparently include the concept of a brave space into our collaborative
discussions. Similarly, in this study I only intentionally unpacked the discussion agreement of
challenge by choice; the other three suggested brave space discussion agreements are still
included below, as I ultimately intend to use them in future learning environments. When that
happens, I intend for participants to discuss offered discussion agreements with a collectivist
approach (Arao & Clemens, 2013), to increase buy-in and create a shared expectation at the
onset of our time together.

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I began this study by introducing the discussion agreement challenge by choice, which
sets the condition that participants can determine to what degree they participate in each activity.
Participants were initially asked to join the study and gave initial consent, but I continued to
reiterate their choice in each session of the study. This study and theory of change are grounded
in the ways in which adult learning facilitator’s power and position impact the learning
environment of teachers; this discussion agreement is therefore essential to combat the pressure
participants might have felt in this study, as well as the way that I encourage movement toward a
brave space in future learning environments. This will be addressed in more detail in the methods
section in relation to this study. In this study, all teachers agreed to participate. In future work, if
teachers choose not to participate in the learning, I will ask them to reflect on how their silence
impacts the group and the degree of learning that they will experience by making that choice
(Arao & Clemens, 2013). 
For controversy with civility, I align with Astin and Astin’s (1996) definition: “a value
whereby different views are expected and honored with a group commitment to understand the
sources of disagreement and to work cooperatively toward common solutions” (p. 59). Although
this was not operationalized in this study, moving forward this will look like teachers sharing
their sights and descriptions, considering how their identities shaped those sights and
descriptions, and seeking to understand other participants’ views. They will incorporate other
views into their analysis and, ultimately, work toward imagining new ways to notice and
leverage student funds of knowledge and identity in their classrooms. Similarly, the next
discussion agreement, own your intentions and your impact, will look like participants
acknowledging the inadvertent harm caused by their implicit biases. In future learning
environments, I anticipate pushing participants and myself toward this one by grounding all

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reflections-on-action during our cycle in both, asking us all to think about both intent and impact
during our sights, description, and analysis. The fourth discussion agreement, respect, was
already in place within our department. However, in this study I intended to include the idea of
multipartiality by calling attention to the fact that different cultural contexts view respect
differently. I did not transparently do this within the scope of this study; in the future, I will
attend to this idea when discussing students during our critical reflection by asking participants
to reframe deficit statements. This will look like reframing words like “lazy,” “low performing,”
and “disrespectful” by seeking details, sights, and analysis overlooked by our own identities and
considering ways in which other identities might view the scenarios differently. This will also
occur in collaborative spaces when teachers are speaking to each other’s actions and words. The
final discussion agreement, no attacks, was already informally in place in our department
meetings as “use I statements.” This discussion agreement was intended to assist us when
comments were made due to defensiveness or direct disagreement; however, in the scope of this
study this did not occur. In future work, I will use no attacks to push participants to investigate
their own reactions instead of lashing out at others. My (critical) reflections during this study at
times attended to how my identity and biases affected the degree to which I was personally
upholding these discussion agreements, as well as the ways in which my actions assisted others
to uphold them; in the future, I will do so with more consistency. Although our space did not
fully reach a brave space, I did use the theory to inform my andragogical decisions and
transparently used the challenge by choice discussion agreement to push us closer to a space in
which we are vulnerable, exposed, and taking the risks required for authentic social justice
learning (Arao & Clemens, 2013).

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Forms of Assistance
Tharp and Galimore (1991) offer forms of assistance as cognitive tools to support
learning. I argue that cognitive structuring and questioning are forms essential for supporting
teacher reflection-on-action. Forms of assistance are often “intertwined, occurring in
combination and at times simultaneously” (p. 47); in my theory of change, I use Rodgers’s cycle
and a funds of knowledge and identity lens as the main cognitive structures to provide
frameworks for thinking and acting. Questioning is used in conjunction with cognitive
structuring to support teachers in turning toward their practice and noticing student funds of
knowledge within each phase of the cycle. In this section, I begin by describing how I used
cognitive structuring to provide a framework for thinking and acting. I then elaborate on types of
questions and the ways that they work within the cognitive structures to promote noticing student
funds of knowledge and identity. I end by describing how different forms of assistance can
support different types of knowers in reflecting on their practice; the effectiveness of these forms
of assistance on different types of knowers is analyzed in my findings.
Cognitive Structuring. Cognitive structures provide “explanatory and belief structures
that organize and justify” (Tharp & Gallimore, 1991, p. 63). In my ongoing theory of change, I
use Rodgers’s reflective cycle (2002) to explain and organize consistent reflection-on-action. I
use funds of knowledge and identity as the belief structure; this serves as the lens through which
we deepen our reflection from descriptive to critical. The first cognitive structure, the Rodgers’s
cycle (2002), provides an organizing structure to slow teachers down and prevent hasty
interpretation (2002). As teachers work through the see, describe, analyze, experiment phases,
their actions (in this case, reflection on their practice) are organized into sets with distinct
expectations for acting. This formalized structure can support teachers in internalizing a

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reflective process that they can refer back to beyond the scope of our learning experiences
together, and supports the cognitive work of reflection-on-action. Rodgers’s reflective cycle on
its own does not explicitly consider the ways that our own interpretation is often fueled by
internalized racial bias or attend to what we are reflecting on specifically; I therefore weave a
funds of knowledge and identity belief framework within Rodgers’s cycle to provide more focus
for teachers during the see, describe, and analyze phases of the cycle. To support teachers in the
cognitive activity of taking up this belief framework, I depend on questioning within Rodgers’s
cycle.
Questioning. In my theory of change, I depend on questioning in order to move
participant reflection from descriptive reflection towards critical reflection. This movement
towards critical reflection is necessary for participants to adopt the funds of knowledge and
identity belief framework (Jay & Johnson, 2002; Moll et al., 2002; Rodgers, 2002). When I refer
to questioning, I refer to the collection of factual, guiding, and probing questions (Sahin & Kulm,
2008) that I believe to be essential to my theory of change. The first type, factual, mainly
supports teachers in taking up the cognitive structures mentioned previously, while the last,
probing, mainly supports deepening teacher reflection. Guiding supports both purposes.
In order to (critically) reflect on our practice, we must consider the ways in which our
identities impact the ways in which we notice student funds of knowledge. Factual questions
serve to orient us to our own identities and to the identities of our students. These questions are
particularly useful in the see and describe phases of Rodgers’s cycle, as they call attention to
details that we initially missed. Questions like, “Who was speaking? What do we know about
that student’s identity? What do we know about their home experiences? What knowledge did
the student share?” serve as mental prompts for teachers as they attempt to see as many details as

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possible, and invite teachers to attend to identity-based details that they may not have
immediately considered. Guiding questions, or those that ask a series of intentions to lead or help
(Sahin & Kulm, 2008), assist learners in seeing how the belief framework fits into the structural
framework of Rodgers’s cycle. These direct teachers when they are unsure of what to consider
next, and serve as cognitive training for considering funds of knowledge and identity in each
phase of the cycle. Questions like, “What should we consider next? How might what you said
relate to funds of knowledge? What might that say about your own identity?” assist teachers in
taking up both the organizing framework with a funds of knowledge and identity lens. Finally,
probing questions are open-ended, higher-order questions that push learners into places of
(critical) reflection on their practice (and ultimately, disorientation), as we seek to examine their
current ways of knowing and imagine alternatives (Brookfield, 2017; Rodgers, 2002; Sahin &
Kulm, 2008). These questions, “which ask for clarification, justification, or explanation” (p.
224), push participants to provide explanations for why participants noticed what they did, how
they understood student thinking, and why they responded to students in the way that they did. In
collaborative settings in the scope of this study, probing questions can push participants to
explain their own perspectives to the group and to justify where they believe their interpretations
are coming from. As a result of this study, I include in my theory of change an increased
criticality of my probing questions. For this, I turn to Milner’s (2003) list of critical reflection
questions, which include,
How do I, as a teacher, situate myself in the education of others, and how do I negotiate
the power structures around race in my class to allow students to feel a sense of worth?
How might racial influences impact my and my students’ interests in the classroom? How
might I connect lessons to those interests? To what degree are my role as teacher and my

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experiences different than the experiences and expertise of my students? What
knowledge is there to be learned from my students? (p. 205).
Additionally, I include in my theory of change increasing transparency about these types
of questions and using their descriptions frequently, to assist participants in noticing the types of
questions that they are using and how those types might be affecting the ways that they are
leveraging student funds of knowledge and identity. I did not do so in this study, as I feared that
introducing too much new knowledge at once could overwhelm teachers’ cognitive loads and
also place me too much in the role of the “expert,” and moving forward I intend to introduce
them when learners are cognitively available for more information.
Types of Knowers. In my revised conceptual framework, I recognize the continued
importance of strategically using forms of assistance in ways that best challenge each teacher as
an individual learner. In this study, my inability to fully be present to my role as adult learning
facilitator inhibited my ability to do so in real time, particularly in the first phase of the study. As
I grew in my role and in my ability to attend to my learners as individuals, I began to use forms
of assistance more strategically; however, I did not achieve everything outlined in this section.
This remains in my conceptual framework as a continuing part of my theory of change, with the
intent of growing in this skill as I continue to develop as an adult learning facilitator.
Prior to this study, I reflected upon my prior relationships and interactions with each
participant to gather evidence toward the type of knower they aligned with most (DragoSeverson & Blum-DeStefano, 2017). This section describes instrumental, socializing, and selfauthoring knowers and the ways in which the forms of assistance described previously will push
each type to engage in constructive disorientation. The fourth type of knower, self-transforming,

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is included here as my ongoing theory of change, although it was not relevant to this study as no
one, including myself, is a self-transforming knower yet.
According to Drago-Severson and Blum-DeStefano (2017), instrumental knowers orient
to concrete strategies and appreciate a “right way” of doing things. Prior to this study, two of my
participants provided evidence of this type of knowing; this evidence is described in greater
detail in later sections. For these knowers to experience constructive disorientation, learning
opportunities required clear expectations. This is not to be confused with instructing teachers
how to think or what instructional choices to make; rather, the clear expectations were in our
brave space discussion agreements, in the organizing cognitive structure of the Rodgers cycle
process, in the form of note catchers and written prompts, and in clearly defined learning
objectives for each session. To create constructive disorientation within these clear structures and
expectations, questioning assists participants in thinking about who defines the “right way” and
how their identities inform their need for concrete strategies. More specifically, factual questions
support instrumental knowers with a concrete way of answering, guiding questions helped orient
them within the cycle, and probing questions helped them to consider other “ways” that they had
not considered. Although not analyzed in my findings, I additionally included modeling as a
form of assistance to support instrumental knowers; this provided concrete strategies in the form
of me modeling each activity before teachers engaged. For example, I chose to use my own
video as our first artifact for reflection-on-action, so as to provide an example of what reflectionon-action using the Rodgers’s cycle could look like.
Socializing knowers typically orient themselves to others’ opinions, values, and
assessments. Additionally, socializing knowers may be overly concerned about disappointing
others or sharing intimate thoughts and disrupting relationships (Drago-Severson & Blum-

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DeStefano, 2017). A space with deeper levels of trust can support participants in believing that
they are validated by peers, even as they experience challenge and risk. Socializing knowers are
then able to operate from a grounded commonality, rather than feeling insecure about
differences; when differences are encountered, the vulnerability and trust in the space can help
them be honored as alternative perspectives. In providing Rodgers’s cycle and the funds of
knowledge and identity approach, socializing knowers are provided with a grounded
commonality in the language being used and the purpose of our reflection. However, as stated
above, too much commonality could enable socializing knowers to blame systems, rather than
take responsibility (Horn & Little, 2010). To combat this, probing questions should push
socializing knowers to consider how their own actions or biases impacted their shared
experiences, to move them toward disorientation.
I did not believe any of my learners to be self-authoring or self-transformative during this
study; however, as I continue to use this theory of change in my future work, I include tailored
forms of assistance to support self-authoring and self-transforming learners here. Self-authoring
knowers, “have grown the internal capacity to consider others’ expectations, assessments, and
suggestions in relation to their own bench of judgment” (Drago-Severson & Blum-DeStefano,
2017, p. 464). Self-authoring knowers therefore may not need guiding questions to assist them
towards a framework, and instead should be probed to determine where their “bench of
judgment” came from and how that impacts the instructional decisions that they make with their
students. Milner’s (2003) questions, posed in the previous section, could be more accessible to
self-authoring teachers and serve as a structure for movement towards more independent
reflection. This independent reflection could then be a starting point for deeper discussions
around funds of knowledge and identity. These questions could also assist self-transforming

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knowers; however, self-transforming knowers “yearn for interconnection and co-construction of
meaning” (Drago-Severson & Blum-DeStefano, 2017, p. 465). They therefore may benefit from
more public discussions around Milner’s prompts, as well as using Rodgers’s cycle in larger
collaborative groups where they can benefit from more viewpoints and increased levels of
collaboration. In my revised theory of change, I recognize that my novice state as a new adult
learning facilitator limited me to providing similar forms of assistance to all learners, despite
their type of knowing; moving forward, I intend to particularly attend to the types of questioning
I use and the structures I provide for each learner. The progress that I did make in turning toward
my learners as individuals is addressed in my findings, and my plans moving forward are further
elaborated on in my afterword.
Critical Reflection
Critical reflection remains an essential part of my theory of change. Prior to this study, I
worked to increase the criticality of my reflections during my coursework, and was still at a
novice state when I entered research. Throughout the study I wrote reflections that I intended to
be critical; however, they often were not and I therefore refer to them as (critical) reflections to
indicate attempt at criticality, rather than reaching truly critical. Critical reflections are intended
to examine how my own identity and power affect the ways that I act as an adult learning
facilitator. They are informed by this theory of change, and additionally examine the extent to
which I incorporate the concepts already laid out in this framework into the learning experiences
that I facilitate. Critical reflections are intended to minimize harm to my school community, for
as Milner states, “when researchers are not mindful of the enormous role of their own and others’
racialized positionality and cultural ways of knowing, the results can be dangerous to
communities and individuals of color” (2007, p. 1); post-study, I revise this to apply both in and

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out of the formal research field. In my ongoing theory of change, I define critical reflection as
the intentional and iterative process of identifying, checking, and analyzing assumptions to
engage in subsequent action. This definition is grounded in Brookfield’s definition of critical
reflection, which is “the sustained and intentional process of identifying and checking the
accuracy and validity of our teaching assumptions” (2017, p. 3). Rather than stopping at
identifying, checking, and analyzing assumptions, I believe in using critical reflection to make
meaningful change in my context. In this study specifically, the change I sought was two-fold;
first, to make meaningful change in the way that I impacted my school community as an adult
learning facilitator and second, to support teachers in making a meaningful change in their
instruction using a funds of knowledge and identity approach. I include iterative in this definition
as iteration is an essential part of action research (Herr & Anderson, 2015), and as I intend to
continue to reflect and grow using this framework over the course of my career. In my revised
theory of change, I assert that I will continue to strive towards critical reflection to uncover my
own assumptions and the ways in which they are informing my actions as an adult learning
facilitator.
In speaking of “assumptions,” I seek evidence of both explicit and implicit assumptions
in my own written reflections and in the verbal exchanges between teachers and me. Explicit
assumptions are those “at the forefront of our consciousness,” and implicit assumptions are those
that “soak into consciousness from the professional and cultural air around you” (Brookfield,
2017, p. 3). As Brookfield states, assumptions “usually can’t be seen clearly by an act of selfwill.” He therefore recommends four lenses of critical reflection to help us “see ourselves from
unfamiliar angles” (2017, p. 61). According to Brookfield, our students’ eyes help us to uncover
assumptions around power. As an adult learning facilitator, my “students” are the teachers who I

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work with. I will therefore refer to this lens as “adult learners’ eyes” or as “student learners’
eyes” in this study to not confuse teachers with the students who they teach. I use this lens, both
in this study and moving forward, to reflect upon the power I hold as a White Instructional
Coordinator, and how this impacts my interactions with my participants. I also use this lens to
recognize when I may have unintentionally reverted to a colorblind stance, why I may have done
so, and how I can model identity-conscious language in future interactions. The second lens is
theory, and for this aspect of reflection I draw from the literature in this conceptual framework.
Although I did so inconsistently in this study, going forward I will return to this framework to
reflect upon the ways that I am engaging with funds of knowledge and identity, perpetuating
White supremacist culture, perpetuating, or defying deficit mindsets around Black and Latine
students, leveraging andragogical moves, and engaging in critical reflection. My reflection on the
degree to which my andragogical moves create moments of constructive disorientation for
different learners informs adjustments for future learning experiences. Brookfield’s third lens is
personal experience. As I continue to teach AP Calculus courses and work with teachers to
notice and leverage students’ funds of knowledge to affirm students’ mathematical thinking, I
will also be thinking of my own AP Calculus pedagogy. I intentionally placed this lens third, as
it is the one that comes most naturally to me. I am a socializing learner, which will be explained
more below, as I enjoy connecting with others over shared experiences. Often my conversations
involve discussing similarities. Using this lens, I consider what is different; how does my identity
make my experiences different from my participants? How did my education as a White female
student in a predominately White public school district inform the pedagogical moves that come
most naturally to me? How does my identity continue to impact my teaching and coaching? I
will also use this lens to consider the personal learning experiences I’ve had that made me (a)

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reflect on my identity and (b) change my mindset and behavior because of those realizations, to
compare these moments of disorientation to the moments of disorientation that my
participants/colleagues experience.
Brookfield’s fourth lens is colleagues, and in this study, I was the sole researcherparticipant. I therefore did not have true colleagues within the study but used my dissertation
chair as a fourth lens during my research and analysis phases. Following the conclusion of this
study, I will maintain relationships with colleagues from this program as well as with my
participants; this will be discussed further in the afterword. Regardless of formal positional
power, these colleagues “unravel the shroud of silence in which our work is wrapped” (2017, p.
66). Although I did not do so during this study, I ultimately intend to share my critical reflections
with colleagues, seek their feedback, and use their offerings to dig deeper into the assumptions
that I am carrying into my work. 
The next section of this study details the methods that I used to (a) critically design the
study in a way that attended to race, bias, White supremacist tenets, and learner experience (b)
engage with teachers in Rodgers’s reflective cycle to see, describe, and analyze the ways in
which we are creating opportunities to notice and leverage student funds of knowledge and
affirm students’ mathematical thinking and 3) collect and analyze data to assess my own
andragogy and criticality and the effects that they had on teacher reflection and growth.
Research Methods
This section describes the action research approach, data collection, and data analysis that
I used to complete this study. The purpose of this study was to examine how I, as an adult
learning facilitator, could use andragogical moves and a critical adaptation of Rodgers’s
reflective cycle to support teachers in recognizing the ways their identity impacted the noticing

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and leveraging of student funds of knowledge in their math classrooms at PS 103. Prior to the
start of implementation, I engaged in (critical) reflection, used previously collected informal
observations to assess my participants according to Drago-Severson and Blum-DeStefano’s
(2017) descriptions of social justice orientations for types of knowers, and chose andragogical
moves that I believed would best move my participants to places of deep learning via
constructive disorientation. In the first phase of the study, I used theory and participant personal
experience to ground three participants in a common language around funds of knowledge and
the Rodgers cycle. As mentioned previously, I depended on participant prior knowledge of funds
of knowledge and chose not to overwhelm participants in this stage with including funds of
identity. I next supported participants in practicing the see and describe portions of the cycle
within 1:1 coaching sessions, using forms of assistance to assist teachers in slowing down and
seeing my practice. In the next phase, I engaged teachers in the Rodgers cycle in a larger
collaborative department meeting setting to increase the number of sights and descriptions
available to us. In individual meetings of this cycle, we applied the see and describe portions of
the cycle to their own practice and began to look for trends and reasons for the things we were
seeing. The final phase involved teachers completing the see, describe, and analyze portions
again, both individually with me as well as in pairs during our final collaborative session. We
ended by engaging in descriptive reflection of the process and what we discovered about our
own identities and brainstorming how we might engage in the experiment phase post-study. The
data I collected, in the form of audio recordings of meetings, transcripts, written (critical)
reflections at the end of each cycle, and fieldnotes, were used to answer the following research
question: Within my role of Instructional Coordinator, how did I (a) develop myself as an adult
learning facilitator and (b) assist participants in using a (critically) reflective cycle to see,

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describe, and analyze how their identity impacted the ways they noticed student funds of
knowledge in their math classrooms?
Participants and Settings
This action research study took place during the Fall 2022 and Spring 2023 semesters at
one of my school sites, PS 103. I engaged in self-study action research to address a specific
problem in a practice-based setting, with the goal of facilitating change in my current context
(Herr & Anderson, 2015; Merriam & Tisdell, 2016). I used non-random, purposeful sampling
when choosing participants, which provided me with a small, intentional sample from which I
could learn the most (Merriam & Tisdell, 2016). My sample was composed of three teachers
who taught full-time middle school mathematics. When I began coaching at PS 103 in the Fall of
2021, I began working with two of the participants in this action research study. This meant that
by the time that the study began in Fall 2022, I had already spent a full year understanding them
as adult learners and instructional professionals. While this meant that I had already started the
process of building trust with these participants, it also meant that I had already built a
foundation that may or may not have been working toward the same goals of this study. In the
following sections, I describe in greater detail the specific participants involved in the study, the
settings, and my actions and the data collected within each action research cycle. 
As the primary research instrument and a collaborator in the cycle, I considered myself to
be a participant in this work. At the outset of this study, I placed myself as a socializing knower
working toward a self-authoring knower, which would look like “learning, leading, working,
living, and loving according to self-determined values and internally derived standards is of
utmost concern” (Drago-Severson and Blum-DeStefano, 2017, p. 464). I am driven by my
passion for providing equitable math education opportunities to all students, particularly students

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of color, and am working on intentionally grounding all the decisions that I make in these values.
Prior to this study, I found myself still caught in prioritizing others’ feelings over my own and in
looking for my worth in the acceptance or praise of those I deemed superior to myself (as
socializing knowers are described to do). As I already had relationships built with my
participants, I feared prioritizing their feelings over my own during the study, thereby choosing
not to challenge them as deeply as I would need to if I was going to create constructive
disorientation. I also considered the temptation to adjust my study if I received push-back from
administrators in the case that I created destructive disorientation for learners. Throughout this
study I analyzed my own (critical) reflections and discussion contributions for examples of ways
as well as looking for ways that I was naming and confronting my own internalized racial biases;
in the afterword, I consider my current growth toward becoming a self-authoring knower.
Participants
PS 103’s mathematics department was composed of three teachers, and all three agreed to
participate in this study. All three had taught for more than 4 years and two had been at PS 103
for multiple years. Both returning PS 103 teachers had, at the time of the study, experienced 13
months of coaching with me. As research began in November of 2022, the third had received 3
months of coaching with me. All three attended the UnboundEd Standards Institute in June of
2022, in which they received basic training around using funds of knowledge to affirm student
math identity. They therefore already had basic exposure to a funds of knowledge approach in
math instruction prior to beginning this study.
Blake was a Korean, cishet (cisgender, heterosexual) woman who began her sixth year of
teaching and her first at PS 103 in Fall 2022. I initially assessed Blake as an instrumental
knower. Evidence for instrumental was based on ways that I had heard her discuss social justice;

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she wanted students to perform well and was willing to try any technique to improve their math
performance, which is an illustration of “demonstrates commitment to social justice in concrete
ways” (Drago-Severson & Blum-DeStefano, 2017, p. 474). At the time of designing this study, I
had not yet noticed evidence of “co-constructing realities” or “orienting to inner states about
diversity, equity, and inclusion.” In her discussions and descriptions of students she did not
mention race, socioeconomic status, or other identity markers, and had not yet shared with me
the way that she viewed her own identity independently or in relation to students. While I had
not yet seen evidence of movement toward socializing, I did think that Blake had considered her
own identity and was committed to educational equity. After choosing to teach in a low-income
neighborhood in New York for 5 years, Blake moved to Korea to learn to speak Korean and to
discover more about her family’s ancestry. She had described the experience as “powerful” and
shared that her intent was to better understand her Korean culture. This showed me that she
valued understanding one’s culture and was willing to change her daily behavior to learn more
about herself and those that she valued. It may be that I was assuming she was an instrumental
knower because she had not openly spoken to me about race, but I had only known her for 3
months; I therefore predicted that she would share much more as I gained her trust. Her
reluctance to speak about race could also have been due to her own cultural identity and ways of
understanding race, which I believed could be unpacked within this study. I also considered that
I had not explicitly asked her how her identity informed her teaching, perhaps due to
assumptions that I had that it would make her uncomfortable or that it was only acceptable to do
so after trust had been formed, which was a bias founded in my own colorblind upbringing. In
talking about instruction in general I found her to be more of a socializing to self-authoring
knower, driven by her own goals (as seen in the numerous goals she had already set and worked

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toward in the first 3 weeks) and appreciative of colleagues’ perspectives (as evidenced in her
requests to observe peers and her quick implementation of their suggestions). I therefore began
by providing effective forms of assistance for instrumental knowers that I described previously:
these included offering cognitive structuring for organizing support, using factual questions to
ground Blake in identity-based details, using guiding questions to direct her towards a funds of
knowledge and identity approach, and using probing questions to ask Blake what she believed
was the “right” way, why she thought she believed that, and what other ways might have been
considered. I additionally provided multiple opportunities for her to learn alongside her
colleagues, including her instructional assistant, in order to attend to the parts of her as a learner
that appeared to be more socializing.
Dante was a Latino, cishet man teaching Algebra I. He entered the classroom 4 years
prior to the study following a career as an engineer, and frequently exposed his students to
above-grade-level procedural work. He related to his students as a second-language learner, as he
learned English after coming to the United States in eighth grade. Based on our previous year
working together, I classified Dante as an instrumental knower. His content knowledge was
based on his own math courses as an engineering major in college, and his overall style was
dependent on lecture and routine practice. When asked why he enjoyed teaching, his response
was that he liked watching students acquire the skills they needed for college and finding success
in the classroom. This aligned with the instrumental knower desire for concrete strategies; in
teaching his students concrete math strategies, he was demonstrating that these were a part of his
own epistemology. Over the 21–22 school year, Dante incorporated more student voice into his
classroom and began to experiment with new ways of engaging students. Most of these included
implementing discourse routines, which again lent itself to instrumental knowing. The routines

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he chose were those offered up by me, which was again in alignment with an instrumental
knower. However, Dante attended the UnboundEd GLEAM institute twice; possibly as a result,
his mindset shifted slightly. Prior to the conference, I suggested that we replace 8th-Grade Math
with Algebra I to increase opportunity and access. He was willing to follow my suggested plan,
but his response was hesitant and therefore seemed to be out of compliance. Following the
conference, he was excited; he wanted to have planning meetings with me during the summer to
jump into the new curriculum and voiced to me that he understood that, by not offering Algebra
I, we were holding low expectations for our students. As his experience happened at a
collaborative conference, his mindset shift could have been due to those surrounding him; he
therefore could have been moving toward a socializing learner. As such, I used forms of
assistance like those I mentioned for Blake. I began by providing cognitive structures for us to
work within, used questioning to direct him towards a funds of knowledge and identity approach,
and shared my own teaching experiences when he demonstrated evidence of a socializing
learner. In my questioning, I focused on unearthing more about how Dante’s own background, as
a second-language learner and an engineer, had shaped his understanding of what math
understanding was and how this might have been impacting the ways that he viewed student
math understanding.
Julia was a Latina cishet woman in her early 30s. At the start of the study, she had been at
PS 103 for 6 years. Previously she taught a combination of sixth grade science and math, for the
22–23 school year she requested to move into seventh grade math when an opening became
available. She preferred teaching math to science because she said that she had a stronger
understanding of the content and liked it better, which led me to believe that, like many learners,
she liked things that she believed she was good at. During the study year her goal was to increase

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discussion in her math classroom as well as to increase confidence in her math learners. Her first
activity of the year centered around math identity, in which she asked students to write letters to
her about their own math identity. This was evidence that she was already questioning how her
students responded to math instruction and saw themselves as learners prior to the study; I
therefore assumed that she would be open to this study and use it as an opportunity to reflect
further. I was initially unsure as to whether Julia was an instrumental knower or a self-authoring
knower. She did not appear to be socializing; prior to this study, she was frequently the first
person to volunteer opinions in group discussions and had a clear idea of how math education
should look, as evidenced by her push toward conceptual and collaborative learning for the math
department. I was unsure as to where this vision came from, however. During the study, I asked
probing questions about why she made the instructional choices she did, as well as how she
believed her own background as a math student and adult learner impacted her instructional
choices. Her responses to these questions informed the instructional choices that I made for our
subsequent sessions together.
Settings of Actions
I began my study by asking the Principal and the Chief Academic Officer for permission
to conduct this action research proposal, and once approved, reached out to my preferred
participants. I approached each potential participant individually and described the intentions of
the study, which were to (a) deepen my understanding of ways in which my biases and
andragogical choices affected teacher learnings and (b) support teachers in recognizing how their
own identities affected the ways that they noticed student funds of knowledge. 
This action research study was conducted in three phases. Each phase consisted of one
individual coaching meeting per participant as well as one collaborative, 1-hour meeting. The

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scheduling of these meetings was already established by my school. This meant that participants
did not need to commit to more time to participate, and also that I needed to consider power,
obligation, and conflicting school requirements; these will be discussed further in limitations,
delimitations, ethics, and my findings. The intimate settings of the individual sessions allowed
me to build greater levels of trust with participants, as well as decreased the emotional load that
may come with asking participants to share intimate details with their other colleagues.
However, Rodgers’s cycle is strengthened by greater collaboration, particularly in the analysis
piece. Rodgers defines analysis as “generating a number of different explanations for or
‘conjectures’ (Lampert & Ball, 1998) about what’s going on and settling on a theory or
hypothesis that one is willing to test in action” (2002, p. 244). For this reason, I included the
second collaborative setting during three department meetings. The first, smaller setting was
designed to allow teachers to gain self-efficacy in the use of the Rodgers cycle, and the second
collaborative setting, involving people with different positionalities and narratives than just mine
and the individual participant, served to push teachers further toward alternative perspectives and
a funds of knowledge and identity framework. When I designed this study in the Spring and
Summer of 2022, department meetings were attended by classroom teachers and myself. In the
Fall of 2022 Instructional Assistants were included and expected to attend; I therefore included
them in our session’s learning experiences, although they were not formal participants. The
Instructional Assistants were also in the room during instructional coaching sessions; their level
of input varied depending on their relationship with the teacher, and were leveraged to provide
additional perspectives that could help us move our reflection toward comparative and critical.

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Actions
This research study was composed of three action cycles, all working toward the action
research study intentions of (a) developing myself as an adult learning facilitator and (b)
assisting participants in using a (critically) reflective cycle to see, describe, and analyze how
their identity impacted the ways they noticed student funds of knowledge in their math
classrooms. Each individual phase initially had its own learning objective; however, as I moved
through the study my (critical) reflections upon demonstrated learner understanding led me to
adjust. As such, each session worked toward the following learning objectives:
1. Use the Rodgers cycle to reflect on our practice.
2. See, Describe and Analyze our classroom evidence from different viewpoints.
3. See, Describe and Analyze, noticing students’ funds of knowledge.
Each phase involved participants working through the reflective cycle, andragogical moves
chosen based on the types of knowers participating, and my own attempted critical reflection.

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Table 1
Planned Action with Teachers
Learning Objective Facilitator Actions Setting Data Collected
Before Study
Communicate the purpose
and objective of the study, the
learner’s role in the study.
Communicate structure of
study.
Introduce the purpose and
process of the research study.
1:1 Coaching Agenda
During Study
Phase 1
Reflect on aspects of their
own identity, specifically
around mathematics,
teaching, and learning.
Week 1:
● Brave Space Discussion
Agreement: Challenge by
Choice
● I Am From and
identity discussion 
Department
Meeting
Agenda
Audio
Recording +
Transcript (1)
Fieldnotes (1)
Understand the connection
between identity, funds of
knowledge, and the Rodgers
cycle.
Engage in the see and
describe cycles. Begin
analyze conversations.
Weeks 2–3:
● Introduction to Rodgers’s
cycle.
● Introduce “see” and
“describe” phases.
● Model “see” and
“describe” phases with
Instructional Coordinator
video.
● Engage in initial
collaborative “analyze”
discussion.
Week 4: Out of Field Analysis
Individual
Coaching (3)
Agenda
Audio
Recording +
Transcript (3)
Fieldnotes (3)
(Critical)
Reflection (1)
Out of Field Analysis and (Critical) Reflection: Analyze transcripts for ways that my
andragogical choices pushed teachers to see and describe in multiple ways. How did my
positionality and biases impact interactions with participants and my own contributions to the
cycle? How did participants demonstrate their type of knowing? Was this like my original
interpretation? Do the andragogical moves I chose push teachers toward recognizing places in
which they valued or devalued student finds of knowledge? Are participants demonstrating
progress toward the learning objectives? How do I use critical discourse moves to support more
critical conversation? Did disorientation occur and if so, was it constructive? What adaptations
could I make to the next cycle to further promote constructive disorientation?

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Learning Objective Facilitator Actions Setting Data Collected
Phase 2
Participants will “see,”
“describe,” and “analyze,”
considering ways that their
own identities and the
identities of their students
impact their practice.
Week 5:
● Co-engage in “see” and
“describe” pieces of
critically reflective
cycle.
● Discussion—How did
our identity affect the
ways that we saw and
described? 
● Return to “see” phase and
generate more detailed
sights.
Department
Meeting
Agenda
Audio
Recording +
Transcript (1)
Fieldnotes (1)
Weeks 6–7:
● Discussion: How did the
cycle feel when engaged
with collaboratively?
How did different
viewpoints affect seeing
and describing?
● Co-engage in see,
describe, and analyze
pieces of reflective
cycle.
● Discussion—How did
our identity affect the
ways that we saw and
described? 
Week 8: Out of Field Analysis
Individual
Coaching
Meetings (3)
Agenda
Audio
Recording +
Transcript (3)
Fieldnotes
(3)
(Critical)
reflection (1)
Out of Field Analysis and (Critical) Reflection: Analyzing recordings for ways that my
andragogical choices pushed teachers to see and describe in multiple ways. How did my
positionality and biases impact interactions with participants and my own contributions to the
cycle? How did participants demonstrate their type of knowing? Was this like my original
interpretation? Do the andragogical moves I chose push teachers toward recognizing places in
which they valued or devalued student finds of knowledge? Are participants demonstrating
progress toward the learning objectives? How do I use critical discourse moves to support more
critical conversation? Did disorientation occur and if so, was it constructive? What adaptations
could I make to the next cycle to further promote constructive disorientation? How did
participants interact with each other in collaborative discussions?

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Learning Objective Facilitator Actions Setting Data Collected
Phase 3
Participants engage in see,
describe, and analyze
phases in ways that attend
to identity and funds of
knowledge.
Participants discuss the
interactions between
identity, funds of
knowledge, and
mathematical success.
Weeks 9–10:
● Engage in see, describe,
and analyze pieces of
critically reflective cycle
around original
recording.
● Discussion—How do we
notice identity, funds of
knowledge, and
mathematical success
interacting?
Week 11:
● Article and Discussion—
Allen and Schnell (2016):
multiple ways to redefine
mathematical success.
● Discussion—how do
identity, funds of
knowledge, and
mathematical success
interact?
● Engage in see, describe,
and analyze pieces of
critically reflective cycle
around own classroom
recording.
● Discussion—How do we
notice identity, funds of
knowledge, and
mathematical success
interacting?
Individual
Coaching
Meetings (3)
Department
Meeting
Agenda
Audio
Recording +
Transcript (3)
Fieldnotes (3)
Agenda
Audio
Recording +
Transcript (1)
Fieldnotes (1)
Week 12: Out of Field Analysis (Critical)
reflection (1)
Out of Field Analysis and (Critical) Reflection: Analyzing recordings for ways that my
andragogical choices pushed teachers to see and describe in multiple ways. How did my
positionality and biases impact interactions with participants and my own contributions to the
cycle? How did participants demonstrate their type of knowing? Was this like my original
interpretation? Do the andragogical moves I chose push teachers toward recognizing places in
which they valued or devalued student finds of knowledge? Are participants demonstrating
progress toward the learning objectives? How do I use critical discourse moves to support more
critical conversation? Did disorientation occur and if so, was it constructive? What adaptations

80
could I make to the next cycle to further promote constructive disorientation? How did
participants interact with each other in collaborative discussions?
Data Collection
The long-term purpose of this study was to investigate how I, as an adult learning
facilitator, used the concepts set forth in my conceptual framework to ultimately support teachers
in noticing and leveraging student funds of knowledge and identity to affirm students as
mathematical thinkers. Within the time frame of this study, I was looking for how I engaged my
learners in reflecting on their practice in identity-conscious ways, as a step toward engaging in
(critical) reflection.
As the action researcher, I was the primary instrument for data collection and data
analysis (Maxwell, 2012). I collected multiple forms of data throughout this study, which
included: documents in the form of meetings agendas, fieldnotes, memos, and my own written
descriptive and (critical) reflections; artifacts in the form of audio recordings, transcripts, and
researcher-developed resources; and observations notes. These data sources were analyzed both
in- and out-of-field and provided insight into adjustments that I made and my ultimate findings.
Together, they demonstrate the growth that I showed as an adult learning facilitator, the change
in the depth of my reflection, and the growth that my participants showed in reflecting on their
practice. Each type of data collected will be further explained in the next section.
Documents and Artifacts
Each research phase contained recordings and transcripts of four sessions, one
collaborative meeting agenda, one individual coaching agenda per participant, my written
memos and fieldnotes, and one post-phase written (critical) reflection. The artifacts in my study
were self-generated. For the first collaborative session, which was the very first session of my

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study, I created an agenda and a note catcher, which included learning objectives, excerpts of
relevant literature, guiding questions, and places for participants to write notes and reflect. I also
provided the I am From template (Klein, 2018); all of these were provided electronically and
physically to study participants and to the instructional assistants present during the meeting. I
did not collect participant notes at the end, so their written notes did not serve as data. Instead, I
analyzed the transcript and the audio recording of our session, as well as the voice memo that I
recorded immediately following the meeting. The remainder of the sessions involved similar data
collection. In each session I provided an agenda and a note catcher, and produced an audio
recording, transcript, and a post-session descriptive reflection by me. Additionally, I periodically
produced methodological memos, as well as a formal analytic memo and (critical) reflection
following the completion of each of the three phases.
Observations
I conducted insider action research as the primary research instrument of this study. This
role meant that I was participating in and observing my meetings simultaneously (Herr &
Anderson, 2015); this limited my ability to fully observe. I therefore relied on jottings and postsession descriptive reflections as observations. As I observed in-person while simultaneously
participating in the reflective cycle, I attempted to take jottings that included “speculation,
feelings, problems, ideas, hunches, impressions, and prejudices” (Bogdan & Biklen, 2007, p.
122). However, my novice-researcher state and my inability to fully inhabit my teacher,
researcher, and adult learning facilitator roles simultaneously made it difficult for me to create
jottings about my participants; instead, most of my jottings were from the view of me as a
participant, rather than a researcher. I also found that jotting made it difficult for me to attend to
my learners and facilitate meaningful discussion; I therefore stopped jotting during phase 1 and

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relied on immediate descriptive reflection instead. These descriptive reflections, as well as
review of the transcript, informed my analytic memos and (critical) reflections.
Data Analysis
Action research is cyclical in nature (Coghlan, 2019; Herr & Anderson, 2015), and so I
therefore engaged in analysis throughout the study. As I was a novice researcher, I waited until I
was out-of-field and had completed my coursework before undertaking formal analysis (Bogdan
& Biklen, 2007). I did, however, engage in informal analysis throughout the study to inform
ways in which I could strengthen each imminent session and phase. Following each session, I
recorded an immediate descriptive reflection and, following most sessions, reviewed the
transcript for trends. Additionally, I reviewed each previous individual session with a participant
while designing the upcoming one; for example, I reviewed Dante’s first session transcript while
planning for his second session. As I reviewed and reflected, I paid attention to trends; some of
these trends were more immediately visible because they were expected in my conceptual
framework and were therefore labeled with a priori codes (Merriam & Tisdell, 2016). Some of
these included funds of knowledge and identity, questioning, and critical reflection. In other
cases, I saw trends that were not expected that became emergent codes. Some examples of these
were clear expectations, knowledge-of-practice, and adult learning facilitator role vs. teacher
role; these became more relevant as I wrote my findings, and were used to revise my conceptual
framework.
After I finished the third phase, I exited the field and engaged in a period of formal
analysis. Data analysis involves “working with the data, organizing them, breaking them into
manageable units, coding them, synthesizing them, and searching for patterns” (Bogdan &
Biklen, 2007, p. 159). Once out of the field, I was able to use the a priori codes and some of the

83
emergent codes discovered in the field to systematically review each piece of data mentioned
previously. As “analysis is a process of generating, developing, and verifying concepts—a
process that builds over time and with the acquisition of data” (Corbin & Strauss, 2008, p. 57),
my codes were adapted as I moved back and forth between phases. As I did so, I used analytic
tools to draw conclusions about my ability to enact change in my school context. Specifically, I
consistently used the analytic tools “making comparisons,” “looking for the negative case,” and
“looking at emotions that are expressed” to help “stimulate the analytic process” (Corbin &
Strauss, 2008, p. 67). For example, during analysis I frequently compared the types of questions I
asked and the responses that they provoked from participants (making comparisons), or looked
for questions that prompted responses that were different from the majority of responses (looking
for the negative case). These tools helped me to create more codes, which I then entered into a
codebook. These tools further helped by causing me to break my broad a priori and emergent
codes into more specific codes with descriptions; for example, I used “looking for the negative
case” to break my original code of “clear expectations” into “clear expectations—learner
followed” and “unclear expectations—learner followed” so as to differentiate when my learners
did what they were expected, but as a result of my unclear expectations we did not reach the
objective. A similar process, in addition to “looking at emotions that are expressed” helped me to
recognize my difficulty in embracing my role as an adult learning facilitator and the
consequences; these examples are discussed at length in my findings.
As I continued to add and edit codes in my codebook, I began to group them into themes;
many of these became the headings that appear in my findings. I used analytic memos, written at
the end of each cycle of analysis, to seek themes, name them, and create definitions for them. As
I built my codebook and noticed new themes, I consulted with my advisor; she often assisted me

84
in clarifying those themes into new emergent codes and creating definitions, as well as pointing
out potential codes that I may have missed. I then applied these codes in the next phases of
analysis. Some of these emergent codes, for example turning toward practice, were missing from
my original conceptual framework and were added to my revised conceptual framework.
Additionally, some of my a priori codes were dropped, as they were replaced with different
codes or became less relevant than other major themes that emerged throughout analysis. These
were removed from my conceptual framework if they no longer applied to my theory of change,
or were clarified as intended future goals (for example, participant critical reflection). All of this
analysis informed my answer to my research question, discussed in my findings.
Limitations and Delimitations
This section addresses the limitations and delimitations that affected the design,
implementation, and analysis of my study. I will first describe the limitations that constrained my
study. I then speak to the delimitations, how I attempted to address them, and their implications
moving forward.
Limitations
This study is bounded by the context, which includes the time, setting, participants, and
researcher. Time is one of the biggest restraints, for although my context provided multiple hours
per week for me to interact with my teacher-participants, that time also came with pre-existing
responsibilities that often conflicted with the goals of my study. Teachers were already
frequently overwhelmed with their typical role responsibilities, and this study asked them to slow
down and attend to student funds of knowledge and identity, something that has not been
prioritized before at our school sites. The existence of two separate school sites also impacted my
participant recruitment; teachers were spread between two school sites, and the schedules were

85
such that there were almost no windows in which true collaboration could occur between sites.
As two of the three participants had already experienced a year of coaching with me, we had preexisting strong relationships. I had developed professional trust with all three, evidenced by the
vulnerability they showed when telling me about their areas of growth in their classrooms,
coming to me with problems, and even asking me to support them in interactions with
administration; however, this also impacted our researcher to participant relationships. I felt
tension between how we typically operated and this new proposed curriculum, which often
informed the ways that I chose to implement the study. This will be discussed more in the
delimitations section.
Additionally, my school site decided to adopt standards-based-grading in the Spring of
2023. We also partnered with an outside organization to assist us with learning walks and schoolwide instructional initiatives; this limited both the time that I had available to coach, as well as
the freedom that I had previously had to support teachers in their learning. Many of our
department meetings in the Spring came with predetermined objectives, coming from the
leadership team, or set goals for teachers; these were often aligned to more of a knowledge-forpractice approach, and therefore conflicted with the goals of my study.
Lastly, I was a novice researcher. This impacted the way in which I design, enact, and
analyze this study. This was evidenced in the infrequency of jottings, novice analysis while in
the field, and the quality of my memos and (critical) reflections. While I could not control my
novice status, I worked to mitigate some of the constraints that result from little experience; this
is detailed in the delimitations section.

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Delimitations
In choosing participants, I intentionally asked teachers who did not have additional
responsibilities—for example, I chose to exclude one teacher who was getting her master’s
degree, because I recognized that her cognitive load was already high. For a similar reason I
chose not to include brand new teachers, as they had additional expectations placed on them by
administration and credentialing programs. I did this so as to mitigate additional conflicts that
would compete for time or attention during the study. I additionally considered school site when
choosing participants, in I decided to only enact the study at the middle school. This decision
was because the middle school had a smaller group composed of returning teachers, none of
whom were currently enrolled in other professional development or credentialing programs.
This study design depended on the use of classroom videos, as they served as the artifact
that we used for reflection-on-action. In designing the study, I chose to use personal and
participant videos. In the beginning sessions, we used my own videos so that I could build trust
by demonstrating vulnerability around my own practice (Spikes, 2018). While this may have
built trust, as evidenced in the findings, it also may have limited the amount teachers engaged
due to the power imbalance in our roles. In the second and third cycle we used participant
videos, which placed the study into teachers’ immediate contexts. However, this may have led to
participants feeling self-conscious or uncomfortable, thereby decreasing the amount that they
were willing to critique or engage in critical discourse with peers (Copur-Gencturk & Rodrigues,
2021). I also attempted to address my status as a novice researcher within the design of this
study. Although I could not control the amount of experience I had, I used (critical) reflection
and frequent informal analysis to monitor my work, as explained above. In doing so, I assessed
my growth and participant reactions to the study; this held me accountable for any unintentional

87
harm that I caused and assisted me in adjusting accordingly. Finally, I met frequently with my
advisor and with my colleagues to discuss my research, ask questions, and share trends; this also
helped to keep me accountable and to view any additional harm that I might have unintentionally
caused due to my novice status.
Credibility and Trustworthiness
As this study was an action research study, it was deeply rooted in the relationships with
and experiences of me, my participants, and my school context. The reliance on qualitative data
and my dual role as participant-researcher meant that bias was inevitable (Herr & Anderson,
2015); I therefore attempted to mitigate this with data triangulation (Merriam & Tisdell, 2015).
Data triangulation, according to Patton, “increases credibility by counteracting the concern (or
accusation) that a study’s findings are simply an artifact of a single method, a single source, or a
single investigator’s blinders” (2014, p. 674). As I stopped jottings early in the study, as
mentioned above, I triangulated transcripts, audio recordings, and my own descriptive postsession reflections. The reliance on transcripts meant that the words that I was analyzing were
directly the participants own, free of synthesis or summarization, and I used the audio recordings
to confirm the auto-transcription (Bogdan & Biklen, 2007). Listening to the audio transcription
enabled me to pick up on tone, laughter, and silence; of these, tone was subjective and
potentially could have been analyzed with bias, but these also served to add context to the raw
transcription and therefore acknowledged the humanity of me and my participants in our
interactions. My descriptive reflections also involved bias; to combat this, I analyzed them
alongside the transcripts to see if my descriptive reflections were triangulated by data. When
there were discrepancies, I used them to consider potential biases that I held that led to false

88
conclusions; these were analyzed both during my (critical) reflections and, occasionally, with my
advisor. Doing so in the field helped me to notice and work against those biases in future phases.
As I had pre-existing relationships with all three participants, they entered the study with
previous experiences and biases about who I was, what I believed, and how I acted in our school
context. I also was aware that my pre-existing relationships with participants and my positional
power could pressure teachers into becoming participants. To combat both, I consistently
emphasized that I was co-constructing and learning with participants, and that the intention of
the study was to learn from one another, rather than from me. I leaned on my concurrent role as
an AP Calculus teacher as a way to relate to participants and build trust and modeled my own
vulnerability throughout the study; this is discussed further in my findings.
I am aware that my experiences as a learner, teacher, adult learning facilitator, and now
researcher have biased me toward certain pedagogical math moves and certain mindsets around
mathematics. I therefore tried to refrain from acknowledging responses as right or wrong, and
instead considering them as counternarratives to my currently held beliefs. Milner (2007)
reminds us that “Truth, or what is real and thus meaningful and “right,” for researchers and
participants, depends on how they have experienced the world” (p. 395), and I intended for my
participants to trust that their truth is essential and honored. My participants identify as Latino/a
and Asian American. All participants were highly educated, with many holding master’s degrees
in addition to their bachelor’s degrees and teaching credentials and held a multitude of
experiences that had affected the ways that they interacted with math learning and the ways in
which they viewed themselves or were treated as students. I therefore strove to not make any
assumptions as to their experiences. Spikes asserts, “much of the ignorance as it relates to race
and racism is largely due to institutional and societal oppression and not individual intent” (2018,

89
p. 9); in this study, I used (critical) reflection to confront the assumptions both that I held as an
individual, and those that were results of the institutional and societal oppression discussed
previously. In modeling my own experience and understanding of racist structures, as well as
openly discussing my differences, I exposed my own vulnerability to build additional trust
(Seidman, 2013; Spikes, 2018). In both this study and beyond, I am committed to attending to
the pieces of my positionality that fit the dominant culture and hold positional power (White,
cishet, upper-middle class) and reflecting upon how my potential insider pieces (female, teacher,
and member of the PS 103 community) can help me to build trust with the teachers I work with.
Ethics
As the Math Instructional Coordinator of my network, I held positional power that
allowed me to push toward change at a network level. Examples of this included being able to
choose curriculum, co-setting individual goals with teachers, recommending different strategies
and instructional moves, and providing regular feedback on teachers’ current practices. My role
also gave me direct access to relational conversations with teachers on a frequent and consistent
basis. Overall, the decisions that I made as Instructional Coordinator had a direct impact on each
participants’ job performance, responsibilities, and satisfaction. I therefore attended to this power
throughout the study, acknowledging it and making it clear that the findings of this study would
in no way impact participant job security. Although participants were required to engage in the
learning opportunities that I presented as a part of their job, it was made clear that I would not
collect data without their explicit permission and that they could be removed from data collection
and analysis at any time if they wished. I changed the names of both the school site and my
participants within the study. Finally, I made use of the structured time already designated for

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professional development, to not be an additional time burden for those who chose to
participate.
Findings
In this section, I discuss my findings in relation to my short-term research question: How
did I, in my role as Instructional Coordinator, assist participants in using a (critically) reflective
cycle to see, describe, and analyze how their identity impacts the ways they noticed student
funds of knowledge in their math classrooms? This section will answer my research question in
terms of the progress that my participants demonstrated and the ways that I developed as an adult
learning facilitator.
Increasing Trust in the Learning Environment
I argued in my conceptual framework that, for teachers to ultimately affirm students as
mathematical problem-solvers, they needed to notice and leverage student funds of knowledge in
their math classrooms. Within the scope of this study, I sought to assist participants in using a
(critically) reflective cycle to see, describe, and analyze how their identities impact the ways they
noticed student funds of knowledge in their math classrooms. To engage in this (critical)
reflection, I needed to push our current learning environment toward a brave space (Arao &
Clemens, 2013). This type of learning environment could then support us in taking the risks
necessary to engage in reflection-on-action, challenge our assumptions (Brookfield, 2017),
experience constructive disorientation (Wergin, 2019), and ultimately grow in our practice. For
us to take risks, our learning environment required a deeper level of trust than that which was
currently present in both our collaborative department meeting space and our individual coaching
spaces. This deeper trust would be evidenced by increased vulnerability by participants

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(Boostrom, 1998; Holley & Steiner, 2005) and increased relatedness in our space (Wergin,
2019).
To increase trust in our space, I myself demonstrated vulnerability. This is in alignment
with Spikes’s (2018) assertion that facilitators can build trust by demonstrating vulnerability. I
also attended to Wergin’s (2019) definition of relatedness as “an environment where participants
felt socially connected and cared for by others’’ (p. 71), and looked for evidence of social
connection and care as evidence of trust. If I was successful in increasing trust, participants
would be able to “reflect and grow and not feel judged” (Spikes, 2018, p. 9) as they considered
their identities in both our individual and collaborative spaces. As a result of my displayed
vulnerability, I gradually saw increased vulnerability and relatedness in our space and therefore
concluded that we had increased the level of trust present in our collaborative space. In our
individual spaces, I saw this happen more quickly due to the pre-existing level of trust between
me and each participant; this growth in individual spaces also contributed to the movement
toward our braver collaborative space. Although we were not able to reach a truly brave space in
either setting, our increased trust within our learning environments enabled us all to take risks
(Arao & Clemens, 2013), move towards critical reflection, and grow as adult learners (Spikes,
2018) over the course of this action research.
I demonstrated vulnerability in all three cycles to deepen trust. In the first cycle, I used
each session to engage in the activities that teachers would be expected to do themselves in
cycles 2 and 3. For example, in the first session of the first cycle, I set out to build upon my
participants’ current understanding of a funds of knowledge approach by using an I am From
poem to get us thinking about where our own funds of knowledge and identity came from; this
would later support us in recognizing our students’ funds of knowledge and identity. I

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recognized that this activity would require a higher degree of vulnerability than participants had
previously demonstrated in our collaborative space, and so I made intentional moves to increase
trust in our learning environment throughout the meeting.
I started the meeting by providing participants with a handout that included our learning
objectives, a new discussion agreement offering, and a space to document our current
understanding of funds of knowledge. I then offered the new discussion agreement, challenge by
choice (Arao & Clemens, 2013), and asked participants if they had any questions or concerns
about the new discussion agreement. They did not. I then asked participants to share their current
understanding of the term “funds of knowledge,” and each participant offered their current
understanding. I then directed participants to a selection of quotations from literature on the
handout and asked them to read them silently. Following a brief discussion of how the quotations
added to their previous understanding, I introduced the I Am From activity to examine where our
own funds of knowledge come from. As shown in the following excerpt, I began by setting the
stage to share my own I Am From, after which I publicly shared my pre-written poem. This was
the first example of me demonstrating vulnerability and thus revealing my own level of trust in
our space (Spikes, 2018). Participants then had time to write their own I Am From and were
given the choice to share out pieces to their colleagues, which served as an opportunity for
participants to display vulnerability and demonstrate the level of trust they were experiencing.
K: So, this next piece is to get us thinking and reflecting on where our own funds of
knowledge came from. Whether that was in your home or experiences that you
had in school, probably a combination. And so, this activity is called the I Am
From. Has anybody done an I Am From or seen an I Am From before? So, in your
packet on the next page, there’s a template there. So, an I Am From it’s not just

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about geographical location, more about the set of values, feelings, experiences,
that you came from that you consider to be a part of you or something that shaped
you. So, I’m going to read my own. I wrote a version that were some things that
came up for me as I was writing my dissertation and thinking about why I am the
way I am and how I learn and then how that affects my teaching, and then I’ll
give you all some time to write your own.
When I said, “this next piece,” I referred to the act of writing and then publicly sharing our I am
From poems in the space. Implied in my language, “thinking and reflecting on where our own
funds of knowledge came from” (emphasis added), was the need for all of us to be willing to
explore pieces of our own identities (Boostrom, 1998). This could lead to discomfort, and
therefore, participants needed to trust that they could feel discomfort in this space and around
these colleagues. I more specifically highlighted the vulnerability required of the task when I
said, “Whether that is was in your home or experiences that you had in school, probably a
combination.” In doing so, I was asking them to think beyond their professional roles and to
expose their personal lives; this was something that they had not previously done, which could
again have caused discomfort. When I said, “So I’m going to read my own,” I was
communicating that I was going to perform an act that was consistent with what I was expecting
them to do. Additionally, in saying that I was going to read my own, I implied that sharing
publicly was expected; this moved the previously mentioned possible discomfort into a potential
fear of judgment from colleagues. Implied when I said, “I wrote a version that were some things
that came up for me as I was writing my dissertation,” I was sharing that I had reflected upon my
own experiences and had grown in my awareness of my identity and funds of knowledge
(Spikes, 2018). I was also sharing that things had “come up” for me as a result of my

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dissertation, which messaged that things could “come up” for participants as well; again, a
potential cause for discomfort. When I said, “and thinking about why I am the way I am and how
I learn and then how that affects my teaching and then I’ll give you all some time to write your
own,” I demonstrated vulnerability (Tharp & Gallimore, 1991) by showing participants that I
was willing to expose things about “why I am the way I am and how I learn.” This foreshadowed
that I was prepared to risk judgment (Spikes, 2018) in sharing my own act of self-discovery.
When I said, “and then how that affects my teaching,” I was revealing that I recognized that my
identity had consequences on my actions, which again exposed me to their possible judgment.
When I said, “I’ll give you all some time to write your own,” I was again implying that they, too,
would be asked to consider the way that they were and the way that they learned, which would
require levels of vulnerability like the level that I was about to expose.
Following this statement, I read my own I Am From poem. The following is an excerpt
from my poem that I read aloud:
K: I am from a White school in a White suburb filled with teachers who looked
exactly like me with students who looked exactly like me with lessons that were
written exactly for people who looked like me. I’m from learning from watching
my parents and then learning from watching my teachers, and then expecting my
students to watch me until I realized it wasn’t working. I’m from a family that
speaks loudly and always on top of each other that spends hours discussing or
arguing or agreeing and from learning to learn within a loud, messy, chaotic
space. I’m from stop talking, you’re giving away the answers or you’re distracting
or just go in the hallway and work out of next year’s textbook. I’m from your
poor students, they’re so low and anger that I couldn’t make others see that my

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students knew so much more than anyone including myself gave them credit for.
I’m from Southern California. Where racism doesn’t exist, except that it definitely
does. I’m from we don’t see color until I was forced to see color when I was the
only different color. I’m from working to be an ally in a community that is
racially ethnically, culturally different than I am and failing and trying again
every day to do better and learn more. I’m from too much confidence and never
enough confidence that I’m doing what I should be doing in the way that I should
be doing it. I’m from fear of doing something and fear of doing nothing within a
system in which something desperately needs to be done. I’m from I’ll never need
math until I became a math teacher. I’m from an unshakeable belief that students
can learn math.
When I said, “I am from a White school in a White suburb filled with teachers who
looked exactly like me with students who looked exactly like me with lessons that were written
exactly for people who looked like me” I named race explicitly, reflecting on how Whiteness
framed the way that I learned. By naming my Whiteness in a room of non-White colleagues, I
risked calling attention to my racial differences and therefore risked judgment. In saying “with
teachers who looked like me with students who looked exactly like me,” I again risked
“othering” myself from my colleagues/participants; I was juxtaposing the community I grew up
in, all White, with our school community, and therefore risked judgment of my experience being
different from the experiences of my students and colleagues. Together, these statements
demonstrated that I reflected, and as a result chose to grow; I was now risking their judgment to
continue to do so (Spikes, 2018). My next statement, “I’m from learning from watching my
parents and then learning from watching my teachers” shared a reflection I had about the way

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that I learned; I then said, “and then expecting my students to watch me until I realized it wasn’t
working,” which shared a realization that I had due to my reflection. In sharing this, I risked
judgment by implying that I held the assumptions that (a) everyone learned in the same way and
that (b) I could therefore ignore the fact that my students’ identities and lived experiences were
different from my own. As a result, I failed as a teacher and, in admitting this to my participants,
I was risking that my participants would think that I still held these assumptions. In saying, “I’m
from a family that speaks loudly and always on top of each other that spends hours discussing or
arguing or agreeing and from learning to learn within a loud, messy, chaotic space” I invited
participants to a personal space, one that exposed information about my culture, the way I grew
up, and how I performed in the world. These, if different from theirs, could elicit judgment. I
then returned to my own learning experience when I said, “I’m from stop talking, you’re giving
away the answers or you’re distracting or just go in the hallway and work out of next year’s
textbook.” In this statement I shared that, while my race did not “other” me, I felt “othered” in
different ways; this could invite relatedness from participants and therefore increase trust
(Wergin, 2019), or could invite judgment if participants did not view my experience as
something that they could connect to. My statement “I’m from your poor students, they’re so low
and anger that I couldn’t make others see that my students knew so much more than anyone
including myself gave them credit for” acknowledged that I had begun to recognize tension
between my previous beliefs and my experience as a teacher, and that that tension caused strong
emotion. “I couldn’t make others see” represents my lack of perceived control, and implies that
lack of control added to my negative reaction, which implied an admitted weakness that I saw in
myself. I then said, “I’m from Southern California. Where racism doesn’t exist, except that it
definitely does. I’m from we don’t see color until I was forced to see color when I was the only

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different color.” Together, in these statements I admitted more explicitly to the colorblind way I
had been raised, and “until I was forced to see” shared that it was not a choice I made, but rather
an experience that caused me to reflect and grow from what I had previously known (Boostrom,
1998; Spikes, 2018). I then continued to share the impact of that experience when I said, “I’m
from working to be an ally in a community that is racially, ethnically, culturally different than I
am and failing and trying again every day to do better and learn more.” “I’m from working to be
an ally” named my intention in our work together, and “racially, ethnically, culturally different
than I am” is evidence that I was trying to no longer operate in a colorblind manner. I was
expressing vulnerability as I was admitting to ways that I wanted to be different than I was
previously. “I am failing and trying again every day” is evidence of my reflection and continued
pursuit of growth (Spikes, 2018), and represents the persistence in vulnerability that I intended to
display throughout this study. I then said, “I’m from too much confidence and never enough
confidence that I’m doing what I should be doing in the way that I should be doing it” which
implied to my participants that, although I might appear confident outwardly, I too feared
judgment and disagreement with my decisions and was, in actuality, coming to them from a
vulnerable place. In my final statement, “I’m from fear of doing something and fear of doing
nothing” I shared both my fear of and my motivation for making decisions, and “within a system
in which something desperately needs to be done” stated my opinion that things needed to be
changed. “I’m from an unshakeable belief that students can learn math” stated another strongly
held opinion. Both, again, could invite relatedness (Wergin, 2019) or judgment (Spikes, 2018)
depending on how my participants felt about the current state of the educational system and
student ability. Overall, my poem exposed participants to personal pieces of my life (Boostrom,
1998) and demonstrated vulnerability around my reflection and growth (Spikes, 2018), which

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showed participants that I had enough trust in our learning environment to display that
vulnerability.
Following my reading, participants then had 15 minutes to privately write their own I Am
From. What follows is my framing for sharing our I Am From poems, as well as excerpts from
participants that demonstrate the levels of trust in our collaborative space at the time.
K: Thank you for honoring that reflective time. We are going to share out if you
would like to. I think we’ll just go around in a circle and you can read as many or
as few as you want. If you do not want to share you can just say pass or next and
that will be that. We want to take like 30 seconds to read through yours, decide
which ones you feel comfortable sharing with us. Do you (Blake) mind starting us
off?
B: I am from fantasy and adventure stories of far-off places in between worlds in
books with flimsy paper covers are totally destined cracking spines, where my
curiosity and spirit is as fierce as the dragons and pirates I write about, my
empathy and emotions are as fragile and soft as the most desperate of star-crossed
lovers. And from a broken home broken with anger and distrust. I’m from a
childhood of textbook middle child peacekeeping evolved into an adulthood of
I’m not going to take no shit from anyone. I am from the sudden shift from when
the world thought that the Sharper Image Store was cutting edge tech to personal
computing devices to personal computing devices in the palm of everyone’s hand.
And I wanted to flush this out. Well, my thought was I’m from not Whiteness, but
also from not Blackness. That’s all.
K: Thank you for sharing. Would you like to share Dante?

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D: I’ll pass.
J: Okay, hopefully this makes sense. So, I’m from South LA, where I was raised to
be, where I was raised to be the best I could be. I’m from a strong female family
or my mom and sister my role models even though I fought with my sister all the
time growing up. I’m a middle child where I felt like I was constantly being
compared to my sister and by family and teachers where teachers would
constantly say, why aren’t you as smart as she is? Even though I also excelled in
school. I am from Mr. Jackson’s high school math class, who helped me realize
how much I liked math. And nourished my love and perseverance for it. I am
from attending an affluent liberal arts university in the East Coast and realizing
that maybe I really didn’t excel in school, even though I got straight As in high
school. I’m from being an advocate for our students even, yah. I am from being an
advocate for students because I do not want them to experience imposter
syndrome as I did about an undergrad. I am from bringing out the best in each
other as we work toward achieving our same goal.
Following writing time, when I said, “Thank you for honoring that reflective time,” I
reemphasized our goal of reflecting (Spikes, 2018). My next statement, “We are going to share
out if you would like to,” provided an opportunity for participants to reciprocate. When I said, “I
think we’ll just go around in a circle,” I demonstrated that, while they had a choice whether to
participate, I was providing a structure in which they were encouraged to share. I then
emphasized that sharing was encouraged when I said, “you can read as many or as few as you
want,” as I implied that everyone would share something. However, I then confirmed that
sharing was still an option when I said, “If you do not want to share you can just say pass or next

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and that will be that.” This gave them back some control over the amount of exposure that they
wanted to risk, and therefore the amount of trust they wanted to put in our space. I then provided
space for participants to choose what they were going to share when I said, “We want to take like
30 seconds, read through yours, decide which ones you feel comfortable sharing with us.” This
both allowed participants to choose the degree of vulnerability they wanted to demonstrate, and
set up an opportunity for me to gain evidence about the level of trust that participants felt in the
space. When I prompted participants to start by asking Blake, “Do you mind starting us off?” I
implied that I felt safe enough in the space to request her participation, assuming, based on our
previous relationship, that she would not mind sharing.
Blake began with “I am from fantasy and adventure stories of far-off places in between
worlds in books with flimsy paper covers are totally destined cracking spines, where my
curiosity and spirit is as fierce as the dragons and pirates I write about,” which implied that she
hid behind her imagination or in other “worlds.” She did not yet trust that she could expose more
personal things without judgment (Boostrom, 1998; Spikes, 2018). When Blake said, “my
empathy and emotions are as fragile and soft as the most desperate of star-crossed lovers,” she
exposed that her emotions were “fragile;” this implied a potential reluctance to display emotional
vulnerability. She then said, “And from a broken home broken with anger and distrust,” which
shows that, due to her past, trust might be something that was not easy for her to have in others.
When she said, “I’m from a textbook middle child peacekeeping evolved into an adulthood of
I’m not going to take no shit from anyone,” she shared her reaction to that pain and the impact
that it has had on how she moves through the world; her use of future tense in “I’m not going to
take no shit” implies that she continued to hold this mentality and that it would continue to
impact the way that she interacted in our learning environment. Her statements thus far

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demonstrate her current lack of trust in this space; she refrained from exposing pieces of her
identity (Boostrom, 1998), thereby defending herself from potential judgment or harm (Arao &
Clemens, 2013; Spikes, 2018). She then switched to an experience that was entirely racially and
emotionally blind, when she said “I am from the sudden shift from when the world thought that
the Sharper Image Store was cutting edge tech to personal computing devices to personal
computing devices in the palm of everyone’s hand;” her shift further away from vulnerability is
more evidence that she did not yet trust enough to risk judgment in this space. Her final
statement was the only place in which she began to reflect upon her racial identity when she said,
“And I wanted to flush this out. Well, my thought was I’m from not Whiteness, but also from not
Blackness. That’s all.” When she said, “and I wanted to flush this out,” she demonstrated some
hesitance to share the statement and could have been using the qualifier to signal that we should
suspend judgment, as it was an unfinished thought; this also could be demonstrating that she did
not trust this environment to risk sharing anything unfinished. When she said, “I’m not from
Whiteness, but also not from Blackness,” she named things that she is not; she was not trusting
us to tell us what she considered herself to be. She demonstrated brief vulnerability in
recognizing that she did not fit into the labels that society recognized. Overall, her willingness to
share and her brief attempts at vulnerability showed the potential for her to engage in eventual
disorientation; however, her vulnerability was mainly hidden behind figurative language and
demonstrates that she did not trust our learning environment fully enough to expose pieces of her
identity or previous experiences without fear of judgment (Boostrom, 1998; Spikes, 2018).
After Blake finished, my brief statement “Thank you,” reinforced the expectation that we
would not be giving feedback or responses to each other at this time. This could have increased
trust by eliminating the fear of judgmental responses (Spikes, 2018); it also could have prevented

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the level of trust from increasing by eliminating opportunities for relatedness or social
connection (Wergin, 2019). My statement “Would you like to share Dante?” gave Dante a choice
to share or not to share; in his response of “I’ll pass,” he demonstrated that he did not yet trust
that this was an environment that he could be vulnerable in without judgment (Spikes, 2018).
When Julia said, “hopefully this makes sense,” she mitigated risk in acknowledging that
her statement could not “make sense” to others; however, the fact that she continued does show
some degree of willingness to take risk. She then named, “So I’m from South LA” followed by,
“where I was raised to be the best I could be,” which seemed to defend where she grew up; this
implies that she recognized risking potential judgment in exposing where she was from. Her next
statement, “I’m from a strong female family or my mom and sister my role models” emphasizes
strength, which again could be a defense mechanism against displaying vulnerability. Her next
statement, “even though I fought with my sister all the time growing up,” juxtaposed role models
with fighting, which implies that she was used to conflict while learning; however, the “even
though” could be evidence that she did not consider conflict as a typical part of the learning
process and therefore was risking potential judgment. She then spoke about her sister again,
saying “I’m a middle child where I felt like I was constantly being compared to my sister and by
family and teachers where teachers would constantly say, why aren’t you as smart as she is?”
When she said, “constantly being compared” and “why aren’t you as smart as she (Julia’s sister)
is?” she exposed that comparison to others made her feel judged. Her statement, “I am from
being an advocate for students because I do not want them to experience imposter syndrome as I
did about an undergrad” admits to a weakness she saw in herself, one that she considered so
detrimental that she was actively working to prevent that weakness from persisting in her
students. She then said, “I am from bringing out the best in each other as we work toward

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achieving our same goal,” which shows that she viewed our team’s intent as “achieving our same
goal;” this implied social connection could have increased relatedness for participants (Wergin,
2019). Overall, her statement did not demonstrate vulnerability around her identity, which is
evidence that she, too, did not yet trust this space enough to expose herself without fear of
judgment (Spikes, 2018).
As stated above, I argued in my conceptual framework that I needed to increase trust in
both our collaborative settings and our individual coaching settings for us to reflect and grow in
our practice without fear of judgment (Spikes, 2018). Our individual coaching spaces, which
consisted of me, one participant, and occasionally an instructional assistant, were designed to
support participants in engaging in the reflective cycle around their individual practice. I
intended to leverage the higher level of trust already present in individual spaces and the more
private setting to encourage vulnerability in participants as they reflected on how their identity
impacted the ways they noticed student funds of knowledge and identity in their math
classrooms. Although I had already spent a year building individual trust with participants, a
deeper level still had to be present for us to move beyond professional conversations into more
personal reflections regarding identity. This was true for all three participants, and over the
course of the study I displayed my own vulnerability in each individual coaching session. As a
result, all three participants moved toward places of deeper trust in these sessions; this also
increased their willingness to be vulnerable in our final collaborative session. In individual
coaching sessions of Cycle 1, I set out to introduce Rodgers’s (2002) reflective cycle; this cycle
would be used as a cognitive structure (Tharp & Gallimore, 1991) in the remainder of our
sessions to support our reflection and growth (Spikes, 2018). I again demonstrated vulnerability
when I engaged in the activity that I expected participants to do individual coaching in Cycle 1.

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Rather than immediately asking participants to examine their own practices using the reflective
cycle, I invited them to watch me reflect on a video clip of my own practice, and then participate
with me in the see, describe, and analyze phases. In my public reflection-on-action, I risked
judgment of both my professional actions and what I shared about my own identity; I therefore
revealed vulnerability in my action and demonstrated my trust in the learning environment and
my participants. This served as our foundation for their own reflection on their practice in Cycles
2 and 3.
I engaged with each of my participants in a similar manner in each of their individual
meetings. With all of them, I recognized that I had previously only demonstrated vulnerability
around my practice as a teacher and needed to deepen the level of trust by exposing more about
my personal funds of knowledge and identity. I therefore started all participants’ first meetings in
the same way, by providing an agenda and a handout. This included a summary of the reflective
cycle, guiding questions for the see, describe, and analyze pieces, and space to take notes; this
provided a structure that was intended to eliminate some of the discomfort of not knowing what
to expect in the space. I then stated that we would first be going through the “see” and “describe”
components of the cycle using my video, and that the “analyze” piece would come in the
following collaborative session as we all compared what we saw and described. I then provided
context prior to watching the video, and then we watched the video together. In the video clip, I
was teaching a lesson to my 12th grade AP Calculus students. I chose the clip because it was an
activity in which students were called upon to say something true about a graph; most of the clip
was students sharing what they knew and the ways that I chose to respond to them, which set us
up to see, describe and analyze why I made the choices that I did. After watching the video, the
participant and I each shared what we saw. All my actions were similar with each participant.

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However, in analysis I paid particular attention to Dante’s growth in vulnerability as evidence of
his trust in the space, as prior to the study he had displayed a lower amount of trust than the other
two participants. This was already evidenced in he had refrained from sharing his I am From
poem in the first collaborative meeting and therefore had not shown evidence of the amount of
trust he had in our environment prior to his first individual coaching meeting. As such, I am
using Dante as a representative sample of the way I demonstrated vulnerability as evidence of
increased trust. In the excerpt below, I demonstrated vulnerability by connecting my own
identity to my instructional decision, which led to Dante increasing his own level of vulnerability
and exposing personal experiences that he had previously refrained from sharing. This increased
vulnerability in response to my own was representative of all three participants’ reactions
throughout the course of their individual coaching meetings, with Dante’s being the largest
amount of growth.
K: As I was watching this, I was like, why am I not like writing on the board? Like, I
feel like that would have been helpful. Yeah.
D: Why, were you not writing their responses on the board?
K: No, I was just pointing at the screen. And I think, yeah, like, I think that
visualization would have been helpful. I think I took for granted how much
vocabulary we were going, like I didn’t notice how much vocabulary we’re going
over. Because to me, they’re not new vocabulary words. So, to me, it’s just,
they’re words I use every day. And I mean, we obviously we took notes at the
beginning of the unit up like what is acceleration what is but I think I assumed
that because students had seen it, they didn’t need that initial vocabulary support,
but … and that’s probably an assumption because I was privileged to go to a

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school in which everything was in my language already. And so, I did pick up
things more quickly because it’s the language that was spoken at home and all of
that so I don’t know if that has something to do with it.
D: It’s funny how you you’re saying this Ms. Risbrough because I struggled a lot
when I was in, you know, going to high school in college. I wish it would have
been in my my my primary language. I think I would have excelled more than
what I did. Because it’s like when you’re listening to an instructor, you are
processing what they’re saying. And they need to translate it for you to
understand it. And then by the time you’re doing that he’s explaining something,
something else something different. This is why when I was in high school, even
though I hated I hated reading, I hated writing because that was not my language.
The only class that I loved was math. Math is my most, it’s a different language. I
understood, you know, even though they were speaking in another language is by
looking at the process and the steps and all that I was able to catch up. (K: Yeah.)
And I can relate this to when I was going to engineering school. Like sometimes I
needed to read. And it was hard for me to see exponential, like the concept, like
behind like reading and all that. But yeah, you’re right. It was easier for you
because it was your first language. And I don’t I don’t know if that’s like a
disadvantage for students. Because it was for me.
K: Yeah, I think it’s definitely unfortunately framed as a disadvantage. And because
teachers are not thinking about it as much as they should, becomes harmful. And I
think it should be looked at as you speak two languages and can learn all these
things in new languages. That is to me a superpower because I could not do that.

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And I was never expected to do it. And so, but yeah, I think like, how do we
frame that as, this is really impressive what you’re doing. It’s not a deficit. I think
so often it’s framed as a deficit. And it’s not.
D: I think of my students, there’s like a couple of students who, at first, I knew there
were they needed to help and I’m not helping them as much. Maybe translating,
but I know that with their ESL classes, they’re actually helping them and they’re
becoming better. And all I do is I would just check in with maybe Samantha and I
will say like, oh, did you understand it? And she’s like, Oh, yes or no. And then,
but I’m not translating as much as semester one because I think that’s one of the
goals for them not to just to try to just use English and I think she’s doing a good
job, but I could also relate back to when I was going to school. Yeah. Got to work
twice as much.
When I said, “As I was watching this, I was like, why am I not like writing on the board?
Like, I feel like that would have been helpful,” I displayed professional vulnerability in admitting
that an instructional decision that I made should have been different. When Dante responded
with the question, “Why, were you not writing their responses on the board?” his clarifying
question gave me an opportunity to become more vulnerable. When I replied, “I think I took for
granted how much vocabulary we were going, like I didn’t notice how much vocabulary we’re
going over.” I admitted to an assumption that I had made about my learners, which could have
invited judgment. When I then said “Because to me, they’re not new vocabulary words. So, to
me, it’s just, they’re words I use every day,” I again demonstrated vulnerability in considering
how my instructional decision was subconsciously influenced by my personal experience. When
I said, “And I mean, we obviously we took notes at the beginning of the unit up like what is

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acceleration,” my use of “obviously” suggests that I was concerned about judgment. I justified
that I had implemented an instructional support that Dante may have assumed I needed. I pushed
through that concern and said, “but I think I assumed that because students had seen it, they
didn’t need that initial vocabulary support, but, and that’s probably an assumption because I was
privileged to go to a school in which everything was in my language already.” I displayed
vulnerability by exposing a piece of my upbringing and sharing how that personal experience
impacted my professional judgment (Boostrom, 1998). I then continued to show vulnerability
around my own experience when I said, “And so I did pick up things more quickly because it’s
the language that was spoken at home and all of that.” I displayed vulnerability in saying that
that difference made me overlook the support that some of my students needed (Holley &
Steiner, 2005). When I said, “so I don’t know if that has something to do with it,” I retreated
backwards, potentially to protect myself after stating a vulnerability; my use of “so I don’t
know” was leaving space for an alternative reason, which demonstrates that I was trying to
increase vulnerability even as I myself did not fully trust that I could be fully vulnerable in this
space.
In Dante’s response, he began to demonstrate a degree of vulnerability when he said “It’s
funny how you’re saying this Ms. Risbrough because I struggled a lot when I was in, you know,
going to high school in college.” When he said, “It’s funny how you’re saying this” he was
acknowledging that speaking to my assumptions or upbringing was not a part of our typical
coaching sessions, which is evidence that I increased my previous level of vulnerability. Coupled
with his use of “Ms. Risbrough,” he could be speaking to our power imbalance, as I called him
by his first name; this power imbalance could impact the level of trust he feels in the space.
Alternatively, he could have been using my name to connect and demonstrate relatedness

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(Wergin, 2019). When he continued to say, “I struggled a lot,” he was honest about something
that could invite my judgment, as he was admitting to struggling with academics, which was
directly connected to his job. In saying that he “struggled a lot … in high school in college,” he
exposed a weakness from his past, and then connected to my reflection when he said, “I wish it
(English) would have been in my my my primary language. I think I would have excelled more
than what I did.” His “wish” admits that his past experience was not how he would have wanted
it to be, and his repetition of “my” could be evidence of nervousness in admitting this. In being
this vulnerable, he demonstrated trust that I would not judge him for his past. His next statement
demonstrates that he was reflecting about how he felt as a student, when he said,
Because it’s like when you’re listening to an instructor, you are processing what they’re
saying. And they need to translate it for you to understand it. And then by the time you’re
doing that he’s explaining something, something else something different … I hated
writing because that was not my language.
He let me into his experience and shared something that he needed to learn, and both actions
demonstrate that he trusted me to react without judgment. When he said, “that was not my
language” he acknowledged the difference between us, and when he said, “It was easier for you
because it was your first language. And I don’t, I don’t know if that’s like a disadvantage for
students” he made a direct comparison between our experiences. When he finished with
“Because it was for me,” he clearly named a disadvantage that shaped his learning experience;
both making the comparison and naming the disadvantage are risks in a typical professional
setting, and therefore demonstrate vulnerability.
In saying, “Yeah, I think it’s definitely unfortunately framed as a disadvantage,” I agreed
with his conjecture, and in doing so reciprocated with vulnerability to build trust. My use of

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“unfortunately framed as” implied that I disagreed with that negative lens of a piece of his
identity, which could have built relatedness as I demonstrated care (Wergin, 2019). When I said,
“And I think it should be looked at as you speak two languages and can learn all these things in
new languages. That is to me a superpower because I could not do that,” I reassured Dante that I
was not coming from a place of judgment; in fact, I was coming from the opposite place in
which I viewed what he expressed as a weakness as a strength. When I said, “This is really
impressive what you’re doing. It’s not a deficit. I think so often it’s framed as a deficit. And it’s
not,” I was again dispelling judgment to make Dante feel more comfortable and cared for in the
space (Wergin, 2019) in the hopes that he would continue to pursue the level of vulnerability that
we would require for him to reflect and grow (Spikes, 2018).
In response to my encouragement, Dante did begin to reflect on his interactions with his
multilingual students as he said, “I think of my students, there’s like a couple of students who, at
first, I knew there were, they needed to help and I’m not helping them as much.” He was
reflecting back on his experience and being honest about a way in which he did not support them
as he could have. When he continued,
Maybe translating, but I know that with their ESL [English-Second-Language] classes,
they’re actually helping them and they’re becoming better. And all I do is I would just
check in with maybe Samantha and I will say like, oh, did you understand it? And she’s
like, Oh, yes or no.
he was reflecting on possible reasons about why he did not support his multilingual students; his
use of “all I would do” implies that he thought that he could have done more, and was exposing
that, prior to this conversation, he depended on ESL classes to support students instead of him.
He then said, “but I could also relate back to when I was going to school,” which is evidence of

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potential growth moving forward, as he considered an alternative path forward based on his own
experience. His overall increased level of vulnerability moved him to reflect and begin to
imagine a potential place for growth in his practice (Spikes, 2018), which is evidence that (a) my
displays of vulnerability increased the trust Dante had in the space (Spikes, 2018; Tharp &
Gallimore, 1989) and (b) that this was more effective for him in an individual space than the
initial collaborative space.
I continued to display vulnerability in both collaborative and individual spaces over the
course of the action research, and as a result participants began showing greater degrees of
vulnerability, and therefore trust, in both spaces. The following excerpt, from our third and final
collaborative session of the study, demonstrates the growth that all participants showed in their
willingness to expose personal information to their colleagues. I began the final collaborative
meeting by asking participants about a conference that they had just attended. I then asked
participants to individually read the provided article Developing Mathematics Identity (Allen &
Schnell, 2016). Following 10 minutes of individual reading, I directed participants to consider
guiding questions, which they then answered with their assigned partners. Following the partner
discussions we engaged in a brief whole-group share-out. For the final section of the session,
participants were paired with a different partner and were provided with clips of each teacher’s
recent lesson. Together, pairs chose a video clip to watch and engaged in the see and describe
phases of the reflective cycle; this was the first time that teachers did this without my facilitation.
Following the see and describe time, I instructed participants as to how to engage in the Circle of
Voices protocol (Brookfield, 2017) around the question “How do I see my own mathematics
identity reflected in that of my students? In my classroom?” After 2 minutes of silent reflection,
participants spoke for 2 minutes. Non-speaking participants were instructed “Please refrain from

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interruptions or statements while each person is sharing.” The following excerpt is the responses
of each participant.
K: So, we already did the reflect activity. So now this first round, you’ll spend 1
minute presenting. Presenting is just sharing whatever you’re thinking right now,
and then the second round we’ll get the opportunity to respond to others. Okay.
All right. Does anybody want to start us off?
Blake raises her hand.
K: Go ahead.
B: Um, so, when I was in elementary and middle school, I was really, really bad at
math. I know that many people have heard this story but like I never took Algebra
1, no I had to take algebra one twice. And I never took calculus because I was just
so, I just really firmly believed I wasn’t good at math. I was a reader. I was a
writer. And I think that because of, because of that, I think that I want to be the
math teacher that doesn’t, doesn’t put that idea in kids and helps kids come out of
that idea. So, I think that the biggest math identities that I’m trying to build are
just like normalizing error. And then also trying to have students understand
through goal setting that like learning and mastery can happen anytime. Like I
don’t feel like I really felt good about math until Algebra 1 the second time, and
that’s okay. Like I’m a fully functional human who can like work in the world
with math and it’s okay. Like I you know, I’m never going to be like an engineer,
but I lucky I don’t want to be an engineer. You know, like, if I wanted to be an
engineer, I probably could still figure it out. Like it’s okay.
K: Does anyone want to go next?

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J: For me, I’m really trying to push kids with annotating their word problems
because I need to reread information over and over and over again. So, I want to
normalize that for them. That is that the information isn’t going to disappear once
you read it through once, it’s still there, go back and reference it, because it takes
me a while to like process the information and really figure out well what do I
need to do? So, I want them to realize that it’s okay for me to do that. And it’s
also okay, if you don’t need to do it and you’re able to go ahead and start solving
those solving those problems. And I like to plan, I like to make lists so I think
that’s where else I like to push their, like to come up with their action plan. How
are you going to approach a problem? Because then, inevitably, that helps me as
our teacher figure out, like, where is it? Where are your gaps? Is it the math, like
computation gaps, or is it more of a conceptual gap?
D: I guess for myself, it’s kind of like similar to Blake’s because when I was in
elementary school, I was really good in math. But I was very quiet. I guess for
that reason, I chose to go into engineering. I don’t really like to talk and I could
see it in my students. And it’s hard for me to make them you know, talk and I, I
understand that. So, I’m working on, working on that and also just trying to make,
trying to see how the things that we go over in class is connected to, like, it has a
sequence like whatever we learned before it we’re doing it now how is this gonna
be connected to the next lesson and so on. So, I want them to see those different
connections so. Because I think even adults that were they asked this question a
lot like … cut off by timer.

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When I said, “So we already did the reflect activity,” I was restating the purpose of our
space, which was to reflect and grow (Spikes, 2018); this requires vulnerability. I then said, “So
now this first round, you’ll spend 1 minute presenting. Presenting is just sharing whatever you’re
thinking right now, and then the second round we’ll get the opportunity to respond to others,”
which set up a space similar to that of our first sharing of our I am From poems in the first cycle;
however, this time I prepared the team to be able to respond to others, which demonstrates that I
was pushing participants to take a bigger risk in the space than I had in the first collaborative
meeting of our action research. When I said, “Does anybody want to start us off?” Blake selfselected to start by raising her hand, which again shows growth in her willingness to risk sharing
personal information with her peers in our space, compared to the first session when I had to
request that she share first.
Blake started with, “Um, so, when I was in elementary and middle school, I was really,
really bad at math,” which immediately demonstrates vulnerability in exposing a weakness
directly related to her job and therefore carrying possible judgment. When she continued, “I
know that many people have heard this story,” she acknowledged previous vulnerability and then
persisted in sharing several details. In saying, “but like I never took Algebra 1, no I had to take
Algebra 1 twice” she again admits failure at mathematics, something that her colleagues could
judge her for. When she continued, “And I never took calculus because I was just so I just really
firmly believed I wasn’t good at math” she reflected on how her beliefs about herself informed
her choice to take an advanced course as a student. She then returned to her practice by saying,
“And I think that because of, because of that, I think that I want to be the math teacher that
doesn’t, doesn’t put that idea in kids and helps kids come out of that idea,” which is evidence
that she was trying to provide her students with a different experience than she had growing up

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and therefore was her sharing a judgment of her own experience. She then shared how she was
trying to grow in her practice when she said, “So I think that the biggest math identities that I’m
trying to build are just like normalizing error. And then also trying to have students understand
through goal setting that like learning and mastery can happen anytime.” Her reflection, “Like I
don’t feel like I really felt good about math until Algebra 1 the second time, and that’s okay.
Like I’m a fully functional human who can like work in the world with math and it’s okay” is
evidence that she has reflected on how her mindset has changed since she herself was a student.
She concluded with,
Like I you know, I’m never going to be like an engineer, but I lucky I don’t want to be an
engineer. You know, like, if I wanted to be an engineer, I probably could still figure it
out. Like it’s okay.
which is evidence that, through her reflection, she had come to terms with this piece of her own
mathematics identity and had grown to accept it (Spikes, 2018).
When I said, “Does anyone want to go next?” I again provided everyone with the choice
of sharing. Julia took up the invitation with, “I’m really trying to push kids with annotating their
word problems,” which shows that she, too, felt more comfortable sharing in the space than she
did in the first collaborative session. Her statement shares how she was trying to grow, and her
next statement, “because I need to reread information over and over and over again” shows that
her growth was due to reflection about how her own experience impacted her professional
choices (Spikes, 2018). She took a risk in admitting to her own weakness, and then continued to
share about how she might change her practice because of it when she shared,
So, I want to normalize that for them. That is that the information isn’t going to disappear
once you read it through once, it’s still there, go back and reference it, because it takes

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me a while to like process the information and really figure out well what do I need to
do?
This is more evidence that she was relating her reflection to possible growth and doing so in a
vulnerable way that shared a weakness that she saw in herself. When she said, “So I want them
to realize that it’s okay for me to do that. And it’s also okay, if you don’t need to do it and you’re
able to go ahead and start solving those solving those problems” she acknowledged that,
although she needed something as a student, not every student would need the same thing, which
displayed vulnerability in recognizing that every experience was not the same as her own.
In the first collaborative session, Dante refrained from sharing. In this session, he did not
have to be prompted and shared immediately following Julia’s statement. When he shared, “I
guess for myself, it’s kind of like similar to Blake’s because when I was in elementary school I
was really good in math. But I was very quiet,” he acknowledged a strength, and then used “but,”
which implies that he viewed “being very quiet” as something that made him less of a “good”
student. His statement “similar to Blake’s” demonstrates relatedness as he connected to someone
in the space (Wergin, 2019). He then reflected, “I guess for that reason, I chose to go into
engineering,” as he related a trait that he held to a decision that he made. He then displayed
honesty when he said, “I don’t really like to talk;” this could also be him admitting that he might
not be comfortable sharing currently or at all in this space. He continued, displaying vulnerability
in doing something that he didn’t like doing, and related to his students by saying “and I could
see it in my students.” He continued to be vulnerable when he said, “And it’s hard for me to
make them you know, talk and I, I understand that. So, I’m working on, working on that,” as he
was admitting to wanting to grow in his practice based on a reflection that he had about himself
(Spikes, 2018). Consistent with Spikes (2018), demonstrating my own vulnerability did increase

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the amount of trust in our space, as evidenced by the increased vulnerability in all three
participants’ responses between the first and third cycle of research.
Forms of Assistance to Promote (Critical) Reflection-on-Action
In my conceptual framework, I argued that I needed to deepen the level of trust present in
our learning environment for participants to be able to reflect on the way that their identities
impacted the way that they noticed student funds of knowledge and identity. I also argued that to
reflect on how our identities were impacting our instructional moves, we needed to ultimately
reach critical reflection. Prior to this study, any form of reflection was unstructured. The Rodgers
cycle (2002) served as a structure to help us engage in consistent general reflection-on-action. As
we became more used to using the cycle, I intended for us to move from descriptive reflection
toward comparative reflection so that we could “reframe the matter for reflection in light of
alternative views” (Jay & Johnson, 2002, p. 77). Ultimately, we could then engage in critical
reflection to be able to “establish a renewed perspective” (Jay & Johnson, 2002, p. 77); in this
study, that renewed perspective would be aligned to a funds of knowledge and identity mindset.
In this study, I provided two main forms of assistance to support participants in moving from
inconsistent reflection to consistent descriptive reflection, and then towards comparative and
critical reflection. The first was the use of cognitive structuring in both collaborative and
individual spaces, which provided teachers with a “structure for thinking and acting” (Tharp &
Gallimore, 1989, p. 63) as they engaged in reflection. Within the cognitive structures provided, I
used questioning as a second form of assistance, particularly during our individual sessions, to
push participants to turn toward their practice (Horn & Little, 2010; Tharp & Gallimore, 1989;
Sahin & Kulm, 2008) and to seek the alternative views required for critical reflection (Jay &
Johnson, 2002). Together, these forms of assistance enabled participants to engage in consistent

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descriptive reflection-on-action and, within that structure, move toward comparative reflection
with their peers in our third collaborative session. Within the scope of this study, we did not
reach critical reflection; this will be addressed in the afterword.
Cognitive Structuring
I used cognitive structuring to provide organizing and belief structures for teacher
reflection-on-action (Tharp & Gallimore, 1989). These cognitive structures supported learners to
“evaluate[], group[], and sequence[] perception, memory, and action" (Tharp & Gallimore, 1989,
p. 63) during both collaborative and individual sessions. By the end of the study, participants had
grown from inconsistent reflection to supported, structured, descriptive reflection-on-action as a
result. The first cognitive structure, Rodgers’s cycle (2002), provided a structured, organized
process for consistent general reflection-on-action (Rodgers, 2002; Tharp & Gallimore, 1989).
My main goal in adopting the Rodgers cycle as a cognitive structure was to assist teachers in
slowing down their thinking and helping them to be more present; in slowing down, they could
then work toward “seeing [themselves] from unfamiliar angles” (Brookfield, 2017, p. 3). To
provide more cognitive support for movement towards critical reflection-on-action, I additionally
provided the funds of knowledge and identity approach as a second cognitive structure; this one
as a belief structure. This oriented teachers to the belief that consistent reflection-on-action
would support them in better noticing our students’ funds of knowledge and identity (Moll et al.,
1992; Tharp & Gallimore, 1989; Rodgers, 2002). This consistent noticing could then eventually
lead to our long-term goal of leveraging those funds of knowledge and identity into lessons so as
to affirm students as mathematical problem-solvers.
In my first individual session with each participant, I introduced Rodgers’s cycle (2002)
as the cognitive organizing structure for our reflection-on-action. Although I did not name types

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of reflection explicitly to participants, I directly introduced the cycle as an organizing structure
(Tharp & Gallimore, 1991) for general reflection. My learning goal for the session was that
participants would “LO 2: Engage in the see and describe cycles, beginning to attend to
identity” (Cycle 1 Handout, p. 5). I began each individual session by explaining how I came to
my dissertation, and then provided participants with a note catcher that contained the learning
objectives, my conceptual framework image, and relevant excerpts from the literature. I next
explained why I chose to use my video in our initial reflective cycle experience, and then
provided context behind my video. Next, we watched a video of my practice together. I then
asked participants to describe what they saw and then described what I had seen. A reflective
conversation followed, during which I used guiding questions and the structure of the cycle to
push us toward comparative reflection (Jay & Johnson, 2002; Sahin & Kulm, 2008). The
following excerpt of Blake’s first individual session is representative of the way I introduced the
cycle to all three participants in their sessions, and the conversation that follows demonstrates
how Blake began to use the cognitive structures of Rodgers’s cycle and a funds of knowledge
and identity belief framework to engage in structured reflection-on-action and move toward
comparative reflection.
K: Um, well, so I basically, based on … I basically read a whole lot of things and
pulled together some pieces of literature that I thought would be an interesting
way to explore this idea. So, there’s a lot of literature around noticing student
thinking and I just put this together for you so you kind of have an idea of what’s
going on. So, there’s a lot of …
B: Why did I think that that said, LOL?

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K: Oh no LO1. (K: Laughs.) (B: Sorry.) If you want to laugh at it, you can! Um, our
learning objectives. Um, yeah, so the idea is that we’ll explore the connection
between identity funds of knowledge and something called the Rodgers cycle. So
that picture there is a version of the Rodgers cycle. Basically, Carol Rodgers
created this reflective cycle in which, is mainly geared toward teachers and
professionals that are working with other humans, in which you see and describe
some kind of event. And then you analyze it, and then you create some kind of
experiment based on what you saw, and then that cycle repeats again. (B: Ok.) In
our work together, we’re probably going to stay in the see describe, analyze piece,
if there’s something that naturally comes up that we’re like, ooh, that would be
cool if we try it, we can, but since it’s a shorter amount of time together, we’ll
probably just do the see, describe, analyze. And then like I said, if we want to
continue this work, if we find this helpful, we can keep it going for as many years
as we work together as frequently or non-frequently as we want. If at the end of
this we’re like that really did not make us think anything differently, then that’s
great feedback for me to think about how to change this process in a way that’s
more meaningful. So as honest and open as you can be about the experience, I
really appreciate it. (B: Yah.) And then the other thing that I mentioned like I’m
also a learner in this completely and so I will be asking you questions, obviously,
but also hope that you’re asking me questions and challenging me with the things
that I’m thinking (B: Sure.) so that we can hold each other accountable and push
each other and challenge each other a little bit. (B: Ok.)
…

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B: Okay, so then when So then when you’re describing what you think happened
before, watch the video. So then, when we’re analyzing it when we’re when we’re
writing everything down, is that see or is it analyze?
K: So, we’re … I’m going to describe what I think happened, then we’ll see what
actually happened and then we'll come back to the describe and kind of think
about What was real? What did I miss? Maybe things did I overlook when I
described it the first time and then why do I think I overlooked those things.
Okay, okay. Um, which kind of then leads us into the analysis because
B: Yep. I was in the wrong place on the circle.
Watch video
K: Okay all right. So, what are some things that you saw?
B: I felt like I saw three and three entries of the tell me something true. So, your first
one about when you said tell me something true a student talked about where the
line was flat that one was like wrapped up pretty quickly seems like everyone
agreed. You clarified and then the next one told me something true the student
chose to talk about like the first portion of your line. I think between zero and two
is what it was. You pushed? You added another question about acceleration. And
then the third tell me something true. You talked about the downward turning
portion. I guess that’s like four to six or something like that. Where our student
had said it was negative velocity. You turn them into a turning talk. You came
back. A kid said it wasn’t negative. To clarify that the student you and the
students then talked about the part of the graph that is negative and then circled
back and said it’s not negative clarifying also what we meant by it and how kind

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of like in a annexed in an addendum, we talked about how that was you talked
about how that was acceleration and not velocity and then the video stopped.
…
B: Am I doing this right (B: Whispers.)
K: (K: Laughs.) There’s no right way. Like I said this No. And I mean, I think I
would say yes, because I’m thinking about a lot of things. I totally have my
teacher hat on, I’m probably gonna listen to this recording back and be like, I
didn’t ask any of the questions I want to do, because I totally have my teacher hat
on. But yeah, just thinking like, yeah, I feel like timing is a big thing that I didn’t
formally connect to funds of knowledge, necessarily, like, now I am thinking
about of, like, depth over quantity, and like slowing down and thinking about
even like, think about, like, what that laughter represents? And like, is that, how
to dig deeper into that.
…
B: So, we did, do you feel like we did—just so when it’s about me. (K: Yeah.) So,
we saw it. You told me about it. (K: Yes.) Yeah, we described it. And then we
kind of like did some
K: I would say we kind of moved on to the analyze piece. I think we I think we
moved to the analyze piece. (B: Yeah.) And then I think when
B: It didn’t seem particularly formal, like we didn’t have a structure to it. (K: Yeah).
Do you feel like we talked about your concerns about what you what we saw, like
we you did, we did talk about the concerns that you had going into it? We like
kind of analyzed whether or not the description matched what you like, my

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external perspective, if we like matched. (K: Yeah.) And then we kind of
analyzed, maybe if there were any ways to improve?
K: Yeah, well, I think the analyzed was more of like, when we were saying like, “Oh,
where did that come from?” (B: Oh, okay, those pieces.) And then I think that
yeah, I think that, like, what can we do next is kind of moving toward the
experiment piece of like … (B: oh right!) If I chose to do something, and okay,
yeah. And so, I think that piece would be if we like, planned that out more.
B: This is fun! Because it’s not quite so rigid to like, well, you should have laughed
every 3.5 seconds. Like it’s a little bit more like, yeah, why did you ask that
question in that way? You know, it’s like a little bit more.
When I said, “I read a whole lot of things and pulled together some pieces of literature
that I thought would be an interesting way to explore this idea,” I began to ground our work
together in a belief structure that we could use during our time together. I continued to do so in
continuing, “So there’s a lot of literature around noticing student thinking,” which gave Blake an
idea of what we would be focused on during our time together. I then provided her with a
physical representation of the Rodgers cycle structure in the form of the note catcher; in saying
“so you kind of have an idea of what’s going on,” I implied that she could use this as a thinking
and acting tool (Tharp & Gallimore, 1991) as we worked. When Blake interrupted, “Why did I
think that that said, LOL?” it was evidence that she was taking up the tool and reading the
learning objective. When I replied, “Our learning objectives,” I messaged that we had goals that
we were working toward. I then named that goal and connected it to the cognitive structures we
would be using in saying, “we’ll explore the connection between identity funds of knowledge
and something called the Rodgers cycle.” As I did so, I provided the language for the cognitive

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structures that we would use throughout the study to keep us thinking and acting strategically. I
began to explain the first cognitive structure we would use when I said, “So that picture there is a
version of the Rodgers cycle.” I also directed her to the piece of the physical note catching tool
that would orient her to our process; she could refer to this as she learned to use the Rodgers
cycle as a cognitive structure for reflection-on-action. When I continued with, “Basically, Carol
Rodgers created this reflective cycle in which, is mainly geared toward teachers and
professionals that are working with other humans, in which you see and describe some kind of
event,” I provided more explanation of the structure, and then explained how it could be used to
sequence our thinking and acting (Tharp & Gallimore, 1991) when I said, “And then you analyze
it, and then you create some kind of experiment based on what you saw, and then that cycle
repeats again.” In saying, “In our work together, we’re probably going to stay in the see,
describe, analyze piece,” I again explained our learning goals and named the specific thinking
and acting activities I was asking her to adopt. When I said, “if there’s something that naturally
comes up that we’re like, ooh, that would be cool if we try it, we can, but since it’s a shorter
amount of time together, we’ll probably just do the see, describe, analyze,” I provided context
for the structure and also, consistent with Tharp’s and Gallimore’s stated purpose of cognitive
structures, “provide(d) an organization without calling for a particular action” (1991, p. 66). I
continued to do the same when I said, “And then like I said, if we want to continue this work, if
we find this helpful, we can keep it going for as many years as we work together as frequently or
non-frequently as we want. If at the end of this we’re like that really did not make us think
anything differently, then that’s great feedback for me to think about how to change this process
in a way that’s more meaningful.” My statement offered suggestions for actions following the
cycle, and therefore provided sequencing but without declaring a particular final action (Tharp &

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Gallimore, 1991). I also implied that this was a cognitive structure that we could continue to use
in our future work together. I then directed her how to provide learner feedback to me about
using the cognitive structure when I said, “So as honest and open as you can be about the
experience, I really appreciate it.” I provided a structure for the thinking that we were going to
engage in during the session. When I said, “I’m also a learner in this completely and so I will be
asking you questions,” I messaged that I would be using the structure alongside her to engage in
similar thinking and acting. When I said, “[I] hope that you’re asking me questions and
challenging me with the things that I’m thinking so that we can hold each other accountable and
push each other and challenge each other a little bit,” I named “push” and “challenge” as goals,
thereby providing another purpose as to how and why we were going to use the cognitive
structure during our reflection-on-action.
Following some more conversation, Blake summarized what she had taken up of the
structure when she said, “Okay, so then when, so then when you’re describing what you think
happened before, watch the video;” this demonstrates that she was thinking about how we would
engage in reflection using the provided structure. She then continued with a clarifying question,
“So then, when we’re analyzing it when we’re, when we’re writing everything down, is that see
or is it analyze?” which is further evidence of her attempting to understand the structure that I
had provided. I then reinforced the provided sequencing and acting structures when I said, “So
we’re I’m going to describe what I think happened, then we’ll see what actually happened and
then we’ll we’ll come back to the describe.” I then reinforced the thinking structure when I
provided the questions, “What was real? What did I miss?” I provided more thinking structures
when I said, “Maybe things did I overlook when I described it the first time and then why do I
think I overlooked those things.” I then started to sequence with, “which kind of then leads us

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into the analysis because.” When Blake interrupted with, “Yep. I was in the wrong place on the
circle,” she expressed understanding of my response to her question, as well as demonstrated
evidence that she was using the note catcher, which was a physical representation of the
cognitive structure, to support her understanding.
Following watching the video, I asked the question, “So what are some things that you
saw,” which gave Blake the opportunity to demonstrate how she was taking up the cognitive
structures I had provided. When she said, “I felt like,” she could have been expressing some
doubt in that what she was stating was factual. She continued with, “I saw three and three entries
of the tell me something true,” which was factual and is evidence that she was beginning to take
up the see portion of the structure. Her next statement, “So your first one about when you said
tell me something true a student talked about where the line was flat that one was like wrapped
up pretty quickly seems like everyone agreed” contains multiple instances of summary and
interpretation with the phrases “talked about,” “wrapped up pretty quickly” and “seems like
everyone agreed:” this is evidence that she has not yet completely taken up the structure of
factual description. Her next statement, “You clarified and then the next one told me something
true the student chose to talk about like the first portion of your line,” also includes
interpretation, and then she attempted to recall facts when she said, “I think between zero and
two is what it was.” Her description continues in this way, moving between fact and
interpretation, which shows that, while she is still practicing and has room to grow, she is
beginning to take up the cognitive structuring provided.
After continuing in this way, Blake’s whispered question “Am I doing this right?” is
evidence that she understands that there is a thinking and acting structure that we are attempting
to follow, and that she is concerned about following it correctly. My response, “There’s no right

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way,” is evidence that I have not yet fully internalized the structure or determined how to clearly
support her through it; as stated above, her statement did not fully remain factual. My inability or
unwillingness to name that in the moment weakened the overall structuring that I was attempting
to provide. I came closer to returning us to the thinking structure when I said, “I think I would
say yes, because I’m thinking about a lot of things.” My next statement, “I totally have my
teacher hat on, I’m probably gonna listen to this recording back and be like, I didn’t ask any of
the questions I wanted to, because I totally have my teacher hat on” is evidence that I was
somewhat aware that I was not supporting her in the way that I had originally intended. I did
then return to the belief structures of the funds of knowledge and identity approach when I said,
“I feel like timing is a big thing that I didn’t formally connect to funds of knowledge.” When I
said “now I am thinking about of, like, depth over quantity, and like slowing down and thinking
about even like, think about, like, what that laughter represents? And like, is that, how to dig
deeper into that” I implied a return to the Rodgers cycle in speaking to “slowing down and
thinking,” although I did not explicitly name that return. My responses in this excerpt of the
conversation did not provide strong cognitive structuring, and therefore may have impacted the
way that Blake was able to take up the structures as she was speaking.
At the end of the session, when Blake said, “So we did, do you feel like we did—just so
when it’s about me,” she demonstrated that she understood that the structure that we had used is
something that we would use again in the future. In saying, “So we saw it. You told me about it.
Yeah, we described it” she restated the sequencing structure of the cycle, demonstrating
beginning understanding of the Rodgers cycle as a reflection-on-action framework. When she
said, “And then we kind of like did some” and then paused, it implies that she did not know what
had followed the description piece. My response, “I would say we kind of moved on to the

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Analyze piece. I think we, I think we moved to the analyze piece” again demonstrates that I am
still learning how to use the cycle myself, with the phrases “we kind of” and “I think.” When
Blake responded, “It didn’t seem particularly formal, like we didn’t have a structure to it,” this
implies that my lack of clarity impacted the way that she understood the cycle as a clear thinking
and acting structure. In asking, “Do you feel like we talked about your concerns about what you
what we saw, like we you did, we did talk about the concerns that you had going into it?” she
demonstrated that she was still attempting to understand and internalize the structure that we
used. She continued to summarize the process with, “We like kind of analyzed whether or not the
description matched what you like, my external perspective, if we like matched. And then we
kind of analyzed, maybe if there were any ways to improve?” and in doing so demonstrated that
she was beginning to understand the analyze phase as a structure for potential future action.
When I responded, “I think the analyzed was more of like, when we were saying like, Oh, where
did that come from?” which lacks clarity and also still prompted Blake to reply with “Oh, okay,
those pieces”—more evidence that she was working to orient herself within the Rodgers cycle
structure. In saying, “And then I think that yeah, I think that, like, what can we do next is kind of
moving toward the experiment piece,” I directed her attention to the sequencing nature of the
structure (Tharp & Gallimore, 1991). Her response, “Oh right!” is evidence that she was
recalling previously provided information. Her final statement, “This is fun! Because it’s not
quite so rigid” aligns with the concept of organization without particular action (Tharp &
Gallimore, 1991), and her statement “it’s a little bit more like, yeah, why did you ask that
question in that way?” is evidence that she is beginning to take up the thinking structure
provided. Overall, the evidence provided in this session demonstrates that she is beginning to
take up the Rodgers cycle as a cognitive organizing structure for reflection-on-action and that we

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both had room to grow after this initial attempt. There was less evidence as to how she was
taking up the funds of knowledge and identity belief framework; this will be discussed in later
sections.
By the time of our second collaborative cycle, each participant had experienced using the
Rodgers cycle as a cognitive organizing structure once (as analyzed above). For our collaborative
session, I continued to use the Rodgers cycle as the cognitive organizing structure (Tharp &
Gallimore, 1991), as well as the funds of knowledge and identity approach as the cognitive belief
framework. These cognitive structures served as ongoing structures for cognitive activity and
aided participants so that they could “evaluate[], group[], and sequence[] perception, memory
and action” (Tharp & Gallimore, 1991, p. 63) during reflection-on-action. I began the session by
providing participants with the same note catcher that they had used during their individual
session, to provide a physical representation of both “structure(s) for thinking and acting” (Tharp
& Gallimore, 1991, p. 63). Next, I summarized the cycle and the intent of collaboration; an
excerpt is analyzed below. Following that summary, we collectively watched the same video of
my AP Calculus lesson that we had each individually engaged with, during which I asked
participants to see and to use their note catchers to collect their thoughts. I then asked
participants to describe their sights to the group. Following this, I asked a question about funds
of knowledge in order to provide the belief cognitive structure as a framework that could support
(critical) reflection. An excerpt of our conversation is also analyzed below. Although every
participant did not fully reach comparative reflection, this practice with the cognitive structure of
the cycle supported participants in engaging in collaborative reflection-on-action and ultimately
supported them in moving closer to comparative reflection in their final individual and
collaborative sessions.

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K: Okay, so we are going to go back into the cycle the same way that we all did it
independently. So just a reminder that for the see portion, that is the independent
part where you’re watching the video, naming as many factual things as you
possibly can. So, what are you seeing? What are you hearing? What are students
doing, who is speaking? All of those things. So, there’s a place on page two for
you to write that down and also have some prompts there.
Watch video
K: So, this next stage of the cycle, now that we’ve individually seen, now we’re
going to go around and describe what we think we saw to our colleagues. So, we
will just kind of go in a circle. If you want to name anything that you saw. As
you’re listening to your colleagues, if you want to take notes in that describe
section, noticing anything that they saw that you might have seen differently or
didn’t notice. On that second page, there’s a describe box if you want to be
listening. Great. So, anybody want to start us off with what they saw?
Dante raises hand
D: Um, I’ll start. I noticed that every time you were asking someone a question, or
you were cold calling, you were making them accountable to to give a reason
why. You were checking for understanding. Like it wasn’t just like, “Oh, I agree”,
but you were like “why?” You were waiting for that response.
J: So, what I saw in your classroom, and I know it’s because it’s not your classroom
but I saw students sitting in rows, there was a lot of vocabulary being used in this
activity. And similarly to what Sanchez mentioned, like asking follow up

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questions and having students clarify, based on using the word “it” because that’s
very important. What does that actually mean? What are you referring to?
B: I saw a traditional classroom. It was clean and had usable technology.
K: When you say traditional classroom can you expand on that a little bit?
B: Like what’s it called? When they’re all facing the front? Like stadium stadium
seating? something like that? Isn’t that, I feel like I’ve heard it called that before
sorry if at some point.
K: Is there anything else that we saw that other people didn’t point out? Just make,
just kind of generate as many things as we possibly saw.
D: Another thing that I saw, I think I noticed it now that I didn’t notice the first time
is when you took like a time, time off, timeout. And have you told the students to
talk to their partner about, I think you mentioned that one student got the answer
wrong. But you didn’t wanna like point it out to the student. So that’s when you
decided to like as pair share, I was able to see it now but that was because we
talked about it so I was paying attention to where that was happening. And I know
that I also saw the student standing up.
Conversation continued, with Blake and Julia continuing to describe and interpret “sights” from
the video. I then asked a guiding question to move us toward comparative reflection and the
concept of funds of knowledge and identity
K: So, based on all the things that we saw and that colleagues saw, what are some
things that we might be thinking about in terms of funds of knowledge? And just
clarifying again, that like this is, I have, this is a new process for me too. And I’m
being vulnerable with showing my own teaching, but really, really hoping that

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you’ll, we’ll, generate things, places that I could have better affirmed and
leverage student funds of knowledge as well. So be ruthless in your feedback. I’m
totally okay with it. What are some things that we’re thinking about funds of
knowledge in this space?
B: I guess my gut reaction is that this is I feel like this is a very good example of a
classroom where, I think, and I know this to be true because I know you but like if
I, maybe if I just saw this code, I would just think that this teacher really does
believe in their students. And like is trying to get their students to say more and
take more ownership of the classroom and to like be more vocal and verbal and
like, like more and commit like take a higher lift as a percentage of the
conversation. But just that there’s like a missing piece and I don’t know if the
missing pieces now, whether or not, yeah, so like the intent is there. I think that
the background knowledge is there. But there’s just something where I don’t
know, there’s just something there’s a piece missing where maybe the kids don’t
believe that they’re allowed to do it? or the kids don’t think that they should do it
or they don’t know how to do it or if there’s something about, whether there’s no
like they there’s no perceived social capital in it. I don’t know like that’s what I’m
that’s what I would say that’s what I did say …
B: Can I say more? (K: Yeah.) also I think that the kids do and I’m thinking back
about it. I do think that the kids know that they can participate because the calling
out and not getting in trouble for it. And then also like the kind of chit chat and
like the laughing suggests to me that the kids feel very comfortable in this class
like it didn’t feel disrespectful. I don’t know how it would feel for the teacher. But

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like I didn’t think perceive the chit chat is like super disrespectful. It was more
just like, you know, like in a professional development meeting would like I
would just mention something to a colleague or something like that. But then it’s
like, how come the kids weren’t like saying longer sentences or half of the kids
weren’t like, giving evidence first. Like why were they why do they need
prompting for evidence? Because they had it when the teacher asked for it. You
know, that kind of thing.
K: That’s interesting. That’s something I didn’t notice from all the times I’ve
watched it or didn’t attend to is that like, is the length of their sentences and the
complexity of their sentences initially.
J: And being that it’s an AP class, I could assume they have a positive or very, very
strong math identity. So, thinking back to my own experiences, my AP class was
maybe eight or nine students. So, the fact that you’re saying there’s 25 of them
like that is amazing. And generally, is like the top math performing students will
typically will go to take the AP Calc class. So, thinking back to what we were
discussing about [student name], like if you’re so used to being the top of her, so
used to always being right. What are students experiencing when maybe they’re
struggling or they get things wrong? Just wondering just wondering, like, what
else can be incorporated to make them feel comfortable, I don’t know, if that
makes any sense?
When I initiated our work with, “Okay, so we are going to go back into the cycle the
same way that we all did it independently,” I was reminding participants of how we used the
Rodgers cycle previously as our cognitive organizing structuring (Tharp & Gallimore, 1991).

134
When I said, “So just a reminder,” I implied that participants already had the knowledge that I
was about to restate. As I continued, “that for the see portion, that is the independent part where
you’re watching the video naming as many factual things as you possibly can,” I set the
expectations for thinking and acting for the first phase of the cycle (Tharp & Gallimore, 1991).
When I continued with, “So what are you seeing? What are you hearing? What are students
doing, who is speaking? All of those things” I prompted the mental operation of descriptive
reflection (Jay & Johnson, 2002; Tharp & Gallimore, 1991) using the structure of the Rodgers
cycle. I then prompted participants to refer again to our physical representation of our organizing
cognitive structure when I said, “So there’s a place on page two for you to write that down and
also have some prompts there.” Following the video, my statement, “So this next stage of the
cycle, now that we’ve individually seen, now we’re going to go around and describe what we
think we saw to our colleagues” reminded participants that we were using the cycle as our
organizing and sequencing structure (Tharp & Gallimore, 1991). When I said, “If you want to
name anything that you saw,” I again expressed expectations for how we were going to act.
When I said,
As you’re listening to your colleagues, if you want to take notes in that describe section,
noticing anything that they saw that you might have seen differently or didn’t notice. On
that second page, there’s a describe box if you want to be listening,
I again prompted back toward using the note catcher as a physical organizing structure. In saying
“anything that they saw that you might have seen differently or didn’t notice,” I was preparing
participants to begin thinking about alternative views to ultimately move us toward comparative
reflection (Jay & Johnson, 2002). When Dante volunteered,

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I noticed that every time you were asking someone a question, or you were cold calling
you were making them accountable to give a reason why you were checking for
understanding. Like it wasn’t just like, ‘Oh, I agree, but you were like why?’ You were
waiting for that response,
he offered a descriptive reflection. Julia’s response demonstrated that she was internalizing the
instruction to be “factual,” as she said, “So what I saw in your classroom, and I know it’s
because it’s not your classroom but I saw students sitting in rows, there was a lot of vocabulary
being used in this activity.” She then cited exact phrases that I had used in the video when she
said “What does that actually mean? What are you referring to?” Blake also followed my
instruction to be factual when she volunteered “I saw a traditional classroom. It was clean and
had usable technology.” I then probed, “When you say traditional classroom can you expand on
that a little bit?” which prompted Blake to volunteer more factual details and re-engage with the
cognitive structure as she said, “When they’re all facing the front? Like stadium seating.” When
I asked, “Is there anything else that we saw that other people didn’t point out? Just make, just
kind of generate as many things as we possibly saw” I supported participants cognitively by
asking for them to re-engage with the Rodgers cycle and, in doing so, generate more descriptive
reflection (Jay & Johnson, 2002; Tharp & Gallimore, 1991). This question did prompt more
descriptive reflection, as Dante shared,
I think I noticed that now that I didn’t notice the first time is when you took like a time,
time off timeout. And have you told the students to talk to their partner about I think you
mentioned one student got the answer wrong. But you didn’t wanna like pointed out to
the student. So that’s when you decided to like as pair share.

136
Dante’s statement began to move toward comparative reflection; he is not comparing with
someone else, but he is moving toward an “alternative view” (Jay & Johnson, 2002) when he
says “I didn’t notice the first time,” as he is comparing his earlier view with a new view. When
he said, “I was able to see now without that was because we talked about this, I was paying
attention to where that was happening. And I know that I also saw the student standing up” he
demonstrated how he was beginning to generate more descriptive reflection due to the cognitive
structuring that I provided.
Once there was a lull in conversation, I asked, “based on all the things that we saw and
that colleague saw, what are some things that we might be thinking about in terms of funds of
knowledge?” The phrase, “based on all the things that we saw and that colleagues saw,”
prompted participants to consider their colleagues alternative views (Jay & Johnson, 2002) and
“funds of knowledge” assisted participants in returning to funds of knowledge and identity as our
cognitive belief structure (Jay & Johnson, 2002; Tharp & Gallimore, 1991). When I said, “really
hoping that you’ll, we’ll, generate things, places that I could have better affirmed and leverage
student funds of knowledge as well,” I’m reminding participants of the purpose of using the
Rodgers cycle, and making a connection between both cognitive structures provided.
When Blake volunteered, “I guess my gut reaction is that this is I feel like this is a very
good example of a classroom where, I think, and I know this to be true because I know you but
like if I, maybe if I just saw this code, I would just think that this teacher really does believe in
their students,” she engaged in descriptive reflection about her feelings about the instruction (Jay
& Johnson, 2002). When she said, “But there’s just something where I don’t know, there’s just
something there’s a piece missing where maybe the kids don’t believe that they’re allowed to do
it? or the kids don’t think that they should do it or they don’t know how to do it or if there’s

137
something about, whether there’s no like they there’s no perceived social capital in it,” she
considered how students’ beliefs impacted the ways that they engaged with my lesson. This is
beginning to move toward comparative reflection as, consistent with Jay’s and Johnson’s
definition, she is considering “how (do) other people who are directly involved describe and
explain what’s happening” (2002, p. 77). Her long pause could indicate further internal
reflection, as she then continued with “Can I say more? (yeah), also I think that the kids do and
I’m thinking back about it. I do think that the kids know that they can participate because the
calling out and not getting in trouble for it,” which shows that she is continuing to consider how
students might be feeling in the space. She then returns to more descriptive reflection with, “And
then also like the kind of chit chat and like the laughing,” but then starts to move back toward
comparative when she considers the students in saying “suggests to me that the kids feel very
comfortable in this class.” However, she then moved back into descriptive reflection in thinking
about her own feelings about the situation when she said, “like it didn’t feel disrespectful.” Her
statement “I don’t know how it would feel for the teacher” recognizes that an alternative view is
possible (Jay & Johnson, 2002), and then she again returns to descriptive reflection in saying,
“But like I didn’t think perceive the chit chat is like super disrespectful. It was more just like,
you know, like in a professional development meeting would like I would just mention
something to a colleague or something like that. She ended her statement by asking the
questions, “But then it’s like, how come the kids weren’t like saying longer sentences or half of
the kids weren’t like, giving evidence first? Like why were they why do they need prompting for
evidence? Because they had it when the teacher asked for it. You know, that kind of thing:” this
last piece is evidence that she is considering student actions and reflecting upon reasons behind

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them, which shows that she is using the cognitive structures provided to begin to move toward
comparative description.
My brief response, “That’s interesting. That’s something I didn’t notice from all the times
I’ve watched it or didn’t attend to is that like, is the length of their sentences and the complexity
of their sentences initially” acknowledged that Blake offered an alternative view to what I had
initially seen. When Julia then said, “And being that it’s an AP class, I could assume they have a
positive or very, very strong math identity,” she considered the identity of the student, which
could be evidence that she has taken up the cognitive belief structure of funds of knowledge and
identity (Tharp & Gallimore, 1991). When she continued, “So thinking back to my own
experiences,” she engaged in descriptive reflection, and continued to do so in saying,
My AP class was maybe eight or nine students. So, the fact that you’re saying there’s 25
of them like that is amazing. And generally is like the top math performing students will
typically will go to take the AP Calc class.
She then began to consider the student experience, thus moving toward comparative reflection,
when she said, “Thinking back to what we were discussing about [student name], like if you’re
so used to being the top of her, so used to always being right. What are students experiencing
when maybe they’re struggling or they get things wrong?” She then began to consider seeking
other ways of accomplishing a goal (Jay & Johnson, 2002), when she said, “Just wondering just
wondering, like, what else can be incorporated to make them feel comfortable, I don’t know, if
that makes any sense?”
For our final collaborative session within my action research study, I created the
opportunity for participants to demonstrate to what extent they had internalized the Rodgers
cycle as a cognitive organizing structure for reflection-on-action. The session started with a

139
check-in, in which participants shared their experience that they had had the past weekend at a
conference. I then provided a brief summary of the way that we had spent our sessions up to this
point, and again provided physical representation of our cognitive organizing structure in the
form of a note catcher. Next, we engaged in our reading and discussion of the article Developing
Mathematics Identity (Allen & Schnell, 2016), as previously analyzed in Finding 1. This
provided an extension to our current cognitive belief structure, which I intended to support
comparative reflection. Jay and Johnson (2002) describe comparative reflection as “reframe[ing]
the matter for reflection in light of alternative views, others’ perspectives, research, etc.,” and
this article served to provide alternative views that we could consider, as well as broaden our
ideas of mathematical funds of knowledge and identity. Our final activity was to engage in the
Rodgers cycle in pairs. An excerpt of the ways of which I provided cognitive structuring in
setting up the partners is analyzed below. After recording their sights while watching the video,
pairs moved into the describe phase of the cycle together. An analysis of the ways in which they
did or did not take up the cognitive organizing structure of the Rodgers cycle and/or the
cognitive belief structure of the funds of knowledge and identity approach are analyzed below.
K: All right. Thanks, everyone for sharing. I think we are going to, well, no, I know
what we’re going to do next is we’re going to move into different groups, so you
have a chance to talk to somebody else. And we’re going to spend just, gonna
watch like a 10-minute clip of your own classroom or your partner’s classroom.
You can decide who you want to watch or if you want to split it half in half, that’s
fine, too. Really not focusing—it’s really hard—but try not to focus on yourself.
(B: Yeah.) Trying really hard to think about what the kids are saying and what
they’re doing and looking keeping this idea in mind of what are the successes that

140
we’re seeing, or where are some places that we can highlight those success that
maybe wasn’t highlighted originally. Alright, so again, really hard not to watch
yourself. Trying to focus on the students and what the students are saying and
doing and learning, and then keeping this idea of mathematical success in mind.
So, I’m gonna move you into groups and give you, oh, I forgot that you could
have used this with the article too but I’m gonna give you a note catcher, and I’m
gonna have Blake and Julia and [Instructional Assistant] work together. And then
[Instructional Assistant] and Dante. You two work together. And then in the
agenda, there are links of videos of your classroom and there’s that (passing out
note catchers) and if you turn to the second page, there’s our see and describe
boxes. This is just a note catcher for you to, as you’re watching, think about
anything that you’re seeing. So, what are you seeing from students? What are you
hearing from students? … I know it’s not comfortable watching yourself.
Hopefully we’re getting more and more used to it as we’re doing it, but thank you
for being vulnerable in that. And then, like I said, the videos are linked on the
agenda that I sent you can choose whichever video you want.
…
J: For yours B, I heard a lot of you affirming kids along the way. It was in the very
beginning, it was, I wrote down a in the very beginning. I wrote down affirming. I
don’t remember what exactly now. But there was, you affirm them at the very
beginning. Like we may not know, I think the vocab, he didn’t know the vocab
but he knew what he needed to do
B: Yeah, the number on top is bigger. Yeah.

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J: So, I saw that consistently throughout your lesson or the video clips that we saw
and just no matter how large the numbers got, just letting them know it’s okay
don’t get discouraged like use a calculator if needed. It’s not a big deal.
B: I think something, well I also think of lessons were so different. Yeah, yeah. But
something I thought I saw the the format or lesson and I don’t know if this, well
I’m just gonna say it, I’m not going to you know, I really think that you are very
clear about your instruction. And I felt like I, from what I from what I could see in
this shot, which is just their heads (all laugh) I felt like the kids were really
participating. Like it looks like, especially from the student work, it looks like the
kids are really involved in the lesson or the activity and I feel like that’s a credit to
having very clear instructions. And having set it up in a way and I think I heard
I’ve heard you do some checks for understandings for instructions to make sure
that the kids knew what was happening.
J: And that’s because it went horribly wrong in the previous class.
B: OHH.
J: Laughs. So, I knew like okay, let me clarify these instructions because other
classes
B: Ain’t that the way! Something that I think is different is that and also this is one
video, but something I noticed that’s different in your video than my video maybe
is that there aren’t hands. You just call. (J: Yeah.) In these two specific videos, I
think that was a different thing.
J: Yah. But then for yours, you also like, you call out the kids like “I want to call on
so and so.” Maybe like were they still working or just see them …

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B: Well in that clip it’s only half of the kids, right? So, in my head if you’re only 16
kids, everybody should talk at least once. So that’s why I’m calling, I’m kind of
calling out the kids that have not like participated yet? Yeah, and like also, I was
trying to encourage [student name] who’s one of the newcomers to like, feel okay
about sharing whatever he could. And so, I felt like I was really happy to see that.
And when people were, when he was able to raise his hands, I felt relieved. So, I
think the types of mathematical success I thought your room is like kids, um, hold
on where’d it go? (B: Refers to article.) I think I saw kids listening carefully and
restating someone’s thinking because they had to be able to understand if they
actually agree or disagree with Annabelle. I think I saw them, I think in the
activity, something that’s built in is representing an idea in any way, because isn’t
it giving, some of the equations are the same? Right? So, I think being able to
make connections like that, so that I you know, the fact that the kids got it right,
that was definitely a mathematical success.
J: And then for yours, obviously using the math tool like using the calculator. They
were doing dividing fractions. So, they had to bring in their knowledge of
multiplying and knowing how to deal improper fractions so doing that all that is
not in isolation. Whatever shows up, you know what you need to do.
…
B: In 6th grade right now, sorry we’re off task right now, in sixth grade like, they’re
really trying to do this. Like 54. Yeah, like, this is what they’re really trying to get
them to do. Which is confusing, but. Something that I definitely am seeing them
seeing differently than the way I remember the lesson is I remember that lesson

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felt really hectic. Like I felt like I was pulling teeth. But then watching it. It
actually just seems more like I’m trying to take my time. Or like let the kids have
this time to like. You know, but in my head I’m like, “I’m dying.”
When I said, “What we’re going to do next is we’re going to move into different groups,
so you have a chance to talk to somebody else,” I provided an expectation for how we were
going to act next. When I continued with, “Really not focusing—it’s really hard, but try not to
focus on yourself,” I was restating acting expectations that we had used previously within the
cognitive structure of the Rodgers cycle. Blake’s response of “Yeah” is evidence that my
statement was consistent with something that she had already heard, and therefore that she was
taking up the thinking and acting framework as we used it repeatedly. In saying, “trying really
hard to think about what the kids are saying and what they’re doing” I was reinforcing the
expectations of the see phase of Rodgers’s cycle. I then referred to the article, an extension of
our cognitive belief framework, when I said, “keeping this idea in mind of what are the successes
that we’re seeing.” I next implied seeking alternative views (Jay & Johnson, 2002) when I said,
“or where are some places that we can highlight those success that maybe wasn’t highlighted
originally.” I again emphasized the cognitive organizing structure of the Rodgers cycle when I
confirmed expectations for the see phase, in saying, “All right, so again, really hard not to watch
yourself. Trying to focus on the students and what the students are saying and doing and
learning.” I then again reemphasized the literature as a piece of our cognitive belief structure
when I said, “then keeping this idea of mathematical success in mind;” this also served as mental
prompting (Tharp & Gallimore, 1991) to use the article within the cycle. I then said,

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I’m gonna give you a note catcher … there’s that and if you turn to the second page,
there’s our see and describe boxes. This is just a note catcher for you to as you’re
watching to write down anything that you’re seeing.
In saying this, I both provided the note catcher as a physical representation of the cognitive
organizing structure (Tharp & Gallimore, 1991) that participants could also use as mental
prompting (Tharp & Gallimore, 1991). I restated the see expectations again when I prompted,
“So what are you seeing from students? What are you hearing from students?” The cognitive
structuring set up participants to engage in a supported, structured reflection-on-action with their
partners, as well as to begin to move toward comparative reflection.
Following watching the video with Blake, Julia said, “I heard about, you are affirming,”
which was evidence that she had taken up the see phase of the reflective cycle. She also repeated
“I wrote down” twice, which is evidence that she was using the note catcher to organize her
sights while watching the video. She then used an exact quote that Blake had said during her
video when she said, “it’s okay don’t get discouraged like use a calculator if needed it’s not a big
deal,” which is evidence that she was attending to the exact words spoken. Blake then said, “I
don’t if this, well I’m just gonna say it” and follows with an opinion; this could potentially
represent her understanding that opinion does not belong in this portion of the reflective cycle,
although that is an assumption. She then switched back to factual sights when she said, “from
what I could see in this shot.” Her next comment involved some interpretation, but also some
facts when she said, “I heard you do some checks for understanding for instructions:” she did not
give exact quotes. She then interpreted “checks for understanding” to mean “to make sure that
the kids knew,” which was not factual, and she was also still describing what she saw in the
video which is evidence that she knew where she was in the cycle. After Julia added some

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context by saying “That’s because it went horribly wrong in the previous class,” Blake continued
to add detail when she described the differences between raised hands in her video and in Julia’s.
Julia responded with details about the way that Blake called on students, and Blake added
context. After doing so, she directed the conversation back to the reflective cycle and the article
when she said,
So, I think the types of mathematical success I thought your room is like kids … hold on
where’d it go? (B: Refers to note catcher.) I think I saw kids listening carefully and
restating someone’s thinking because they had to be able to understand if they actually
agree or disagree with Annabelle.
In saying “I think I saw kids …” after checking the note catcher, she demonstrated that she was
using the cognitive structuring provided to stay in the cognitive organizing structure of the
Rodgers cycle. She also began to move toward comparative reflection with the help of our
cognitive belief framework, as she was considering an alternative view of success when she said
“listening carefully and restating someone’s thinking”—a form of success included in the article.
Julia followed her lead in returning to the article when she said, “And then for yours, obviously
using the math tool and using the calculator:” these were also named successes in the article.
When she continued, “So they had to bring in their knowledge,” she connected back to funds of
knowledge, which was our original learning goal, and which is also evidence of her returning to
the cognitive belief structure. After a brief interlude in which the two compared ways to convert
between fractions and percentages, Blake said, “sorry we’re off task right now.” This is further
evidence that she understood what the task was and recognized that their conversation was not
consistent with the cognitive thinking and acting that they were expected to be engaged in. She
then returned to the Rodgers cycle when she said, “Something that I definitely am seeing them

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seeing differently than the way I remember the lesson is I remember that lesson felt really
hectic.” Although still descriptive, this statement could be viewed as movement toward
comparative reflection as she was comparing her previous view with her current view; her next
statement “But then watching it” implies that viewing the video within the Rodgers cycle made
her consider an alternative view (Brookfield, 2017; Jay & Johnson, 2002). Throughout the course
of this excerpt, both participants remain reflective for large pieces of their conversation.
Although most of that reflection is descriptive, that is consistent with the see and describe pieces
of the cycle. Their references to the literature and funds of knowledge then began to move
toward comparative reflection and could serve as a foundation for continuing this movement
post-study. Overall, both demonstrated that they were able to use the cognitive structures
provided to engage in supported, descriptive and comparative reflection-on-action in order to
consider students’ funds of knowledge and identity.
Questioning
In my conceptual framework I argued that the Rodgers cycle (2002) provided an
explanatory and belief structure for my participants and me as we engaged in reflection (Tharp &
Gallimore, 1991). To assist teachers in growing from descriptive reflection toward comparative
and then critical reflection (Jay & Johnson, 2002; Spikes, 2018), I needed to engage participants
in conversations that elaborated on problems, elicited more details, and imagined alternative
views (Brookfield, 2017; Horn & Little, 2010; Rodgers, 2002). To accomplish this, I used
questioning as a form of assistance to help us turn toward practice (Horn & Little, 2010; Sahin &
Kulm, 2008) with a funds of knowledge and identity lens. In this study, practice referred to using
reflection-on-action in order to notice student funds of knowledge. More specifically, I used
probing questions which “ask for clarification, justification, or explanation” (Sahin & Kulm,

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2008, p. 224), to help us normalize and generalize; this provided teachers with “substantial
agency in defining and elaborating on the problem and in working out possible responses” (Horn
& Little, 2010, p. 192). As a result of my probing questioning within the phases of the cycle, we
moved from turning away from practice as we described to turning toward practice; this, in turn,
assisted participants in deepening their reflections and moving towards a funds of knowledge and
identity approach.
Prior to this study, our individual coaching sessions revolved around planning for future
lessons and therefore did not prompt teachers to engage in any form of reflection on their
previous instructional decisions. If reflection did naturally happen, it remained descriptive (Jay &
Johnson, 2002). In the first individual coaching meeting of this action research study, I used the
same agenda for each participant. I started the meeting by explaining how my work in this
doctoral program and my own teaching experiences led me to formulate my research question. I
then provided a brief overview of the cycle, followed by sharing that I chose to use my own
video for the first session to model what the experience would look like for participants in cycles
2 and 3. Next, we watched my video (described in my first finding) and then took turns sharing
what we saw. The remainder of the meeting was spent in conversation about my video. A similar
agenda was followed in individual sessions 2 and 3, this time, with videos of participants’
instruction. It was during the conversations that followed the videos that I used probing
questioning to turn us toward practice. The following excerpts, one from each participant, were
analyzed to evaluate the use and impact of my probing questions in our effectiveness at turning
toward practice with a funds of knowledge and identity lens. This first excerpt is from Blake’s
first individual session.

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K: Yeah, and I think that’s always the, another thing I struggle with is, I feel like
doing more activities means more learning (B: Ohhh.) And that … (B: Which is
not true.) True. Yeah. And so thinking about like, is it worth it to just like really
dive deeply into this one? And slow down? And I think especially, I like I always
have the fear of the AP test like looming in the distance.
B: I know. And it’s so difficult too to try to, something I’ve found that’s difficult
here, because I don’t have any other sixth grade math teachers to talk to, like at
my old placement I had, like, monthly meetings with, like, 15 other fifth grade
math teachers, is that like, [teacher name] will spend 100 minutes getting kids to
say, Katie learned that her family was important to her because when she didn’t
have them, she realized she couldn’t do all of these things on her own. And you’re
like, 100 minutes for that? Like, got it. Yeah, you know, whereas in here, we’re
like, we’re gonna review area of a triangle. And then we’re gonna talk about
ratios. And then by the end of the day, we’re going to talk about how ratios are
actually unit rates.
K: Yeah, it’s like, yeah, math is very, very quantity heavy, traditionally.
B: And we’re going to try and do like, 20 math problems. (K: Yeah.) You know, and
everybody’s gonna have a chance to talk.
K: Yeah. Yeah, this idea of like, time and speed and quantity.
B: And, of course, like, none of it is right or wrong, you know, but yeah, it is, like,
just very different, I think?
K: Yeah. Interesting.
B: Am I doing this right?

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…
B: I also to when you were mentioning this before, I also repeat what people say, and
I’ve really tried not to do that, but it was very, very hard. Yeah, yeah.
K: Why do you think we do that?
B: Well because I think, also because we do it in modern society as like polite
conversation. Right? Like you’re like, you know, like, Panda Express is the best
food and like, yeah, Panda Express is so good. Yeah. You know, you’re like, that
doesn’t actually you know, why is repetition affirming? You know, yeah, but also
in the classroom setting. It’s hard because it’s like … (K: Yes.) Like, yeah. This is
a cultural thing, but like in Korean, if someone is silent, while you’re speaking to
them, it’s a sign of, it’s disrespectful. (K: Oh, really?) Yeah. So Koreans will be
like, Mmm hmm. And I do that a lot in my, just with my friends but I do not do it
as a teacher. And I don’t know why. Yeah. (K: Oh, interesting.) Yeah.
K: Why do you think that is?
B: Because probably have grunting teacher is weird.
K: I think, Yeah, my family is very loud and vocal at all times. Like I think I put that
in my in front like they are constantly talking over each other, which is not typical
of White culture in a lot of ways. Like if you think about like White churches, it’s
like very silent call and response kind of a thing. It’s very like a lot of children are
seen and not heard. Yeah. and my family is not like that. it’s almost a different
form of Whiteness, where it’s like we all feel entitled to talk at all times over each
other. So, yeah, I don’t know. I wonder if that’s a weird cultural thing too,
because I also make a lot of noises when I listen to someone.

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B: And I also think that my personal attention deficits I don’t I’ve never been
diagnosed with anything and I don’t think I would would pass any diagnosis tests
but whatever attention deficits I do just naturally have I talk over people as part of
that. Like, it’s like, you know, I don’t have all of the ADHD symptoms, but the
one that I do have is that like, because I love what you’re saying, I’ll just start
talking before your sentence is over.
K: Yes, I’m actively trying not to do that right now (B: Exactly!) because I feel like
that too. And I’m wondering if that’s, I feel like I cut off students a lot too.
Sometimes, like I get excited that they’re on the right tracks, and don’t let them
finish their statement, which then is therefore giving, I feel like I want to be
giving the message of like, yes, I agree with you, But maybe I’m giving the
opposite of like, “Ok ok you’re done so I can talk now. (B: I’m nodding my head,
so I don’t interrupt you.) Yeah. And I don’t know I wonder how my kids feel
about that.
B: I don’t know either.
K: Now I’ve now I’m curious if I like filmed. Maybe this is what I filmed next—is
like if I filmed like a small group discussion with my kids, like, do they do that to
each other?
B: Yes. Probably. I would think so, yes.
In saying, “I feel like doing more activities means more learning,” I named an assumption that I
had around instruction. This was a moment that we could have turned toward in order to, as
Brookfield states, “identify[] and check[] the accuracy and validity of our teaching assumptions”
(2017, p. 3); however, instead Blake responded, “Which is not true.” In agreeing, I moved us

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past the opportunity to slow down (Rodgers, 2002). This is an example of one of many places
that I could have used intentional questioning as a form of assistance (Tharp & Gallimore, 1991)
to turn us toward practice and deeper reflection (Horn & Little, 2010; Jay & Johnson, 2002), and
my failure to do so did not set Blake up to slow down her thinking (Rodgers, 2002) or to
elaborate on the problem (Horn & Little, 2010). Blake’s next statement,
[Teacher name] will spend 100 minutes getting kids to say, Katie learned that her family
was important to her because when she didn’t have them, she realized she couldn’t do all
of these things on her own. And you’re like, 100 minutes for that? Like, got it. Yeah, you
know, whereas in here, we’re like, we’re gonna review area of a triangle. And then we’re
gonna talk about ratios. And then by the end of the day, we’re going to talk about how
ratios are actually unit rates
is consistent with Horn’s and Little’s (2010) call for details and elaboration, as she provided a
specific instance with some degree of details. However, my response, “Yeah, it’s like, yeah,
math is very, very quantity heavy, traditionally” turned us away from practice with a sympathetic
expression (Horn & Little, 2010). My next statement also failed to turn us toward practice. Even
as Blake provided something more to turn toward with, “And, of course, like, none of it is right
or wrong, you know, but yeah, it is, like, just very different, I think?” my response of, “Yeah.
Interesting” terminated the conversation. This first excerpt is evidence of my failure to turn us
toward practice, as I neglected to ask probing questions that could have turned us toward
(critical) reflection-on-action.
Further along in the conversation, when Blake said, “I also repeat what people say,” she
normalized, or “moved to define the problem as normal” (Horn & Little, 2010, p. 192) and thus
provided an opportunity for us to turn toward practice. In response, my probing question, “Why

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do you think we do that?” provided Blake with an opportunity to justify her statement (Sahin &
Kulm, 2008) and to begin to consider the reason behind her action. Blake then said, “Well
because I think, also because we do it in modern society as like polite conversation. Right?”
which generalized the situation. She then continued to provide details, thus turning toward her
thought when she said, “Like you’re like, you know, like, Panda Express is the best food and
like, yeah, Panda Express is so good.” Her next statement, “Why is repetition affirming?” is
evidence that, in turning toward practice, she was moving toward some form of reflection. She
then started to turn toward her classroom with, “But also in the classroom setting. It’s hard
because it’s like” and then paused. Coupled with her next statement, “This is a cultural thing, but
like in Korean, if someone is silent, while you’re speaking to them, it’s a sign of, it’s
disrespectful” this is evidence that she was beginning to move toward comparative or even
critical reflection; she attempted to explain what was happening in the classroom by thinking
back to her own culture (Jay & Johnson, 2002). My probing, “Oh, really?” prompted her to
continue with, “So Koreans will be like, Mmm hmm,” which again provided a detailed example.
She then reflected, “And I do that a lot in my, just with my friends but I do not do it as a teacher.
And I don’t know why.”
This reflective question again provided me the opportunity to probe, which I did when I
said, “Why do you think that is?” Initially, Blake turned away from practice when she said,
“Because probably have grunting teacher is weird.” When I next provided Blake with an
anecdote about my own family, I used normalizing to reassure her about the normalcy of
interruption. When I said, “not typical of White culture in a lot of ways,” I provided a cultural
generalization, and then specified when I said, “Like if you think about like White churches, it’s

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like very silent call and response kind of a thing. It’s very like a lot of children are seen and not
heard. Yeah. and my family is not like that.” I then said,
It’s almost a different form of Whiteness, where it’s like we all feel entitled to talk at all
times over each other. So, yeah, I don’t know. I wonder if that’s a weird cultural thing
too, because I also make a lot of noises when I listen to someone,
which is evidence that I was engaging in descriptive reflection of my culture and the way it
impacted my responses because of our conversation. This prompted Blake to reveal some
personal information (redacted for privacy), and then to continue, “if I love what you’re saying,
I’ll just start talking before your sentence is over.” I then normalized when I said, “Yes, I’m
actively trying not to do that right now (B: Exactly!) because I feel like that too,” but then turned
back toward myself and my own practice, rather than toward Blake as a learner, when I said,
I’m wondering if that’s, I feel like I cut off students a lot too … But maybe I’m giving the
opposite of like “Ok ok you’re done so I can talk now … and I don’t know I wonder how
my kids feel about that.
My statement did consider an alternative view and therefore moved toward comparative
reflection (Brookfield, 2017; Jay & Johnson, 2002), but I did not encourage Blake to turn toward
her own practice in order to engage in further (critical) reflection-on-action. Overall, this excerpt,
taken from the same session as the first one, demonstrates that I was using probing questions to
assist Blake in turning toward reflection-on-action. The next excerpt, taken from Dante’s first
individual meeting, was my third attempt at facilitating the reflective cycle and using probing
questioning to turn toward practice.
K: I’m wondering like, how do I get that kid to share even if they’re not sure they’re
right. You know, like, get that discussion going, which I would love to, like be a

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fly on the wall and listen more closely to like their peer conversations. Like I
wonder how much they’re being vulnerable with each other about not
understanding things, versus with me. Like if that power dynamic makes a
difference too about when they’re willing to be vulnerable or not.
D: Because I’m noticing that they’re participating. They’re answering my questions,
even when I’m not- even when I’m just not I’m not cold calling them or I’m just
asking a question in general. They’re raising their hand; they’re shouting out the
answers. But when they’re in the group, they’re not they’re not talking to each
other.
K: Oh, interesting. So, it’s the opposite almost.
D: Like Desiree, she was participating cuz she’s right in front of me, but she’s just
just kind of like just talking to me, giving me the answers, and they’re all correct.
But when it comes to working together, when I give them time to work together,
she’s not she’s not really, you know, sharing or same thing with …
K: [Seating] arrangements, maybe the content and maybe the time of year? Are there
like particular activities that you think help them?
D: Maybe today the birth, there was like a birthday activity where they have to ask
their teammates, their birthday they were I guess they needed to talk to them. (K:
Okay.) They were a little bit more comfortable. Yeah. So, but we, that then we
have the other extent where we have students where they don’t really participate
in and when we when I call when I call on them, they even, they they are being
honest, like I don’t know, or they just, you know, shout any answers just for me to
just stop calling them even though the answer is wrong and they don’t feel they

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don’t feel bad. Because I guess their personality is just that way. They don’t care
if they’re right or wrong.
K: I want to be more like that. (K: Laughs.)
D: But there are students who actually that like, they get nervous, like when
somebody’s going to call on them. (K: Yeah.) I get nervous. (K: Yeah.) When
somebody’s like, when we go to PD meetings, I get like that. (K: Yeah.) I don’t
want to be called on in front of my peers. I still get nervous.
K: Yeah. What makes you feel more comfortable in those situations?
D: Maybe just sharing with a small group. Okay. Yeah, yeah, by like, answering
questions like if like, in front of like, everyone, I don’t feel comfortable. I guess
that’s something that I have always struggled with. Yeah, I guess I could put
myself in somebody else’s shoes. (K: Yeah.) And when I know who was that
those who are those students I don’t really call on them. Because I don’t want to
make them feel uncomfortable. Because I know for more or less who they are (K:
Yeah.) I’d rather go up to them and ask them like you haven’t, do you need any
help, any questions just to see if they’re understanding like within like small
group setup or just individually.
K: Are those students that, like you …? Because it sounds like maybe you see some
of yourself in that, like you relate to them personally, in that way? Or is it because
they told you like, I don’t like to be called on?
D: No, because I see right away who’s shy and who’s not shy, and I relate to them.
(K: Yeah.) And I don’t want to make them more uncomfortable because they’re
uncomfortable just being in a math class because they’re struggling with math in

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general. And I don’t want to make them more uncomfortable. Yeah, like I want
them to be able to come to math class and know that they’re not gonna be called
on just just just to check for understanding. That they know that I will be going up
to them one on one or within their group. (K: Yeah.) In a way, make them
comfortable just being inside a classroom.
K: Yeah. Yeah. And yeah, sounds like giving them that privacy too, of like being
able to … yeah.
D: Yeah, yeah. Because we do have those students in every class. There’s like, few
students like that.
K: Yeah. Well, I think it’s interesting …
When I said, “I’m wondering like, how do I get that kid to share even if they’re not sure
they’re right,” I demonstrated that, in using the reflective cycle, I was considering something
new about my instructional choices. This provided us with an opportunity to turn toward
(critical) reflection-on-action. I then provided another opportunity with, “Like I wonder how
much they’re being vulnerable with each other about not understanding things versus with me.
Like if that power dynamic makes a difference to about when they’re willing to be vulnerable or
not.” In naming the potential impact of our power dynamic, I moved us toward a place in which
we could have turned toward practice or engaged in critical reflection (Horn & Little, 2010; Jay
& Johnson, 2002). Dante’s response, “Because I’m noticing that they’re participating. They’re
answering my questions, even when I’m not even when I’m just not I’m not cold calling them or
I’m just asking a question” normalized my problem, as he expressed an “expected part of
classroom work and teacher experience” (Horn & Little, 2010, p. 192). My statement, “Oh,
interesting. So it’s the opposite almost” served as a probing question, as it gave Dante space to

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provide clarification (Sahin & Kulm, 2008). Dante then had the space to, consistent with Horn
and Little’s description of using normalizing to turn toward practice, provide “a more detailed
discussion of specific classroom instances” (2010, p. 192) through his anecdote about Desiree. In
response, I probed, “Are there like particular activities that you think help them?” which turned
away from practice as I sought an instructional move rather than turning toward reflection on
Dante’s problem of practice. His response ended with, “They don’t care if they’re right or
wrong,” which was an assumption about students. My initial response, “I want to be more like
that (K: Laughs.)” made light of his claim, but Dante continued with, “But there are students
who actually that like, they get nervous, like when somebody’s going to call on them” and then
normalized their reactions when he related to students and said, “I get nervous.” He then
provided a more detailed example when he said, “when we go to PD meetings, I get like that. I
don’t want to be called on in front of my peers. I still get nervous.” I then probed, “Yeah. What
makes you feel more comfortable in those situations?” which asked him to (critically) reflect
more upon his own experience. When, within his response, he said, “Yeah, I guess I could put
myself in somebody else’s shoes,” he demonstrated slight movement toward potential
comparative reflection in response to my probing question. He then said, “I know for more or
less who they are,” which was an assumption that I then probed with, “Are those students that …
you see some of yourself in that, like you relate to them personally, in that way? Or is it because
they told you like, I don’t like to be called on?” which uncovered more assumptions that Dante
was making about the ways in which his students were choosing to engage in class. At that point,
I failed to continue to probe and the conversation turned away from (critically) reflecting on
those assumptions; although this excerpt demonstrated some instances of turning toward practice

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as a result of my questioning, it was not fully successful. The following excerpt is from my final
session with Julia, in the third phase of the study.
K: What are you thinking about ways that students’ like, funds of knowledge were
coming out here?
J: I’m trying to remember the order but I think, from what I remember, there was a
warm-up question that said well what do you know about positive and negative
numbers and that’s where kids were talking about like temperature. They brought
up elevation, one class was talking about an elevator. So, I’m like okay well tell
us what would be the positive, what would be the zero would be the negative
piece? So, they they came in knowing that.
K: Okay. And you feel like that was being pulled out in this discussion? Like, what
were some moves that you made that brought some of their understanding out?
J: Like in that clip?
K: Or before that too, what were some moves that you made that you felt like
brought that out?
J: Umm …
K: Or then so from this clip, specifically, like what are some things that you were
noticing that you did?
J: I think I was just going off of whatever they were saying. I don’t think I was
pulling anything in from previous conversations. Just going based off what
they’re saying. Yeah.
K: What do you think the effect was of that on the discussion?

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J: Some cannot stand it. They’re like just tell us! I’m like, no, no, they did not like it
and they’re very open about that. And then they already know when I say
interesting, they’re like, “Okay, what do you mean by that?” I’ll say “Oh,
interesting” and I’ll keep going. Like I’ll walk away.
K: What do you mean by that? When you say that? (J: Interesting?) Yeah.
J: They’re normally like on a really good like, path and like, oh, you’re onto
something. (K: Okay). And then, what else? I feel like I say something else. They
picked up on my, my little clues.
K: Yeah. So, with interesting, Why do you say interesting versus giving them
something specific?
J: I don’t know. I don’t know why do that? I don’t … I guess I’m just cautious with,
not affirming them, but cautious with them needing my approval. Because then
they’re gonna say, “Well, let me wait for her to tell me whether I’m right or
wrong.” It’s like be confident with whatever you’re thinking there’s nothing
wrong with what your opinions are. And you’re still valid, even if it is incorrect.
There’s nothing wrong with that. So, I’m just always very cautious about doing it
when it’s like the beginning of something new. (K: Mhmm.) Like as we get
further along, then 'I’ll make more, like corrections when whenever it’s needed,
but especially such a beginning of a unit. Then I won’t like confirm, deny, it’s just
very, very neutral.
K: Yeah, it’s it’s interesting because I picked up on that because—like it literally just
popped out of my mouth—but like in these conversations, we’ve all been having
the word interesting comes up a lot and the word comfortable comes up a lot and

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so I’m just wondering, like, why we tend toward those words. And so, when you
just said it again, I was like, “Oh, interesting?” Like, what were you meaning by
that? Like what? And so, it sounds like from what you’re saying to you, it’s it’s a
… like I’m confirming that you’re onto something and now I’m going to walk
away because I don’t want to, like take away the productive struggle piece? Or
to—I don’t know is that?
J: Yeah. or even. I’m trying to think of like another time that I’ve said it. I do it all
the time and don’t even notice it until I’ll see the kid’s reaction. I’m like, oh, I
said interesting. (K and J: Both laughs.) Oh, they’ll give me like the eyes. (K:
Yeah.) But definitely, I think it’s more of, because so many of them still have like
the negative math identity that I don’t want such a low stakes question to affect
the “Well, I’m wrong on a question. Let me just not say anything then anymore.”
(K: Yeah.) Where, because that wasn’t the point of the conversation. It’s not like
you have to have the right answer. (K: Right.) Like, that’s later on. Yeah, it’s
actually okay. Let’s actually do these operations. Let’s be more concrete about
what we’re doing. (K: Yeah.) Versus let’s just talk, tell us what you think.
K: Right. I’m wondering if like, making some of that thinking visible to students
would be interesting as we’re circling, like thinking about instead of saying
something vague, like interesting, which I again, I do all the time with everyone. I
just did it, but like thinking about how to, like confirm the process without
confirming the correctness of the thought? (J: Right. Mmmm ok.) Okay. You
know, yeah, I don’t know what that would like, look like.
Long Pause

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K: But almost like because in here, you said something about like, okay, that’s your
claim, like really prompting that like, CER idea that we’re using like, I wonder if
there’s a way to do that if like, instead of saying like, “Oh interesting,” something
about like, “Do you have a claim?” Kinda like, “Do you have evidence?” like
kinda like?
J: Because I will do that when I’m trying to be intentional about them developing
the reasoning toward the end, right. Like, I just have to remember to do that from
the very beginning. (K: Yeah.) And last year, I did it a lot because of like the
writing piece that they were doing in science. I’m like, “No, you can do this in
any single subject” so I was very clear with them about that. And now, it’s a
disconnect because I’m not teaching them science. (K: Right.) But I want them to
realize that they are doing CERs in every single subject. We just don’t call them
CERS (K: Right) all over the place. So just like you’re saying being more
intentional about throughout, it’s like, okay, you’re making this claim. Well, what
is your evidence? Like, pushing them versus, “interesting” and like, right, keep
going.
When I began with the question, “What are you thinking about ways that students like
funds of knowledge were coming out here?” it prompted Julia to provide more specific details
from the conversation including “temperature,” and “elevation.” I then asked a series of probing
questions, to which Julia remained quiet. When she did respond to my third question, “Or then so
from this clip, specifically, like what are some things that you were noticing that you did?” it was
evidence that, when I made my probing question more specific, I provided her the assistance she
needed to continue the conversation. Her response, “I think I was just going off of whatever they

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were saying. I don’t think I was pulling anything in from previous conversations. Just going
based off what they’re saying. Yeah” was a descriptive reflection (Jay & Johnson, 2002). When I
asked the probing question, “What do you think the effect was of that on the discussion?” her
next response, “Some cannot stand it” considered the student view but did not attempt to reflect
upon why students could not “stand it.” Her use of the word “interesting” then prompted me to
ask, “What do you mean by that? When you say that?” This probe, asking for clarification (Sahin
& Kulm, 2008), resulted in her expanding upon her definition as interesting when she said,
“They’re normally like on a really good like, path and like, oh, you’re onto something.” This
came short of comparative reflection, and so when I asked, “Yeah. So, with interesting, Why do
you say interesting versus giving them something specific?” I was turning toward her use of the
word to seek further details (Horn & Little, 2010). In saying, “I don’t know. I don’t know why
do that?” Julia demonstrated that my question caused her to slow down her thinking (Rodgers,
2002; Sahin & Kulm, 2008) and wonder about her instructional choice. Her next response is
again descriptive reflection (Jay & Johnson, 2010). Although she was not turning away from
practice with sympathy or immediate instructional problem-solving (Horn & Little, 2010), she
was also not yet fully turning (critical) reflection by considering alternative views (Brookfield,
2017; Jay & Johnson, 2002). I then provided a reason behind my questioning when I said, “I
picked up on that because … in these conversations we’ve all been having, the word interesting
comes up a lot and the word comfortable comes up a lot and so I’m just wondering, like, why we
tend toward those words.” I did not structure these as questions, but I provided mental prompting
(Tharp & Gallimore, 1991) to assist Julia in thinking more about her word choice. I then
paraphrased and probed with, “And so it sounds like from what you’re saying to you, it’s it’s a
… like I’m confirming that you’re onto something and now I’m going to walk away because I

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don’t want to, like take away the productive struggle piece? Or to—I don’t know is that?” The
combination of the mental prompting and the paraphrasing served the purpose of a probing
question. In response, Julia said, “I’m trying to think of like another time that I’ve said it,” which
is evidence of her turning back into her practice with reflection-on-action in that she was seeking
a “specific classroom instance” (Horn & Little, 2010, p. 192). She then said, “But definitely, I
think it’s more of, because so many of them still have like the negative math identity that I don’t
want such a low stakes question to affect the “well I’m wrong on a question. Let me just not say
anything then anymore,” which revealed an assumption that she was making that was informing
her instructional choices. It also demonstrates that my question prompted her to consider a funds
of knowledge and identity approach in that she was considering student “negative math identity.”
In response, I said, “I’m wondering if like, making some of that thinking visible to students
would be interesting as we’re circling,” which is evidence that her statement was making me
reflect upon alternative instructional decisions (Horn & Little, 2010); I also normalized, as I used
“we” in my response, which showed that I was considering doing the same in my own
classroom. I then offered an alternative to consider when I said, “thinking about how to, like
confirm the process without confirming the correctness of the thought?” The long pause is
evidence that we were both considering my statement. I then provided more detail, which
prompted Julia to say, “Because I will do that when I’m trying to be intentional about them
developing the reasoning toward the end, right. Like, I just have to remember to do that from the
very beginning.” This statement expressed agency in her ability to make this instructional change
(Horn & Little, 2010). She then concluded, “So just like you’re saying, being more intentional
about throughout, It’s like, okay, you’re making this claim. Well, what is your evidence? Like,
pushing them versus’’, ’interesting’ and like, right, keep going.” Overall, this excerpt is evidence

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that, when I used probing questions consistently, we were able to more frequently turn toward
practice and get closer to comparative reflection-on-action.
My Growth
When this study began, I thought of myself as a classroom teacher and a developing
Instructional Coordinator. In my conceptual framework, I argued that I wanted to be conscious of
moving away from my teacher role and toward my coordinator role in my interactions with
participants; however, I did not clarify the distinction between the roles of Instructional
Coordinator and adult learning facilitator. In my role as coordinator, my primary function is to
support; I provide resources, assist in daily tasks such as lesson preparation and facilitation, and
draw on my own experience to provide solutions. Prior to this study, I often referred to myself as
a “professional helper;” to me, success as a coordinator looked like teachers feeling calmer, more
prepared, and having accomplished something that could help them perform better the next day.
This is in opposition to the ideas of constructive disorientation and brave spaces, in which
discomfort is an essential part of learning (Arao & Clemens, 2013; Wergin, 2019). To become an
adult learning facilitator, I wanted to move away ’’from “helping to accomplished” and toward
Mezirow’s call for adult educators to, “help learners look critically at their beliefs and behaviors,
not only as these appear at the moment but in the context of their history (purpose) and
consequences in the learners lives” (1991, p. 197) so that I could help teacher to “become present
—to see student learning … and respond … ‘intelligently’” (Rodgers, 2002, p. 230) with teacher
and student identities in mind. I also knew, as described previously, that I needed to personally
push my reflection from descriptive to critical if I was going to support my learners in doing the
same.
As I moved through this study, I used reflection-on-action (Jay & Johnson, 2002;

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Rodgers, 2002) and Heifetz et al.’s (2009) move of getting on the balcony to slow my thinking.
These allowed me to recognize alternative perspectives and missed andragogical opportunities.
Through these reflections, I recognized that I was not attending to my learners and their identities
in the way that I had intended to in my conceptual framework. As my reflections deepened
beyond descriptive (Brookfield, 2017; Jay & Johnson, 2002), I became more adept at
recognizing when I was sitting in my roles as teacher or supportive coach, rather than helping my
learners to think critically (Mezirow, 1991). I used that awareness to help me move away from
advice and support and toward probing questions that facilitated (critical) thinking. I did not fully
reach critical reflection for myself nor my participants (Brookfield, 2017), nor a place of
consistent identity-consciousness (Utt & Tochluk, 2020); however, I did occasionally manage to
attend to race, identity and culture in my personal reflections or my discussions with participants
(Howard & Milner, 2014; Utt & Tochluk, 2020), and also grew in my ability to use reflectionon-action (Rodgers, 2002) to recognize moments of colorblindness that had led to missed
learning opportunities. The following excerpts demonstrate (a) how I used reflection-on-action to
recognize ways in which I could develop as an adult learning facilitator and (b) how my written
reflections deepened from descriptive toward critical. While I did not fully succeed in either
within the scope of this study, my increased awareness helped me to imagine next steps beyond
the study; these will be addressed in the afterword.
Moving Toward an Adult Learning Facilitator
When I began this action research in the Fall of 2022, I had 9 years of experience as a
classroom teacher and 2 years as an Instructional Coordinator (one of which was at PS 103).
During this study, I held two roles: one as an AP Calculus teacher, in addition to my main role as
Instructional Coordinator. concurrently taught one AP Calculus class. I anticipated my

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experience as a teacher to be something that would affect my research. I intended to use my role
as a teacher to build relational trust, and anticipated needing to be aware of my instinct to inhabit
this most-comfortable role. My Instructional Coordinator role included multiple responsibilities,
which included administrative tasks, such as serving on the Instructional Leadership Team and
making curriculum decisions for the math department; however, I considered instructional
coaching to be my main responsibility and the one in which this research study was situated.
Prior to this study, I believed “instructional coach” and “adult learning facilitator” to be
synonymous. In my original conceptual framework, I wrote:
Currently, I use my teacher identity as a way to build trust and reliability with the
teachers I coach. My role in this study is as a researcher-participant, and so I will be
engaging in the reflective cycle alongside teachers. I must be conscious of how much I
embrace my teacher identity versus my coaching identity, and reflect on the ways that
both roles inform each other. I expect to use my teacher identity as a way to attend to
race as I model noticing student thinking with my own students, and my coaching role to
create a setting within our meetings for constructive disorientation.
What I did not recognize in my conceptual framework was how my role as Instructional
Coordinator (named in above as instructional coach) fell short of that of a learning facilitator.
Looking back, I do not believe I was aware that there was a distinction. As I started my research,
I noticed what I then referred to as “competing goals” that were hindering my ability to act as a
learning facilitator; however, my reflections still did not recognize a distinction. It was only after
I removed myself completely from my research and entered the analysis phase that I recognized
the extent to which my role as Instructional Coordinator was really set up for activity-driven
knowledge-for-practice (Cochran-Smith & Lytle, 1999), in which teachers “implement, translate,

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or otherwise put into practice the knowledge they acquire from experts outside the classroom”
(p. 255). In my coaching role, I was acting as the expert, rather than using andragogical moves to
facilitate the constructive disorientation (Wergin, 2019), critical reflection (Brookfield, 2017; Jay
& Johnson, 2002), and authentic knowledge-of-practice (Cochran-Smith & Lytle, 1999;
Webster-Wright, 2009) that I set as my intentions in my conceptual framework. Although I did
not manage to make it all the way to where I wanted to, I did move from a place of ignorance
around the distinction between coaching and facilitating to a place in which I was beginning to
recognize, name, and intentionally move away from knowledge-of-practice and toward more
consistent use of andragogical tools.
At the outset of the study, I engaged in reflection-on-action after each session, and at the
end of the first cycle I wrote a more formal reflection and an analytic memo. As a result of this
reflection-on-action (Rodgers, 2002) and getting on the balcony (Heifetz et al., 2009), I began to
notice the ways I was failing to use andragogy to support my participants as learners, and was
instead interacting with them as their teacher-colleague or their coach. I will analyze pieces of
my early reflections from the research phase, in which I focused on activity-driven knowledgefor-practice formal knowledge acquisition (Cochran-Smith & Lytle, 1999), and later reflections
from the analysis phase, in which I began to grow in my awareness of the amount of adult
learning taking place. As I have continued to grow in this awareness since the end of analysis
and will continue to work toward supporting deeper adult learning for the remainder of my
career, I will continue to discuss this growth in the afterword. This first excerpt is from a verbal
recorded analytic memo and is referencing the first collaborative session of the study.
There are multiple pieces of evidence when I return to the agenda, rather than taking time
to develop the current conversation (this is one of them) ... I think it is a piece of whose

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goals I was valuing. I think there are pieces of evidence that show, including this point,
times when I tried to prioritize the planned dissertation agenda over allowing a
conversation to deepen or not even allowing—because it wasn’t inherently happening—
pushing a conversation using my intended andragogical moves that I hoped to use. Like
this could have been a case that I used probing questions. Or that I generalized a
statement in an attempt to turn toward practice and instead I moved on. This again, could
be due to nerves, could be due to my own unconscious fear of what will happen if I try to
make the conversation become more vulnerable and focused on race/identity/culture/
power. Or could be due to the conflicting goals and me feeling like I don’t want to “take
away” time from teachers that they were expecting to use for their own purposes, which
would mean that I’m not viewing them as people who want to learn or not viewing my
session as a valuable learning experience.
…
And so, I think that that’s a constraint that I’m seeing is firstly, the competing goals.
Initially that between what teachers are viewing as a learning experience, their personal
professional goals, administration’s goals, PS 103’s goals, my goals as a coach and my
goals as a researcher, and my goals as a student who is trying to graduate, all of those
goals are competing. And this is making me reflect on how I can attempt to bring some of
those goals together so that they’re not competing, but they’re working alongside each
other. Trying to figure out when it is necessary for my goal as an adult educator to
conflict with some of these existing goals. Because I am trying to change the status quo
for when I need to figure out how to align them for motivation and authentic professional
learning reasons.

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When I said, “I return to the agenda,” I implied that I made an instructional decision to
move the focus of the conversation back to the agenda. When I said, “rather than taking time to
develop the current conversation,” I recognized that I had moved the conversation to focus on the
intended curriculum rather than on the discourse happening, which is a knowledge-for-practice
approach (Cochran-Smith & Lytle, 1999) as I was presenting formal knowledge rather than
attending to the “current conversation” that my learners were having. When I engaged in
descriptive reflection and said, “I think it is a piece of whose goals I was valuing,” I was naming
the existence of multiple goals being present; I was not, however, attributing it to how I was
inhabiting my role. The idea of goal-centered is in alignment with the knowledge-for-practice
approach in which teachers “implement, translate, or otherwise put into practice” (CochranSmith & Lytle, 1999), and, as I have now recognized, evidence that I was inhabiting my role of
coach without being able to name this at the time of my reflection. When I said, “times when I
tried to prioritize the planned dissertation agenda over allowing a conversation to deepen” I
recognized my own agency in choosing what to prioritize. Without naming it, I was again
choosing the coaching knowledge-for-practice rather than pursuing critical thinking as an adult
educator should (Cochran-Smith & Lytle, 1999; Mezirow, 1991). I then recognized alternative
andragogical choices that I could have made based on my conceptual framework when I said,
pushing a conversation using my intended andragogical moves that I hoped to use. Like
this could have been a case that I used probing questions. Or that I generalized a
statement in an attempt to turn toward practice and instead I moved on.
I then engaged in descriptive reflection (Jay & Johnson, 2002) when I said, “This again, could be
due to nerves.” I offered an alternative possibility when I said, “could be due to my own
unconscious fear of what will happen if I try to make the conversation become more vulnerable

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and focused on race/identity/culture/power.” Implied in this statement is the idea that I had not
yet reached a stage of criticality that would empower me to enact the andragogical moves
necessary to support teachers toward critical reflection. When I next said, “Or could be due to the
conflicting goals and me feeling like I don’t want to ‘take away’ time from teachers that they
were expecting to use for their own purposes,” I was operating from my supportive-coach lens,
“helping to accomplish” rather than helping to learn (Mezirow, 1991); this, too, was in line with
teachers enacting rather than learning (Cochran-Smith & Lytle, 1999). In saying, “which would
mean that I’m not viewing them as people who want to learn or not viewing my session as a
valuable learning experience,” I further recognized that I was not approaching my participants as
learners and stating a potential bias that I had, potentially due to my previous roles as a teacher
and as a coach. Overall, this reflection is evidence that I was reflecting upon different
possibilities for why I made the choices that I did; and yet, none of these reasons are linked to
my role or responsibilities as an adult learning facilitator.
I then summarized, “And so I think that that’s a constraint that I’m seeing is firstly, the
competing goals,” which again demonstrates that I am operating from a task-oriented,
knowledge-for-practice approach. I then said, “between what teachers are viewing as a learning
experience, their personal professional goals, administration’s goals, PS 103’s goals, my goals as
a coach and my goals as a researcher, and my goals as a student who is trying to graduate, all of
those goals are competing.” When I said, “what teachers are viewing as a learning experience,” I
removed myself from the learning experience; I was not yet thinking of someone who could
facilitate the learning and was instead focused on the way that the experience was being
perceived by teachers. When I listed multiple other goals, I attended to my goals as a “coach,” a
“researcher” and a “student;” I did not list adult learning facilitator, which is again evidence that

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I was not thinking of myself as such. I then said, “this is making me reflect on how I can attempt
to bring some of those goals together so that they’re not competing, but they’re working
alongside each other,” which shows that I was still focused on the goals, rather than the role that
I was attempting to inhabit. I then said, “Trying to figure out when it is necessary for my goal as
an adult educator,” which is the first time that I refer to myself as such. When I said, “Because I
am trying to change the status quo for when I need to figure out how to align them for motivation
and authentic professional learning reasons,” I recognized a part of my conceptual framework,
without explicitly naming it, and did not continue to unpack the ways in which my actions were
not in alignment with my conceptual framework. While I did not yet clearly recognize why I was
not assisting my participants toward deep learning, my comments about adult learning and the
lack of andragogical moves do serve as evidence that, because of my reflection-on-action, I was
beginning to consider the extent to which I was assisting my participants as learners.
This next excerpt is from a memo that was verbally recorded following Phase 2 and is a
reflection about Dante’s second individual coaching session.
I think I needed more structure in this meeting. I think I actually let—because I was so
concerned in the first cycle about pushing the needs of my dissertation—I pulled back
from that, and I might have pulled back too far in that I didn’t make enough structure and
I didn’t make enough about the cycle we were going through. I do think that teacher
goals and my goals as a coach were prioritized. Not, so, teacher goals—I think we were
speaking to—his goal has always been to have students speak more. And we have not
really made any progress. And so, I think in watching himself, that was a big aha
moment. I think that this was, he saw this as really linked to his everyday practice,
something that he could change and has been trying to change. So, I think in terms of

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that, and the contextualization this was, that matched the intended right? The actions
matched the intended. I think as a coach who is thinking about wanting to see change,
because the principal puts pressure on me to see change around teachers’ goals … So, I
think in that like his teacher goal, his principal’s goal and then my goal as a coach, which
I view as supporting him in reaching the goals that administration want him to reach, like
I want my teachers to do well, a lot because I want teachers to do well, but a lot because I
believe that that will help the students also. Yeah, so anyways, I think, I think in this
session, the goal of the teacher and the coach outweighed the goal of deep learning,
which is separate than the goal of dissertation. Goal of dissertation: I don’t know if that
was met at all. The goal of me as a facilitator of adult learning, Dante had an aha moment
but I don’t think it was a moment of disorientation. I don’t think it was deep. I don’t think
it spoke to race or culture or identity or anything, changed his life view. And I do think
that it was surface level or significant learning may have happened because of just the
watching of the video.
When I said, “I think I needed more structure in this meeting,” I was reflecting on my
enactment of an andragogical move, cognitive structuring; this demonstrates that I was reflecting
from an andragogical standpoint; this was not evident in my initial reflection. My statement, “I
do think that teacher goals and my goals as a coach were prioritized” is evidence that, as in the
first reflection, I was still considering task-oriented goals in a knowledge-for-practice way. When
I said, “his goal has always been to have students speak more. And we have not really made any
progress,” this is again in alignment with the knowledge-for-practice idea that teachers must
implement knowledge to change their practice. When I said, “I think as a coach who is thinking
about wanting to see change, because the principal puts pressure on me to see change around

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teachers’ goals,” in saying, “I think as a coach” I was already considering the role that I was
acting from. The phrase, “thinking about wanting to see change” is not clear as to what type of
change I want to see, but coupled with the next phrase, “puts pressure on me to see change
around teachers’ goals,” they are evidence that I was focused on the outside pressure for teachers
to put new knowledge into practice (Cochran-Smith & Lytle, 1999) rather than the cognitive
change or change in perspective that would be more representative of criticality or deep learning
(Brookfield, 2002; Wergin, 2019). My listing of “his teacher goal, his principal’s goal and then
my goal as a coach” as separate ideas is evidence that I was recognizing the disconnect between
my work and the work of the school, but was still not listing true adult learning as my own
purpose. When I clarified my goal as a coach as “which I view as supporting him in reaching the
goals that administration want him to reach,” I demonstrated that my role as a coach was distinct
from my intended role as an adult learning facilitator. I did ultimately arrive at this conclusion by
saying, “The goal of the teacher and the coach outweighed the goal of deep learning;” however, I
then said, “which is separate than the goal of dissertation.” In separating the goal of the
dissertation from the goal of deep learning, I demonstrated that, following the second cycle, I
was still unclear as to what my objective was; I had distanced myself from my conceptual
framework and research question. I ultimately reached a reflection of the degree of deep learning
that was happening when I said, “The goal of me as a facilitator of adult learning, Dante had an
aha moment but I don’t think it was a moment of disorientation.” I continued to consider why it
wasn’t a moment of disorientation when I said, “I don’t think it was deep. I don’t think it spoke
to race or culture or identity or anything, changed his life view.” While I was reflecting on the
amount of deep learning, I did not reflect on the andragogical moves (or lack thereof) that I made
that impacted Dante’s learning experience; overall, this is more evidence that I had not yet

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internalized my role as learning facilitator, nor was I effectively using reflection-on-action to
consider the impact of my actions.
In this final reflection, written at the end of Phase 2, I consider the growth between the
first collaborative meeting and the second.
There are multiple incidences of participants sharing what they know and me not probing
or turning toward not specifying or normalizing or generalizing, and instead just moving
through the agenda … I do ask a number of probing questions which does seem to
increase the amount that participants are sharing. There are multiple incidences where I
asked a probing question and that leads to all three participants sharing and even to places
where participants are responding to each other rather than to me. So, I do think that
that’s an improvement over the first department meeting … The other trends that I’m
seeing here, which I find incredibly problematic, is that in three different incidents, a
participant brings up something about race. And I not only don’t probe to get more I
actively turn away. And so, I think this is more evidence that I am not comfortable
talking about race, and that that is coming through in the ways that I respond when my
participants do bring it up. So not only am I not asking questions that support all of us in
considering the impact that race in our gender and identity and socioeconomic status have
on our teaching and the way we view the world, I’m actively shutting down situations in
which participants bring that up.
This reflection contains more evidence of me considering andragogical moves, as well as
the impacts that they had on participants. I considered times when I did not probe, generalize,
normalize, or specify (Horn & Little, 2010; Sahin & Kulm, 2008) and instead just “moved
through the agenda;” this is representative of a knowledge-for-practice approach (Cochran-Smith

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& Lytle, 1999). In naming the andragogical moves, I demonstrate increased attention to my
practice as a learning facilitator and to my conceptual framework. When I next considered times
that I did use probing questions, I also considered the impact that it had on participants as it
“leads to all three participants sharing and even to places where participants are responding to
each other rather than to me.” While I did not consider the impact that the sharing had on the
quality of the learning environment or on my participants’ learning, this is evidence that I was
considering my role as learning facilitator. I then reflected upon another way in which my moves
impacted the learning environment by saying, “The other trends that I’m seeing here, which I
find incredibly problematic, is that in three different incidents, a participant brings up something
about race. And I not only don’t probe to get more, I actively turn away.” I then considered
potential reasons for my moves when I said, “I think this is more evidence that I am not
comfortable talking about race, and that that is coming through in the ways that I respond when
my participants do bring it up.” I summarize my shortcomings when I said,
Not only am I not asking questions that support all of us in considering the impact that
race in our gender and identity and socioeconomic status have on our teaching and the
way we view the world, I’m actively shutting down situations in which participants bring
that up.
This reflection is evidence that I am recognizing the places in which I am falling short as a raceconscious adult learning facilitator; however, I remained in descriptive reflection as I failed to
imagine alternative perspectives (Brookfield, 2017; Jay & Johnson, 2002). Further analysis of
my types of reflection and the progress that I made toward critical reflection occur in the next
section.

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Moving Toward Critical Reflection
In my conceptual framework, I argued the importance of all teachers, and particularly
White teachers, “taking up nuanced considerations of their racial identity” (Utt & Tochluk, 2020,
p. 126). I intended to create learning opportunities that encouraged teachers to experience
moments of constructive disorientation (Wergin, 2019) around their racial identities, and this
required my own ability and willingness to recognize and then confront my biases and the biases
of my participants. Prior to this study, I identified some of my biases by writing reflections
during my doctoral coursework; however, even as I intended for those reflections to be critical,
most of them remained descriptive, focusing more on my perspectives and feelings than
considering alternative perspectives (Brookfield, 2017; Jay & Johnson, 2002). I therefore set out
to deepen my reflections toward critical during this study. I engaged in consistent post-cycle
reflections-on-action (Rodgers, 2002) to help me sustain the “intentional process of identifying
and checking the accuracy and validity of our teaching assumptions” (Brookfield, 2017, p. 3). To
increase the criticality of my reflections, I considered Brookfield’s Four Lenses; these were
meant to help me “see ourselves from unfamiliar angles” (2017, p. 61). These lenses included my
learners’ eyes, theory, personal experience, and colleagues’ eyes; in this case, the learners were
my participants, the theory was my conceptual framework, the personal experience was the set of
ideas and experiences that informed my instructional choices, and my colleagues’ eyes were my
peers and advisor from my dissertation program. Throughout the study, I consistently recorded
informal memos following sessions. After completing each cycle, I wrote one formal reflection
and one analytic memo. As I began more formal analysis, I wrote more analytic memos.
Although I set out with the intention of considering all four lenses during all these reflections and
memos, I did not consistently use these and, as a result, the majority of my reflections remained

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descriptive throughout the course of this study. In the following section, I will analyze my
written reflections and memos to examine how close I came to reaching critical reflection, as
well as how much further I still need to go.
The first department meeting, which was the first session of Phase 1, took place on
November 14, 2022. On November 25, 2022, I reviewed the transcript and voice recorded a
memo. The following excerpt is a piece of the transcript from that memo:
I felt like there were moments that I wanted to respond, like when people shared out
about funds of knowledge, but didn’t because I was trying to be a facilitator. Part of me
was also thinking about the idea of “whose voice is being heard” and felt like I was
talking a lot already. Want to prepare question stems for future meetings to have
available so that I can push thinking without contributing too much of my own thoughts/
bias/seeming like the person in power in the room (Whiteness and positional power)?
Blake’s comments make me think that she is actually more of a self-authoring
knower. In 1:1 coaching she frequently asks what she should do, but in this meeting, she
spoke openly about politics (socialist self), economic status (my middle-class bouginess),
and race (not Whiteness but not Blackness). Except now that I look at that evidence, that
seems less like self-authoring, since she didn’t talk about values or why she feels that
way. Will ask more questions in 1:1 about why—didn’t want to push in front of
colleagues, but maybe that wasn’t challenging her as much as I could have? Or was I
making her feel more comfortable since this was the first meeting and we’re building this
space?
My first statement, “I felt like there were moments that I wanted to respond, like when
people shared out about funds of knowledge” is consistent with Jay and Johnson’s (2002)

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definition of descriptive reflection, as I am speaking to how I am feeling and describing what
happened. In saying, “but didn’t because I was trying to be a facilitator,” I expressed tension
between the role that I was trying to serve, “facilitator,” with what I wanted, which was “to
respond.” I then express some recognition of power then I say “whose voice is being heard;”
however, I wrote about how I was feeling rather than considering alternative views, and therefore
remained in descriptive reflection rather than critical (Brookfield, 2017; Jay & Johnson, 2002). I
showed awareness of wanting to check my power and Whiteness when I said,
Want to prepare question stems for future meetings to have available so that I can push
thinking without contributing too much of my own thoughts/bias/seeming like the person
in power in the room (whiteness and positional power)?
However, like my previous statement, I named those pieces of my identity in service of making
an instructional move, rather than slowing down to consider implications or deeper meaning
behind that statement (Jay & Johnson, 2002).
My next reflection, “Blake’s comments make me think that she is actually more of a selfauthoring knower,” is evidence that I was attending to my learners by thinking about where they
fell on the Drago-Severson and Blum-DeStefano (2017) Types of Knowers Typology. When I
said, “In 1:1 coaching she frequently asks what she should do,” I recalled information from my
previous experiences; I then compared to current data when I said, “but in this meeting she spoke
openly about politics (socialist self), economic status (my middle-class bouginess), and race (not
Whiteness but not Blackness).” I named specific phrases but did not unpack anything about
them; I seemed to superficially recognize this when I said, “Except now that I look at that
evidence, that seems less like self-authoring, since she didn’t talk about values or why she feels
that way.” In next saying, “Will ask more questions in 1:1 about why” I expressed a change that I

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intended to make in the next session based on my reflection, and then did attempt to slow down
when I said, “didn’t want to push in front of colleagues, but maybe that wasn’t challenging her as
much as I could have?” I expressed doubt in my decision, and then expressed an alternative
reason, “making her feel more comfortable” for my hesitance that was even more colorblind than
the first. The remainder of this reflection is equally as descriptive and superficial; I at no point
attempted to slow down and consider that my hesitancy could be my own White discomfort
perpetuating hegemonic silence around race and identity (Utt & Tochluk, 2020), or to consider
how my failure to challenge could have been perceived by my participants.
After the completion of the Phase 1, I wrote a formal reflection. My intent was to engage
in critical reflection, in which I considered alternative views, particularly in regard to race and
identity, and then establish a renewed perspective (Brookfield, 2017; Jay & Johnson, 2002). The
following is an excerpt:
I am moving toward being more race- and culture-conscious in my conversations (as
evidenced by me referring to me as white, me asking Julia if she thought something was
cultural, me speaking with Dante about multilingual students, etc.). However, I recognize
that I often speed through these thoughts (like with Dante—I made a comment about not
knowing why multilingual students aren’t celebrated and then off-handedly and hurriedly
corrected and said something like “well I know why, it’s because our society is White
and English centered.” I didn’t stop to unpack that or to ask questions. I still carry a
discomfort that I think comes from not wanting to say something that unintentionally
impacts someone negatively; in that instance, I was talking about multilingual learners to
a multilingual learner. I think at the time I was afraid of continuing to talk and saying
something that might make Dante TOO uncomfortable and therefore shut down, but in

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reflecting I think I was the uncomfortable one. I think in the next phase, I need to think
about turning into race conversations the same way I think about turning into practice.
When I wrote, “I am moving toward being more race- and culture-conscious in my
conversations” and then cited evidence, I used descriptive reflection to begin to assess to what
extent my goals were being met (Jay & Johnson, 2002). I continued my assessment with,
“However, I recognize that I often speed through these thoughts,” which was again descriptive as
I expressed something that I was concerned about (Jay & Johnson, 2002). I then cited evidence
in saying, “like with Dante—I made a comment about not knowing why multilingual students
aren’t celebrated and then off-handedly and hurriedly corrected and said something like “well I
know why, it’s because our society is White and English centered.” Had I moved toward
comparative reflection at that point, I would have considered alternative views of what was
happening. Instead, I continued to speed through my reflection. I did not use any of Brookfield’s
lenses (2017) or Rodgers’s cycle (2002) to slow down my thinking, and, as a result, continued in
descriptive reflection. My next statement, “I still carry a discomfort that I think comes from not
wanting to say something that unintentionally impacts someone negatively;” described what I
was feeling. I then considered why I was feeling that way in saying, “in that instance, I was
talking about multilingual learners to a multilingual learner,” which again I could have slowed
down and unpacked, instead of continuing onto “I think at the time I was afraid of continuing to
talk and saying something that might make Dante TOO uncomfortable and therefore shut down,
but in reflecting I think I was the uncomfortable one.” This statement acknowledges a superficial
analysis of how Dante was feeling, as well as some level of attention to my learner’s needs;
however, I sped through my reflection and thus failed to seek a nuanced understanding of how
my racial identity was impacting my interactions (Utt & Tochluk, 2020). When I said, “I think in

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the next phase, I need to think about turning into race conversations the same way I think about
turning into practice,” I again engaged in descriptive reflection; I considered potential changes in
my actions but did not do so based on alternative views (Jay & Johnson, 2002). I did express
more awareness of my failure to meet my intended goal than I did in my first reflection, which is
evidence of some growth and a potential for change moving forward.
This last excerpt is taken from my final formal reflection, which I wrote at the end of the
study and intended to be critical:
I think that this brings me to the more critical piece of reflection around being a holder of
knowledge and the power structures in this study. I initially had this idea that I don’t
really know what a fund of knowledge looks like in a math classroom without being too
stereotypical/based on someone’s idea of someone else’s race, and I was hoping to find
an “answer” by the end of this with my colleagues. This is in line with the idea that there
is a “right” answer. I think in my actions I was trying not to give that message, but that
resulted more in disclarity in the instructions I gave and the objectives I stated (when I
even stated them, which was rare). In trying to not be the white Woman coming in to give
answers, I still was coming in telegraphing that there was a right one and I think at times,
it seems like I’m just withholding answers rather than authentically talking about the fact
that I don’t know the answer myself. Or grappling with the idea that there is no answer? I
don’t know. And I think as much as I wanted this study to break away from how
professional learning is currently structured at my school, it really remained very similar.
And I can hide behind the excuse that I was trying to balance regulating distress by not
changing too much, or trying to work within the contextual space to align with authentic
professional learning, or building on previous norms and relationships, in reality a lot of

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it is because I feel uncomfortable with change and to be very honest, because the system
was built to benefit me. I’m comfortable in the way that things are. So many of my
choices were made, consciously or unconsciously, because I didn’t want to upset
someone else—but that was because in upsetting someone else, I get upset or reap
negative consequences. For example, not wanting to upset [name] (who is White) or
[name] (who is also White). I’m in a position that I am trusted and never second-guessed.
When I asked [name] for feedback, she literally said “don’t make me laugh.” It is in my
personal benefit to align with them, which is also aligning with a structure in which
White women make up the majority of leadership (at PS 103) and also nationally. If I
were to do this again (and I hope to make changes and try something similar at the high
school next year), I want to take more risks. That’s the only way to make change, and I
think that throughout all of this I played it safe so as to not anger anyone. And I think that
part of that was not harming my relationships with the teachers (learners) by asking them
to get too uncomfortable, but it 100% was also because of my fear of angering leadership,
which makes my “safeness” selfish and hegemonic.
When I wrote, “I think that this brings me to the more critical piece of reflection around being a
holder of knowledge and the power structures in this study,” I demonstrated intention of reaching
critical reflection and, in saying, “this brings me to the more critical piece,” I acknowledged that
what had come before had not been critical; I therefore demonstrated an awareness of the
differences between what I had done previously and what I was about to attempt to do. In saying,
I initially had this idea that I don’t really know what a fund of knowledge looks like in a
math classroom without being too stereotypical/based on someone’s idea of someone
else’s race, and I was hoping to find an “answer” by the end of this with my colleagues,

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I was considering an assumption that I had prior to this study. My use of quotes around the word
answer implies that my thinking had shifted. When I continued, “This is in line with the idea that
there is a “right” answer,” I again used quotes, implying that my mindset had shifted and that I
no longer believed that there was an answer, and therefore that there couldn’t be a right one.
When I said, “In trying to not be the White woman coming in to give answers,” which implies
that my decisions were informed by my awareness that I was White; this is the first time in my
reflections that I acknowledge this, and therefore is not a statement backed up by any prior
evidence. It does serve as evidence that I was considering my race at the time that I wrote my
reflection. I then attempted to consider alternative ways of viewing (although in a colorblind
way) when I said, “I still was coming in telegraphing that there was a right one and I think at
times, it seems like I’m just withholding answers rather than authentically talking about the fact
that I don’t know the answer myself.” I then admitted, “I think as much as I wanted this study to
break away from how professional learning is currently structured at my school, it really
remained very similar,” which was descriptive reflection about the extent to which I met my
stated goals (Jay & Johnson, 2002). I continued in this manner when I said,
And I can hide behind the excuse that I was trying to balance regulating distress by not
changing too much, or trying to work within the contextual space to align with authentic
professional learning, or building on previous norms and relationships, when in reality a
lot of it is because I feel uncomfortable with change.
When I said, “because the system was built to benefit me.” I began to move toward considering
my positionality; however, I did not explicitly name how the system was benefiting me. Implied
in that statement is my Whiteness, but I failed to name that explicitly. When I said, “I’m
comfortable in the way that things are,” I again implied that, because of my Whiteness, I’m

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comfortable in the current system (which I can name now, but didn’t then). I continued to engage
in descriptive reflection as I considered, “So many of my choices were made, consciously or
unconsciously, because I didn’t want to upset someone else—but that was because in upsetting
someone else, I get upset or reap negative consequences.” I then wrote, “For example, not
wanting to upset [name] (who is White) or [name] (who is also White),” which, for the first time,
considered the race of others in the reasons for the ways that I was consciously and
unconsciously making decisions (Brookfield, 2017). I then continued to do so when I said, “It is
in my personal benefit to align with them, which is also aligning with a structure in which White
women make up the majority of leadership [at PS 103] and also nationally.” This statement
began to look at a larger systemic trend, backed by literature (although I didn’t reference
literature directly). My next statement considered implications of my reflection as I said, “If I
were to do this again (and I hope to make changes and try something similar at the high school
next year), I want to take more risks.” When I said, “I think that throughout all of this I played it
safe so as to not anger anyone,” I reflected upon why I did not take risks; this is still descriptive
reflection, as I remain thinking about my own perspective (Jay & Johnson, 2002). My final
statement returns to larger systems, and therefore approaches more critical, when I said, “And I
think that part of that was not harming my relationships with the teachers (learners) by asking
them to get too uncomfortable, but it 100% was also because of my fear of angering leadership,
which makes my ’safeness’ selfish and hegemonic.” In this final statement, I imply with
“hegemonic” that I am thinking about larger oppressive systems; although I do not specify, I am
working toward thinking about the larger systemic consequences of my actions. As the evidence
provided here reveals that I did not reach the level of critical reflection that I intended, I will
state my plan for growth in the afterword.

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Afterword
In this final section, I discuss the ways in which my experiences and reflections over the
course of this action research study will inform my future practice. Prior to my doctoral
coursework, I viewed my position of Instructional Coordinator at PS 103 as an “expert teacher”
rather than an adult learning facilitator, and most of my interactions with teachers involved coplanning, discussing curriculum and content, providing feedback, and sharing best practices. I
now recognize that spending our time this way perpetuated the White Supremacist tenets of
perfectionism and paternalism, as well as aligned with a knowledge-for rather than knowledge-of
approach to teacher development. As I engaged in coursework and began writing my conceptual
framework, I recognized the need to shift my role toward one that would support teachers in
deep learning; to do so, I needed to inhabit the role of adult learning facilitator by intentionally
designing a learning environment and using andragogical moves to push toward constructive
disorientation. Additionally, I recognized the need to become more critically conscious, and that
to do so, I must repeatedly engage in critical reflection so as to discover and confront my own
biases and assumptions. I entered the field believing that I had a novice-understanding of both
adult learning facilitation and critical reflection based on theory; as I progressed through the
study, I noticed just how novice my skill in both was, and how difficult it was for me to facilitate
conversations about race, identity, and funds of knowledge. After leaving the field and engaging
in analysis, I was able to more clearly see how my novice-status and fear of discomfort were
preventing me from enacting the change that I wanted to see; namely, in creating deep, critically
conscious learning experiences for myself and my participants. In writing my findings, I
continued to recognize and reflect upon the ways in which I wanted to continue my growth as
both an adult learning facilitator and a critically conscious educator. The learning that I

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experienced from writing my findings allowed me to revisit my conceptual framework in a way
that more strongly targeted my own long-term growth goals in this area. In this section, I will
offer my thoughts about the ways in which I have already demonstrated growth after leaving the
field, as well as ways I hope to continue to grow for the remainder of my career.
Continuing Development as an Adult Learning Facilitator
As discussed previously, I was not able to fully inhabit my role as an adult learning
facilitator over the course of the action research study. I largely remained in a goal-setting
knowledge-for-practice approach, and my own novice-state at reflection and andragogy made it
difficult for me to fully get on the balcony (Heifetz et al., 2007) and recognize the ways in which
I was failing to attend to my participants as adult learners. As a result of my out-of-field analysis,
I began to recognize missed opportunities for using probing questions, as well as the places
where my own discomfort caused me to turn away from having conversations around race and
identity that could have potentially led to disorientation. I recognized that frequently, I revered to
colorblindness due to my own discomfort, thereby denying participants and myself the space to
have critical conversations about our own races and identities. This led me to include more
language about colorblindness and race-consciousness in my conceptual framework, as it became
clear to me that both were concepts that had majorly affected my inability to reach my short-term
research goal. I also recognized the growth that I had made in both areas by the end of Phase 3,
and so as I left the analysis phase and began writing my findings, I felt both more equipped and
more motivated to continue my own growth. As I wrapped up analysis and wrote my findings, I
became more conscious of the ways my own vulnerability helped to build a deeper level of trust
in learning environments, I was more adept at recognizing when I and others were engaging in
different types of reflection (Jay & Johnson, 2002), and more consistently used probing

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questions to push both myself and others toward a deeper level of vulnerability and criticality.
Additionally, I developed stronger habits of reflection-on-action. I will first discuss ways these
have already impacted my practice, and then state my intentions for how to leverage these new
skills and levels of awareness moving forward.
When I left the field in March of 2023, I still held my Instructional Coordinator role and,
as I had intentionally planned my research to take place during the time structures already set
aside by my school, I continued to meet with each participant weekly and with all of them
collaboratively 1–2 times per month. My original intention was to continue using video and the
reflective cycle to move toward the experiment phase; however, our school network introduced
Standards Based Grading and requested that we use collaborative department meetings to begin
preparing assessments and unit plans for the upcoming year. To balance school expectations with
deep learning, we engaged in the cycle using video once a month. In these sessions, I became
more aware of the ways I was embodying the roles of teacher, Instructional Coordinator, or adult
learning facilitator in the moment, and was able to course-correct and turn toward my learners
more effectively. I also increased the number of probing questions that I used, which began to
shift our discussion from the coach-as-expert knowledge-for-practice approach towards the more
authentic, teacher-experience-centered, knowledge-of-practice approach. Rather than delivering
feedback, I moved towards collecting data and posing probing questions; this further shifted me
away from “expert teacher” and towards adult learning facilitator, as well as kept reflection-onaction consistent. Additionally, I continue to pursue places within conversations that I can ask
about race, identity, and funds of knowledge, as well as (critically) reflect on missed
opportunities.

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As a result of this study, the level of trust that I had with Blake, Dante, and Johanna
deepened. I intend to continue to build this relationship in the same way that I did throughout the
study; by demonstrating vulnerability, asking probing questions, and using reflection-on-action
after our meetings to (critically) reflect upon ways in which my andragogical moves impacted
my learners. With Blake, I recognized that although I had originally classified her as an
instrumental knower, she is much closer to the self-authoring knower description. Although she
does not consistently explain her instructional decisions as dependent on her values, she exposed
much more about her own culture and ways of thinking when provided with probing questions
that asked her to consider her identity. As we continue our work together, I intend to deepen
discussions around the ways my Whiteness, her Korean American identity, and other pieces of
our identities provide us with alternative perspectives than our students, and how those impact
the ways we notice student funds of knowledge and identity in our math classrooms. Our
discussions came the closest to critical reflection, and I intend to use both comparative and
critical reflection prompts (Jay & Johnson, 2002) to push us both toward criticality during future
discussions. I now believe it would not be cognitively overwhelming to introduce more terms,
and therefore intend to share “funds of knowledge and identity” and “critical reflection” with her
as we support each other in noticing and leveraging students’ funds of knowledge and identity.
With Dante, I was able to see him become more vulnerable than I had seen previously; this
allowed us to form a stronger working relationship and helped him to become more comfortable
acknowledging places in his practice that he wanted to grow. As with Blake, I want to continue
to push toward comparative and then critical reflection, and to engage in discourse around how
his identity as a multilingual learner both helps him to connect to students and informs ways that
he makes instructional choices. With Dante, I intend to become transparent about the types of

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questions (factual, guiding, and probing) to provide him with language to help him see how he is
beginning to create opportunities for students to leverage their funds of knowledge and identity.
As Julia has left the classroom since this study and adopted a role of assistant principal, I no
longer work with her on a consistent coaching basis; I will attend to her continued learning in the
next section.
With both Dante and Blake, I intend to build upon our use of the reflective cycle and to
reach the analyze and experiment phases. I also intend to introduce the cycle at the high school,
and based on what I know now, provide clear cognitive structures, display vulnerability, and
incorporate more critically conscious probing questions into all phases of the cycle. I intend to
continue to record our reflective cycle conversations with teacher permission so as to use as a
basis for my own (critical) reflection and growth; this will also be a continued way to display
vulnerability, as I will share with teachers that, just as I am recording their practice and we are
reflecting, I am doing the same for my own.
Overall, this study demonstrated the importance of intentional cognitive structuring for
all learning experiences (Tharp & Gallimore, 1991), as well as an increased awareness of how
current professional learning at our school is set up to honor coordinators as experts who are
delivering knowledge to teachers. This realization inspired me to set aside scheduled weekly
time with my fellow coordinators to set learning objectives and design learning experiences for
our weekly collaborative department meetings. Although these objectives are still aligned with
more of a knowledge-for-practice approach, I am working to move us toward a knowledge-ofpractice approach where we are facilitating conversations that blend practice and literature
(Cochran-Smith & Lytle, 1999) and work against the idea of coordinator/coach as “expert.”

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Additionally, I plan to involve the other coordinators in my own growth by using my recordings
to introduce the reflective cycle in our coordinator meetings.
Throughout the course of the study, I had the hardest time inhabiting the role of adult
learning facilitator with Johanna, as I considered her a true peer and, prior to this study, myself
as more of a thought-partner/colleague than her coach. She has now moved into a leadership role
as an assistant principal, and so her positional power has shifted to be equal to, and in some ways
higher than, my own. I intend to continue our discourse around student identity and the ways our
own identities impact the ways that we notice and leverage student funds of knowledge and
identity. We can now leverage her new position to potentially extend the impact of our work to a
more school-wide level. This is the intention that I am least comfortable in, and so I will need to
consider ways to restructure our learning environment to support both of us as learners. This
relationship is also the one that no longer has a built-in structure of consistent meetings, so I
intend to consider ways to hold myself accountable for building a space for us to continue our
relationship and, ultimately, use her as a critical friend in the work. Similarly, I have begun to
have more critical, race-conscious conversations with my fellow coordinators during our weekly
meetings and interactions, and ultimately want to work toward displaying vulnerability and using
forms of assistance to shift that learning environment toward a braver space (Arao & Clemens,
2002). In a similar way, I want to expand these conversations to those in roles with more
positional power than my own; namely, with principals and my immediate supervisor, the Chief
Academic Officer. If I am to truly make system-wide changes to adult education at my context, I
need to find more allies (Heifetz et al., 2009) and believe that those mentioned in this section are
those that can most effectively assist me in making systemic change.

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Continuing Toward Critical Reflection
Prior to this study, I had attempted to engage in critical reflection during my coursework.
As I did, and as I received feedback from my professors, I frequently experienced my own
(ultimately constructive) disorientation. As I began my study, I believed I had a beginning
understanding of what critical reflection looked like and, over the course of the study, engaged in
what I believed to be critical reflection. However, upon leaving the field and analyzing my
reflections, I realized that my reflection remained firmly in the descriptive space. At times I
reflected on my Whiteness or identity, but each time I remained focused on my own actions and
feelings, rather than considering alternative perspectives. I also said that I was considering
Brookfield’s four lenses but did not consistently use them as the cognitive structuring that I
needed. Upon reflection, I needed a structure; therefore, moving forward, I intend to really
depend on both Brookfield’s lenses (2017) and Jay and Johnson’s (2002) typical reflection
questions to continue to support my own growth toward authentic critical reflection and
becoming a self-authoring knower.
I also recognized, because of leaving the field, the extent of my colorblindness. As I
wrote about in both my context statement and in my own I am From poem in session 1, I was
aware of the colorblind way I grew up and was intentional about wanting to change that. I,
however, believed that my time as a teacher and my experiences as a doctoral student had helped
me become more race conscious. While it is true that I had some growth, it became apparent
during analysis and writing my findings that I am still not considering the subconscious impact
of race as frequently and consistently as I should be. In addition, I still allow my own discomfort
and fear of creating discomfort in others to prevent me from engaging in critical discourse.
However, these realizations also serve as evidence that I have become much clearer in how I

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want to learn, lead, and work in alignment with my values and long-term goal. I intend to
continue this critical reflection journey for the rest of my career and intend to now do so in a way
that I really consider myself as a learner, being intentional about considering the cognitive
structuring that I need to be able to experience constructive disorientation.
On a professional and personal level, I have grappled with my continued colorblindness
in all settings and am working toward using continued reflection to consider my assumptions,
race, identity, and alternative views; most importantly, I am becoming more intentional about
using that reflection to inform the instructional, leadership, and personal choices that I make.
Because of this study, I see more clearly how powerful reflection is as a tool for growth, as well
as how the concepts set forth in this study can help me toward my long-term goal of providing
Black and Latine students with math learning opportunities that are connected to their home
learning contexts, thereby affirming them as mathematical problem-solvers. I continue to strive
toward more consistently being a self-authoring knower, in which I am “learning, leading,
working, living, and loving according to self-determined values and internally derived standards
is of utmost concern” (Drago-Severson & Blum-DeStefano, 2017, p. 464) and, ultimately,
becoming a self-transforming knower in which I can collaborate and co-construct meaning with
colleagues. In alignment with this study, I intend to do so with a funds of knowledge and identity
approach that seeks to defy deficit mindsets and affirm Black and Latine students as
mathematical thinkers and problem solvers.

193
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Abstract (if available)

Abstract This study examines my leadership enactment as an adult learning facilitator within my role as Mathematics Instructional Coordinator at PS 103. To provide a comprehensive structure of my leadership enactment, I deconstruct my use of andragogy and (critical) reflection with the math department teachers. My action research question was: Within my role of Instructional Coordinator, how did I (a) develop myself as an adult learning facilitator and (b) assist participants in using a (critically) reflective cycle to see, describe, and analyze how their identity impacted the ways they noticed student funds of knowledge in their math classrooms? This action research will ultimately move me towards my long-term goal of supporting teachers in (a) noticing alternative forms of mathematical success as student funds of knowledge and identity and (b) leveraging those funds to provide Black and Latine students with math learning opportunities that are connected to their home learning contexts. I collected audio recordings, transcriptions, (critical) reflections, and documents developed in my role as adult learning facilitator. In this study, I found that I was able to move my participants from infrequent, unstructured descriptive reflection to consistent reflection-on-action and increased the amount of trust in our space to support more vulnerable, identity-conscious conversation. These serve as a foundation for future growth toward noticing and leveraging student funds of knowledge and identity. Additionally, I found ways in which I supported and hindered participant learning, as well as my own, throughout the study.

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Asset Metadata

Creator Risbrough, Katherine Ann (author)

Core Title Noticing identity: a critically reflective cycle to leverage student mathematical funds of knowledge and identity

School Rossier School of Education

Degree Doctor of Education

Degree Program Educational Leadership

Degree Conferral Date 2023-12

Publication Date 11/07/2023

Defense Date 11/07/2023

Publisher Los Angeles, California (original), University of Southern California (original), University of Southern California. Libraries (digital)

Tag action research,andragogy,critical reflection,education,funds of knowledge and identity,instructional coordinator,OAI-PMH Harvest,reflection on action,secondary mathematics

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Slayton, Julie (committee chair), Copur-Gencturk, Yasemin (committee member), Pascarella, John (committee member)

Creator Email krisbrough@gmail.com,risbroug@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113766183

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