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Nesting in Nepantla: The importance of maintaining tensions in our work.

Authors:
Nesting in Nepantla: The Importance of Maintaining Tensions in Our Work
Rochelle Gutiérrez, University of Illinois at Urbana-Champaign
In Russell, N. M., Haynes, C. M., & Cobb, F. (2015). Interrogating Whiteness and Relinquishing
Power: White Faculty’s Commitment to Racial Consciousness in STEM Classrooms. New York: Peter
Lang.
Every year, I run an activity with my secondary mathematics methods students in which I make
them feel uncomfortable. It’s called Bungee Barbie1. They are assigned a group activity where they are
given a Barbie doll, a measuring tape, a handful of rubber bands, and tape. They are asked to measure
the distance the doll falls from a fixed point when dropped with one rubber band tied to her ankles.
They are to continue this process with two, then three, up until 10 rubber bands are used in a chainlike
manner, taking note each time how far she falls. They are asked to collect this data and then, based on
their “line of best fit,” make a prediction as to the number of rubber bands to use if she will be dropped
off of my 3rd floor office balcony, fall the maximum distance, and not hit the ground below. The
winning team will have bragging rights. They are told that in our next session, each group member will
be responsible for explaining how their group collected their data, how they accounted for any error
their data might contain, and how they made their prediction.
When they return to class the next day, they are confronted with me running the class completely
in Spanish and at a fairly fast pace for someone who is not a fluent speaker. In directing my comments
to students, I change their names to their Spanish equivalents (e.g., Mike becomes Miguel; Frank
becomes Pancho) or to versions that are pronounceable in Spanish. When individuals are not able to
respond to my questions or requests, I mention how not doing the homework is not a good sign and that
perhaps they (implying families) need to value education more. When they start to confer with each
other, I tell them to pay attention to their own sheet because they were told ahead of time what they
would be responsible for and no “cheating” will be allowed. All of this is conducted in Spanish.
After 5 - 10 minutes, they feel they “get it” and smile, “seeing” how difficult it would be to be an
English learner (specifically a Spanish speaker) in a fast moving math class. At this point, they expect
me to stop. I do not. I continue this activity for 45 – 60 minutes, including calling students to the board
and to the document projector to explain their graphs and justify their reasoning around the topics of
slope and line of best fit; having them take notes from dictation; and finishing up with a text-heavy pop
quiz. Most of these teacher candidates are not fluent in Spanish. Those who took Spanish as a foreign
language are usually two steps behind in translation to be able to participate as well as they would like.
Even those students who are fairly fluent in Spanish are not prepared for the mathematical terminology I
am using. I specifically choose slope as a topic because the Spanish term “pendiente” does not have a
Latin cognate or an easily identifiable everyday use of the term. In the non-mathematical context,
pendiente can mean anything from pendant to dip, descent, incline, earring, drop, or grade. As time
progresses in the activity, I gradually provide more support for students to participate (e.g., a handout
with mathematical terminology explained in Spanish, more gestures, less colloquial terms, notes on the
board that they can reference, and I allow them to work with a partner). In the end, I ask them to write
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1!I!adopted!this!activity!after!first!seeing!it!on!a!teacher’s!website!in!2000.!!Many!versions!
have!been!posted!since,!including!one!you!can!download!from!
http://www.ms.uky.edu/algebracubed/lessons/LinearRegression.pdf!
!!!
down on a blank sheet of paper two things: 1) How did you feel? 2) What, if anything, did you do to
try to participate in class?
I will concentrate on question #1. Every year, the teacher candidates’ responses are more or less
the same. They express exactly what the research literature suggests is experienced by English learners
in mathematics classrooms across the US. When they do not have adequate supports, English learners
(and my teacher candidates) are frustrated, nervous, bored, checked out, or hopeless. They feel their
responses do not adequately reflect what they actually know or have prepared for class. Some teacher
candidates can explain that they have never been made to feel inferior for something that was out of
their control. Most feel unfairly evaluated and as if they were stripped of their identities as “good,”
“responsible,” and “smart“ people. Others are able to express clearly how they are so used to being in a
position of power, of always having something to say and convincing others, that when they could not,
they actually felt angry...and then embarrassed at their self entitlement…and then angry again. Usually
there is one student who is able to point out that on the one hand, the experience they just had lasted less
than an hour and they all knew it was going to end soon; yet, on the other hand, the anxiety and
oppression they felt was real.
The point of this activity is to move beyond reading about students who are “othered” in society
and mathematics classrooms or learning particular strategies to use with English learners when teaching,
though those are revealed in their answers to question #2. Instead, for a brief moment, I want my
students to feel what it is like to be the “other.” Rather than an “intellectual” or “cognitive” experience,
I want them to have a visceral one. When we reach the end of the activity, this is where I want them—
feeling their oppression was both real and not real; uncomfortable with how they are feeling, but also
recognizing the potential to learn from being uncomfortable. If I am going to prepare them to deal with
the uncertainty and politics that are inherent in mathematics teaching, it is important for me to keep them
in this space of tensions, of not feeling they are on firm ground and still being willing to stay in that
space long enough to benefit from it. From there, they will have a better chance of addressing the
systems of oppression that operate through schooling and in society at large.
Addressing Whiteness in Teacher Education
The idea of addressing Whiteness in teacher education is not new. However, its connection to
mathematics usually is less clear or explicit. Often catalyzed by faculty who teach in broader
foundations courses that address issues of diversity and social justice, many teacher education programs
today include some form of teachers reflecting on the fact that they are not like the students they will
eventually teach. Exploring one’s racialized identity is one part of this work. With greater awareness of
the “achievement gap,” more mathematics teacher education programs see value in having teacher
candidates who are “winners” of the system that we are trying to reform reflect on their mathematical
experiences and the likelihood that the students they teach will not be winners or might not be excited
about learning mathematics (deFreitas, 2008; Boaler, 1997).
As such, the problem is not as simple as White teachers (or colleges of education) not
interrogating Whiteness. Some are, with differing degrees of success. Yet, interrogating Whiteness is
tricky because Whiteness itself is complex. Some of my teacher candidates see themselves living in a
post-racial America, denying the concept of race and hopeful that every one else can do the same. Even
if not denying the salience of race, many teacher candidates do not identify as White—thereby making
Whiteness studies and interrogations of Whiteness irrelevant to them.
Whiteness is not as simple as the color of one’s skin. A fair-skinned blonde Cuban is not likely
to be racialized as White once she opens her mouth to voice her opinion and her heavy accent is
revealed. Some of my teacher candidates view their “Asian American” classmates as “Whites” whereas
those Korean American and Chinese American teacher candidates do not see themselves in that way. It
is important to remember that historically, the Irish shared a position with free Negroes in the 19th
century in America and only later, by embracing racism against Blacks2, earned their White identity
(Ignatiev, 1995). The situation is even more complex for Latin@3s, Chican@s in particular. In the
1930s, we were considered a “Mexican” race; earned our “Whiteness” in the courts by 1940 (though
many Chicanos preferred to identify as non-White in the 1960s due to the violence we endured during
the Civil Rights Movement); between 1980 and 2010 we were considered part of a larger “Hispanic”
category independent of race, (López, 1997; 2004); and more recently were given the choice to identify
as White or non-White on the Census bureau. Today, in the US, you can be both white and Latin@ in
Florida, but not in Texas (Peterson, 2015). So, the concept of interrogating Whiteness can be confusing
to teacher candidates and their teacher educators, many of whom have checked various boxes over their
lives (e.g., on census forms, job and scholarship applications, surveys) and not had the luxury of
learning the history and complexity of the social construction of race. Of course, from a postmodern
perspective, racial identities are not static; they are hybridized and constantly open to resignification.
However, postmodernism has its own problems, something I will return to later in this chapter.
The most common form of interrogating Whiteness in a teacher education program is through
autobiographies and reflection assignments. Yet, like the teacher candidates in my opening narrative
who thought they “got it” after 5 - 10 minutes and wanted closure, many teacher candidates (and their
teacher educators) can get excited about (or impatient with) the reflective process and look too early for
a sense of closure or resolution—convincing themselves they will know exactly how to address racism
in their school. At my institution, we have the luxury of having the same students in a cohort for four
consecutive mathematics “methods” courses over two years; I have the same students for a full year.
Most teacher education faculty simply do not have that many math-specific contact hours with their
teacher candidates. They must do the best they can to address any form of social justice during 1 or 2
semesters while also covering lesson planning, peer teaching, assessment, mathematics learning,
pedagogy, the latest mathematics education reforms and professional standards, among other things. As
a result, rather than allowing students to grapple in a messy state of uncertainty, many committed
teacher educators can unknowingly contribute to this eagerness for students to “get it.” Or, they might
simply rely upon their colleagues in foundations courses to help move teacher candidates along in their
abilities to interrogate Whiteness.
Another problem with existing approaches to confronting Whiteness in mathematics teacher
education is that it can devolve into naval gazing, marveling at the progress one has made, or linger in
the phase of the White confession, rather than leading to any real action. Most assignments developed
to interrogate Whiteness are written with Whites as their focus. In some ways, that makes sense, as the
majority of individuals seeking to earn their teaching credentials are White. However, it raises the issue
of how meaningful such assignments are for teacher candidates who identify as Korean American,
Filipin@, recent immigrant from the Ukraine, multiracial, or one of many other identities that cannot
easily be mapped onto Whiteness. And, while well meaning, some cross cultural discussions end up
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
2!I use the term Black, as opposed to African American, to highlight the fact that many Black students living in the United
States have ancestry in the Caribbean, South America, and Asia, among other places. Nonetheless, Black students who
attend schools and live in the United States are racialized in similar ways, regardless of country of origin.!
3! I use the @ sign to indicate both an “a” and “o” ending (Latina and Latino). The presence of both an “a” and “o” ending
decenters the patriarchal nature of the Spanish language where is it customary for groups of males (Latinos) and females
(Latinas) to be written in the form that denotes only males (Latinos). The term is written Latin@ with the “a” and “o”
intertwined, as opposed to Latina/Latino, as a sign of solidarity with individuals who identify as lesbian, gay, bisexual,
transgender, questioning, and queer (LGBTQ).!
serving as another form of being preoccupied with the master’s agenda. That is, students of color are
placed in the role of unpaid sherpas, guides for White instructors and peers (Chinnery, 2008).
Perhaps more importantly, many teacher educators, and thus teacher candidates, are not trained
to understand how White supremacy intersects with other forms of oppression. Instead of Whiteness, I
use the term White supremacist capitalist patriarchy (hooks, 2004)4, as it allows us to think about the
interlocking systems of oppression that we encounter in our everyday lives. That is, as citizens,
teachers, and teacher educators, we will not be able to understand and transform our realities if we
analyze society only through a lens of race, gender, or class. In fact, framing these issues as
“interrogating Whiteness” can inadvertently keep White people at the center of the discussion. By
focusing on White supremacist capitalist patriarchy as a concept, we move beyond the idea that White
males, alone, protect ongoing systems of oppression and shift the focus to developing a discourse of
colonization, decolonization, and the notion of possible collusion by women and people of color.
Although the term does not name it explicitly, White supremacist capitalist patriarchy takes up issues of
language, religion, and sexuality.
Understanding how White supremacist capitalist patriarchy operates globally, not just in the US,
is another aspect of education that rarely gets addressed, particularly in mathematics teacher education
programs. Yet, by highlighting practices for school reform from Japan, China, and Singapore (e.g.,
Singapore Math, Lesson Study, etc.), the field of mathematics education may be resinscribing
stereotypes of Asians as good at math, while ignoring what we can learn from other countries whose
peoples are racialized as brown, Black, primitive, and/or inferior. To interrogate that form of
supremacy, I often introduce to teacher candidates sophisticated algorithms from other countries. See,
for example, Gutiérrez (in press) for an algorithm based on number theory that is used in México to
check the multiplication of two multi-digit numbers. I also highlight how a US math classroom can look
sloppy or confusing to a student from xico (and much of Latin America) where the cuaderno
(notebook) is used in a precise manner that reflects the discipline and becomes a true resource for
students not just in a single math classroom but throughout their lives. In this sense, we challenge the
notion that when it comes to doing mathematics, Asia is superior to Latin America and we raise the idea
that the US has something to learn from both.
Moreover, the Bungee Barbie activity allows me the opportunity to discuss with my teacher
candidates how the countries of origin and the different languages that students speak position them
differently in the classroom and in society. As a teacher, I could not as easily have made disparaging
remarks about “needing to value education” for English learners from China or India. However, based
purely on phenotype, a teacher might apply that stereotype to a recent immigrant Nigerian student.
Then, once the student began to speak with a heavy British accent, a vestige of English colonization, that
student might immediately be viewed as ‘less Black,’ read less inferior. Another way I attempt to
address globalization is through an examination of the Programme of Ethnomathematics (D’Ambrosio,
1990; 2006). This Programme highlights how mathematics is practiced in other parts of the world,
decenters a Western view of mathematics, and documents the contributions that different cultures have
made to the field of mathematics. I will return to this topic later.
In mathematics education programs that attempt to address systems of oppression, there is often
a focus on pedagogy (e.g., culturally relevant teaching, culturally responsive teaching) and/or curriculum
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
4!hooks!later!adopted!the!term!“imperialist”!in!front!of!White!supremacist!capitalist!
patriarchy.!!However,!I!find!the!notion!of!imperialism!can!be!captured!by!simply!reminding!
teacher!candidates!that!these!interlocking!systems!inherently!seek!to!dominate.!I!leave!the!
imperialist!term!off!so!that!it!is!less!awkward!to!say.!!
(e.g., developing lessons that are themed with social justice issues). Both of these approaches are
extremely important and both CEMELA and the TEACh MATH group have made considerable strides
in this area. Understanding, valuing, and drawing upon the funds of knowledge that students bring to
school; creating classrooms that are inclusive and that “assign competence” to individuals who
previously have not been viewed as capable of rigorous mathematics; and using mathematics as a lens to
analyze injustices in society are all critical steps toward breaking down the structures that perpetuate
oppression. However, most mathematics teacher education programs stop there, leaving their graduates
with the impression that their work in addressing oppression and White supremacist capitalist patriarchy
lies in the content of their lessons and the relationships they develop with students. Yet, it is not enough
for teachers to develop deep and flexible knowledge of their field; create meaningful relationships with
their students; and draw upon students’ linguistic and cultural knowledge as they develop and implement
lessons. Teachers who cannot skillfully negotiate the politics of language, White supremacist capitalist
patriarchy, and testing regimes in their working contexts cannot adequately support their students to
learn, especially in this era of high stakes education (Gutiérrez, 2012; 2013a).
Elsewhere, I and others have argued that teaching mathematics is a political activity
(Frankenstein, 1990; Gutiérrez, 2009; 2013b; Gutiérrez, et al., 2013). Specifically, I have suggested that
teachers need to be able to help their students both play the game and change the game of mathematics.
Playing the game involves primarily addressing issues of access and achievement (e.g., rigorous course-
taking, standardized achievement tests, an emphasis on conceptual understanding) so that students are
not penalized later in society. Changing the game includes rewriting the narrative about who is good at
mathematics, who mathematics is by and for; valuing home communities and other ways of viewing the
world (e.g., indigenous ways of knowing); and doing mathematics in ways that challenge hegemony in
society. I argue that in addition to content knowledge, pedagogical knowledge and knowledge of
diverse students, teachers need to develop political knowledge (Gutiérrez, 2012, 2013a). And, part of
the role of teacher educators is to prepare teacher candidates (and thus their students) to “think more
critically about both mathematics and mathematics education so they might become critical citizens
rather than mere consumers of a capitalist society” (Gutiérrez, 2009, p. 11).
At a time when public education and teachers are under attack, teacher candidates need
opportunities early in their development to: 1) broaden and add complexity to their understandings about
teaching, learning, mathematics, and marginalized youth; 2) notice and develop multiple interpretations
on situations they would not normally see (e.g., about mathematics, about students, about issues of
social justice, about the profession of teaching); 3) develop an advocacy stance on teaching, learning,
mathematics, and marginalized students; and 4) become adept at creatively responding to subtractive
discourses that position marginalized students as incompetent and/or narrowly define mathematics as a
predetermined knowledge base to learn, (i.e., be able to use creative insubordination).
Elsewhere I have described some of the ways in which I have prepared teacher candidates to use
creative insubordination (the bending of rules in order to uphold higher ethical concerns), documenting
the kinds of things individuals do in their work contexts as practicing teachers, including the risks they
take and why they take them (Gutierrez, 2013a, c; 2015; Gutiérrez & Gregson, 2013; Gutiérrez, Irving,
Gerardo, & Vargas, 2013). In general, I have found that teachers need adequate time to reflect on
complex ideas within a supportive and critical community of peers, to grapple with uncertainty in a way
that they do not shy away from it, and to be provided with lots of examples of everyday moment-to-
moment ways of deconstructing and challenging White supremacist capitalist patriarchy (i.e., deficit
narratives of students and teachers who are positioned as “other” or “inferior”). Having consistency in
the message and language presented to teacher candidates is important for them to revisit issues, scaffold
new issues, and have a way to communicate with their colleagues and other professionals about their
work.
Like Bartolomé (1994), my approach does not aim to provide teacher candidates with the
“correct” views or help them learn the “best practices.” It is more about becoming critically vigilant
about what is being told to us and deciding how we want to respond to those messages. I do not expect
teacher candidates to adopt my views. Rather, my approach relies upon a metaphor: “The Mirror Test.”
That is, I aim to prepare them with the ability to look themselves in the mirror everyday and to be able to
say “I’m doing what I said I was going to do when I entered the profession.” And, if they are not, they
need to be asking themselves “Why not?” and “What can I do about that?”
Avoiding Typical Stumbling Blocks
In the previous chapter of this book, Craig and Bonner avoid many of the stumbling blocks that
mathematics teacher educators and their teaching candidates face. They recognize that interrogating
White supremacy means more than embracing inclusion and diversity; it requires acknowledging that
public schooling is a racialized space. Rather than feeling personally attacked when people point out
racism, they see it as a new set of eyes to view the world and they work hard to support their teacher
candidates to do the same. Rather than speaking “for” other people, they focus on community walks as
a way to allow students and community members to speak for themselves. Their assignments require
that their teacher candidates follow in suit. Rather than ignoring issues of authority and positionality,
they see the value in assigning competence to all students in the mathematics classroom, exposing their
teacher candidates to curricula such as Complex Instruction. Rather than allowing Whiteness to occlude
their view, they confront it so it can illuminate things. And, rather than doing this work exclusively with
other Whites, they work with and learn from people who are positioned differently by White supremacy-
-their female professors of color and bilingual students. As such, they model for their teacher candidates
a way to address these issues themselves. In this sense, Craig and Bonner consistently raise many of the
important concepts to be explored by mathematics teacher candidates.
In terms of engaging with the political nature of teaching, Craig and Bonner suggest:
…it is important that we recognize public education, including classrooms, schools, districts, and
the overall STEM system as racialized spaces in which structural racism is rarely questioned, and
White supremacy is catalyzed.
I completely agree with them. However, while some teacher educators and teacher candidates have
become more accustomed to understanding how policies like tracking and standardized testing can relate
to racism, they often miss connections between White supremacist capitalist patriarchy to other policies
and practices. For example, students in math courses are not just racialized for their learning of math;
they are sometimes extracted from the math classroom for disruptive behavior, even when that behavior
does not warrant such discipline. Black and Latin@ students, especially males, are overrepresented in
disciplinary infractions (Skiba et al., 2002; Fenning and Rose, 2007). If mathematics teachers want to
be advocates for their students to participate in rigorous and meaningful mathematics, they must be able
to do more than just “recognize public education…as racialized spaces” or control the mathematics
curriculum or their own teaching style. They must also develop a voice on larger school structures and
policies such as discipline, extracurricular activities, graduation requirements, support for mental and
physical health, technology, school infrastructure for testing, and what constitutes proper school dress,
all of which contribute to White institutional and capitalistic spaces within the school system (Gutiérrez,
2013a). If not, teachers risk remaining in a missionary state of “helping others” or only supporting their
students to “play the game” rather than dismantling systems of privilege and oppression.
Understanding some of the concepts that are important for teacher candidates to reflect upon is
critical to moving our field forward. In that sense, Craig and Bonner have nicely outlined some of the
issues they considered; how those issues translated into activities and practices they use with their
teacher candidates; and have included a healthy list of resources. Even so, the manner in which we
contemplate such issues also affects what we notice and how we act on those notions. One strategy that
continues to help me grow is to emphasize the tensions and contradictions in our work. I will begin by
explaining further what it means to emphasize tensions and then suggest three areas to apply that lens:
teaching as a profession; mathematics as Whiteness; and action and coalition building.
Seeing Through Multiple Lenses
I draw on the work of W.E.B. Du Bois and Gloria Anzaldúa to highlight the power of viewing
the world through multiple lenses, something that both Blacks and Chican@s have had thrust upon
them. For Du Bois, Blacks live in two Americas. They are born both an American and Not an
American. As such, they struggle with an ongoing conflict between a spiritual being with roots in
Africa and a materialistic being with roots in America (Du Bois, 1897; 1994). In this sense, there is a
softening influence that Blacks can offer the US.
The Negro is a sort of seventh son, born with a veil, and gifted with second-sight in this
American world, --a world which yields him no true consciousness, but only lets him see
himself through the revelation of the other world. It is a peculiar sensation, this double
consciousness, this sense of always looking at one’s self through the eyes of others, of
measuring one’s soul by the tape of a world that looks on in amused contempt and pity.
One ever feels his two-ness, --an American, a Negro; two souls, two thoughts, two
unreconciled strivings; two warring ideals in one dark body, whose dogged strength alone
keeps it from being torn asunder. (DuBois, 1994; p. 3)
By juxtaposing the notion of “gifted with second sight” and a world that “only lets him see himself
through the revelation of the other world,” Du Bois notes the contradiction that is part of the everyday
lives of people who are Black in the US. It is this familiarity with contradiction, this double
consciousness, that allows people who are Black to see multiple versions of society rather than settling
upon just one. In this sense, they are less likely to be fooled into seeing that the current reality in which
we participate is one reality, one truth.
Similarly, Gloria Anzaldúa sees as an asset the multiple lenses that indigenous people bring to
bear on society. As a lesbian Chicana poet, Anzaldúa had to deal with the pain of being accepted neither
by White feminists who did not understand her indigeneity nor by the Latin@ community who did not
accept lesbians/gays (Anzaldúa, 1987). Yet, for Anzaldúa, it is this very sense of not belonging to any
one world that can be a sign of strength, as it allows us to birth new realities and to develop
unsanctioned ways of knowing. In her writing, she privileges the notion of contradictions, reviving the
indigenous word “Nepantla” as a space of liminality and a process of grappling with tensions. Drawing
on a Mestiza consciousness, she suggests that being in Nepantla is a necessary and positive state in a
cyclical process of knowing and connecting with others (Anzaldúa, 1987; Anzaldúa & Keating, 2002).
In terms of metaphysics, the Aztecs conceived of an individual as both “in” Nepantla and “of” Nepantla
(Maffie, 2013). That is, Nepantla is the space of neither and both, the space between worlds, between
day and night, between being asleep and awake, between male and female, between life and death. So,
being “inNepantla means being between worlds. Nepantla is also a form of moving through life, a
form of being part of the cosmos, a back and forth balancing motion that grounds itself in no single
space. Being “of” Nepantla means that one’s existence is not stable, but tenuous.
This notion of Nepantla applies not just to Anzaldúa’s painful experiences, but to the everyday
experiences of Latin@s in a society where White supremacist capitalist patriarchy reigns. In terms of
the academy, Latin@ faculty live in a space where we are both highly visible (e.g., seen as quotas and
diversity hires; brown skins walking the corridors) and highly invisible (e.g., having little presence in
administration or voice at faculty meetings). Similarly, many Black faculty members continue to
experience the double consciousness that Du Bois wrote about over a century ago. As such, we have
developed the means to be border crossers, to understand things relationally, to deal with multiple
realities and uncertainty. Rather than rejecting this uncertainty, we spend a large part of our time in
Nepantla and embrace it; we are Nepantler@s. I refer to this process as “nesting” in Nepantla because it
requires developing a home and identifying with that place. The ability to hold multiple, conflicting
views is an important aspect of being a Nepantler@, something I have argued can help mathematics
teachers rethink the concept of knowledge and can help them become advocates for their students
(Gutiérrez, 2009; 2012). Unlike Helm’s (1990) model of racial identity development that can focus on a
“destination” and/or implies a linear trajectory, I seek to get teacher candidates to see this process as
organic and relational. However, more than just being able to hold these conflicting views, individuals
must also value that contradiction/tension and see it as a “gift of second sight” and as a “place of
birthing new knowledge.”
Indeed, the notion of contradictions arises in the chapter by Craig and Bonner. However, the
“new set of eyes” that they highlight seem to be of a different sort than those that Du Bois, Anzaldúa, or
I would argue for. Rather than valuing and maintaining the multiple and contradictory views that can be
seen as a strength of people who historically have been oppressed through White supremacist capitalist
patriarchy, Craig and Bonner seem to position this “new set of eyes” in place of an old set of eyes, rather
than existing alongside of, pushing back against, or offering complexity to a singular view. The value of
contradictions is not always clear in the descriptions of their journeys or in their work as teacher
educators. For example, terminology such as “The old identity” versus “The new identityused by
Craig implies a sense of advancement and resolution as opposed to ongoing tensions and grappling. It
makes me wonder: How does this language help others who may be struggling with interrogating White
supremacist capitalist patriarchy? Should others be looking for “aha” moments? Is it always so clear in
a given moment that we are changing? Is change permanent? Is there room for setbacks, failures in
areas where there was previous success? After all, it is not as if one ever becomes fully non-racist or
anti-racist separate from a racist society. Viewing our identities as hybridized and always up for
resignification casts a new light on this topic.
There are moments in their chapter where contradiction arises and is embraced, only to be
clouded over again. Bonner notes,
In short, this journey has been filled with contradictions and uncertainties that I believe
are necessary to becoming a researcher and practitioner whose work is rooted in social
justice. Even in writing this piece, I feel a sense of contradiction – haven’t stories of
people like me been dominant before now?
It would have been wonderful to understand better the particular contradictions and uncertainties that
were necessary for Bonner. Laying them out side-by-side would make it easier for the reader to both
relate to and analyze them. For example, what is the tension that Bonner feels in stories of people like
her? Is it that she simultaneously feels her story is important and not important? Is it that people like
her should not dominate but at the same time need to dominate to reach their audience (people like
themselves)? Or, is it something else altogether? I am not certain.
Later in the chapter, she notes some of the ways in which she is confronted with contradictions.
But, they exist in ways that seem to indicate weakness, not strength. They seem to be a set of questions
that need to be answered.
…the social justice classes became one of the first formative, contradictory, illustrative
experiences in my journey. For example, I was a White doctoral student who was
learning about social justice education from two White professors (my instructors at the
time) in classes consisting of largely White doctoral students at a Tier I University. At
the same time, I was a researcher in a largely Black school, in a Black community. What
I began to realize was, although I was the “researcher,” I was not the expert in this
setting. In fact, my role was to listen to the experts (parents, teachers, students,
administrators) and allow them to tell their story.
In the end, the reader is given a resolution: I was not the expert in this settingmy role was to listen to
the experts. This kind of positioning can leave an individual with a false sense of confidence, as if
“before I didn’t get my role” and “now I get it,” the unintended implication being that I no longer have
to worry about being the expert (authority) because that is not how I am positioning myself. Yet,
identity is not something you are, it is something you do, a kind of performance (Butler,1999). It is
partly in our control and partly in the control of others who interpret our actions and project their own
ideas onto us.5 That is, just because Bonner did not position herself as the expert does not mean that
others did not see her in that way or that she did not, at times, slide into that role without being aware. I
would argue that highlighting how she was simultaneously the expert and not the expert may have
yielded a more productive space from which to work.
It is not clear what role contradictions play for Craig. She seems more fixed on the reflective
process and advancing past the state of not seeing her own blind spots.
My interactions with students from a background different than my own encouraged me
to engage in a constant self-reflection about my own experiences as a White female and
about my assumptions of my students and their communities…Once I recognized my
own implicit, assumed privilege and opportunities as a White, middle class, female, I
could begin my exploration of the issues Latin@s face while learning mathematics.
What I really like about Craig’s process is that it is relational. She recognizes that she cannot think
about her students without also thinking about herself. However, her description implies a step-wise
process (first focus on myself, then I can focus on others). Although clearly this is not her message, it
almost sounds as if this work involves a lot of deep thinking and then after a certain amount of time, you
will recognize your assumed privilege and then can get to work on other issues.
In their conclusion, Craig and Bonner note, “We continually struggle with contradictions that
arise as we help our PSTs to engage in noticing, challenging, and taking action.” Yet, without sufficient
documentation of the contradictions and how they dealt with them, the reader could leave with the
unintended message that the majority of the contradictions they faced were surmountable (and should be
surmounted) and/or that contradictions are not a primary focus of the work that teacher educators or
teacher candidates should do.
For me, contradictions are paramount. The notion of nesting in Nepantla or becoming a
Nepantler@ works not just for me in my research6 and mathematics methods courses, but also for
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
5!See!Gutierrez,!2013b!for!further!explanation!of!how!identity!as!performance!relates!to!
mathematics!education.!
6!See,!Dance, Gutiérrez, & Hermes (2010) for further description of how tensions and the
relational process plays out in my research.!
teachers to take into their classrooms. Teachers benefit from being able to seek and maintain tensions in
their work. My work as a mathematics teacher educator is about more than just helping teacher
candidates obtain the knowledge, skills, and dispositions needed for teaching, it is about helping people
become someone, developing into a Nepantler@. In fact, the teacher candidates I have interacted with
who develop political clarity and commitment to their roles as advocates are more likely to take risks in
their teaching to dismantle systems of oppression (Gutiérrez, 2015). I turn now to three areas to apply
this notion of valuing tensions and contradictory views. I begin with the concept of teaching as a
profession.
Teaching as a Profession
“Teaching happens in the classroom/Teaching happens outside of the classroom”
Most teachers would agree that their primary role is to educate. The term can mean many things
to different people, but most would reject limited views like the banking model where content is poured
into the heads of passive learners (Freire, 1970). And, most teachers, mathematics teachers included,
would argue that education happens in classrooms in schools. After all, that is where they learned about
what teaching is, by sitting in classrooms for over a decade while a young person, something referred to
as the “apprenticeship of observation(Lortie, 1970).
No other professional field apprentices all of society into it. Students who apply to medical
school do not really believe they know what it means to be a doctor; that is why they need to attend
medical school. The same is true for lawyers, business people, and any other professional field. Yet,
because of the apprenticeship of observation in education, many teacher candidates believe they already
know what it means to be a teacher, long before being accepted into a teacher education program. In
fact, it is not uncommon for me to have teacher candidates in my courses that admit to having arranged
to be hired at their old high school once they graduate, even before taking any courses. In some
respects, many teacher candidates are not really seeking to understand the profession. They believe they
already know what it entails—being in front of students, developing and presenting engaging lessons
and activities, giving homework and tests and later grading them, attending some school meetings, and
holding parent-teacher conferences.
Schools of education do little to counter the idea that the profession of teaching is primarily
about what you do in your classroom with your students. Mathematics methods courses tend to focus on
lesson planning, advanced mathematics, assessment, learning and motivation, curriculum, and
pedagogy, including the use of technology and ways of differentiating instruction for different types of
learners. The power of the apprenticeship of observation in mathematics education has been
acknowledged by many researchers who argue that teacher candidates need to “unlearn” what they
learned as mathematics students if they are to teach in a different way (Ball, 1988). And, while many
colleges of education expand teacher candidates’ views of what constitutes teaching a bit (e.g., including
collaboration with other teachers in professional learning communities) by way of portfolios and other
documents required by state agencies, the message that teacher candidates receive continues to revolve
primarily around the idea that teaching happens in the classroom, or at the very least in the school. This
vision about the profession of teaching—what it is, what it takes to be good at it—is underscored by the
actions and discourse promoted by the leading professional society for mathematics teachers (National
Council of Teachers of Mathematics). One look at the types of sessions offered at NCTM annual and
regional conferences highlights the same types of topics that are presented to teachers in mathematics
methods course (lesson plans, advanced mathematics, assessment, pedagogy, effective uses of
technology, motivation strategies, differentiating instruction for a variety of learners). As such, teaching
as a profession is largely about making that classroom interaction a positive and rigorous one for
students.
If teacher candidates who aim to dismantle systems of oppression view the profession of
teaching as primarily concerning what they do with their students in the classroom, then approaches like
social justice mathematics teaching will be critical for them. In fact, most of what has been documented
as social justice mathematics teaching focuses on curriculum7—creating lessons that will allow students
to use mathematics as a lens to identify injustices in society and to address those injustices (Gutstein,
2006). Teachers interested in engaging in social justice mathematics teaching will find a variety of
lessons categorized by topic and grade level at the www.radicalmath.org website.
Let us consider the possible impact of current versions of social justice mathematics teaching on
dismantling White supremacist capitalist patriarchy. Most of the teacher candidates I have taught fall
into one of three typical responses after having been exposed to social justice mathematics teaching: 1)
outright rejection because it is too political and will get you into trouble as a new teacher; 2) excitement
and naivete in how easy it will be to create such lessons; 3) initial interest but some trepidation as to how
difficult it will be to develop rigorous lessons and have enough knowledge of larger social justice issues
in society to be able to guide meaningful discussions with students. It is the last response that is most
rare but always leaves me hopeful. Without a community to support them, most beginning teachers who
seek to implement social justice mathematics teaching become discouraged right away and then back
pedal or create a lesson that unknowingly reduces the mathematical rigor or complexity of the
experience. Other researchers have observed similar findings (Bartell, 2013). This can leave teacher
candidates feeling they are inadequate at addressing White supremacist capitalist patriarchy as a teacher.
At the same time, teaching as a profession is so much more than what happens in the classroom.
In fact, what counts as teaching today is largely determined by individuals outside of schools—owners
of for-profit corporations, policy makers, and politicians, many who have never taught themselves. The
film industry has come on board with recent movies like Waiting for Superman that depicts teachers as
lazy, unaccountable, and/or as the root of students’ failure to learn. The media, rather than helping
unveil the problems in education with a society that does not provide adequate housing, healthcare, or
employment for its citizens, often promotes discourses about teaching like closing the achievement gap,
growth mindset, and helping students to develop grit. The Bill and Melinda Gates Foundation has spear-
headed a number of initiatives, including charter schools, that seek to define what counts as good
teaching and that can ultimately undermine public education. Pearson Education, the corporation that
benefits from sales of Common Core aligned textbooks and the PARCC tests, has developed a system of
“badges” that mathematics teachers can earn for promoting the Common Core State Standards. These
badges are being promoted as a sign of being a true professional. So, in some respect, in order to engage
in the profession of teaching, teachers cannot simply shut their doors and engage their students in
rigorous and positive interactions in the classroom. They need to be able to make sense of, buffer
themselves from, or defend themselves from the deficit discourses circulated between the media,
corporations, politicians, and others.
Being able to hold both views in tandem—teaching as a profession happens in the classroom and
teaching as a profession happens outside of the classroom—can go a long way towards helping teachers
(and teacher educators) prepare for the complexity that is inherent in the everyday work of teachers. It
might open the door for teachers to invent new approaches to address White supremacist capitalist
patriarchy that exist along side of a focus on pedagogy or curriculum. Already, savvy teachers are using
social media to critique testing regimes and spread the word for how parents and students can opt out of
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
7!A!noted!exception!is!Wager!&!Stinson!(2012).!
standardized tests that cause unfair stress to students, take precious time away from teaching, place
undue economic burdens on low income districts that do not have the proper infrastructure to administer
such tests, or weigh too heavily into teachers’ evaluations. The teacher candidates I work with are
required to help develop and host a community event called GeoJam that gets hundreds of students
(especially ones who do not identify as mathematical) and their family members to compete in creative
and rigorous mathematical challenges that help teachers see “unmotivated” or “slow” students in a more
positive light and can change the view for students about what it means to do mathematics. In addition,
teacher candidates in our program volunteer in a weekly, bilingual, after-school mathematics club run
out of a public library. The club supports groups of Black and Latin@ adolescents to do college level
mathematics challenges that involve the body and rely on no formulas or calculators. Some of our
graduates choose to take these experiences and create analogous clubs, steering committees, or events in
their communities, spaces where adolescents can be proud to be brown/Black and mathematical. Others
use social media, like Google Hangout, blogs, or create professional learning communities with
colleagues in their building to discuss and strategize ways to dismantle the oppression they see in their
schools. They see this work as just as important and “professional,” if not more so, than anything they
do in their classrooms.
Mathematics and Whiteness
“Mathematics is White/Mathematics is Not White”
Most mathematics teacher education programs concerned with interrogating oppression or
promoting more social justice focus on teaching and curriculum—in particular, the ways in which
teacher beliefs, teacher practices, and school policies like tracking can be viewed as forms of racism. At
a practical classroom level, it is important for teachers and teacher candidates to recognize how popular
educational reforms in mathematics can have different affects on students who historically have been
marginalized. That is, teachers need to be able to critically analyze the limitations of discourses like the
“achievement gap” or psychology-based reform movements that focus on motivation from an individual
perspective. Two of these popular reforms focus on generating in students “grit” and a “growth
mindset,” things that may prevent teachers from seeing the larger sociopolitical contexts in which
students and learning operates. That is, if students are competing in a space that maintains White
supremacist capitalist patriarchy, where the playing field is not level and where participating in
mathematics class may require assimilating practices that do not align with one’s cultural or racial
identity, then being told to “develop grit” and “perseverance” or to focus on “developing new dendrites”
in the brain may be distractions to maintaining a critical view on the world and a sense of wholeness in
the process of doing mathematics. These reform slogans circulate in the media and their
implementations in schools can make it seem as if the student is in control of their destiny; they simply
need to develop a more productive mindset about learning. Yet, teacher candidates can be supported to
see that this approach may inadvertently be little more than a modern version of the “pull yourself up by
your bootstraps” mentality that students of color have heard before. Persevering in an unfair or unjust
system is not the basis of equity. I have expressed similar concerns with respect to the discourse on
“closing the achievement gap” (Gutiérrez, 2008; Gutiérrez & Dixon-Roman, 2011).
Even so, understanding how mathematics teaching can maintain White supremacist capitalist
patriarchy may not be enough. It is critical for mathematics teacher candidates to see how mathematics
itself is political, to understand the relationship between mathematics as a discipline/practice and White
supremacist capitalist patriarchy (Gutierrez, 2013a, 2015; Warburton, 2014). Without this examination,
teachers are likely to perpetuate the status quo, a version of doing mathematics that continues to oppress.
Let us consider the nature of mathematics.
On the one hand, the face of mathematics is White; the people most credited with “inventing” or
“discovering” it are the Greeks and others of European descent (Connor, 2005; Joseph, 2011). And, in
this sense, mathematics is viewed (and generally treated) as a noun. I will return to this notion later in
this section. When asked about important mathematicians, my teacher candidates can easily conjure up
the names of Pythagoras, Einstein, Gauss, Euler, Fibonacci, and Pascal. They are less likely to know
Srinivasa Ramanujan, Benjamin Banneker, or Baudhayana, the Indian mathematician who first provided
a written proof for the “Pythagorean” theorem at least a thousand years before Pythagoras lived. For the
most part, schools do not teach the global history of mathematics. So, teacher candidates cannot be
faulted for not knowing that Greece benefitted from the flow of mathematical understanding they
received from Mesopotamia, Egypt, and Islam. Some researchers have argued that the contributions of
non-Europeans to mathematics have been not only largely ignored and devalued, but outright distorted
(Joseph, 1992; Connor, 2005). Omitting this dynamic history from the classroom can give students the
impression that excellence in mathematics is the exclusive domain of Europeans, that mathematics is
ultimately an enterprise for and by Whites, especially White men. Again, most teacher candidates do
not recognize that the lack of famous women mathematicians is related to the fact that until fairly recent
in history, women were not allowed to attend universities or engage in research. And, only those who
had powerful fathers or husbands were given any chance at learning advanced mathematics or
communicating with other mathematicians.
More importantly, like Whiteness, mathematics dominates; it exerts a formatting power over our
lives (Christensen, Skovsmose & Yasukawa, 2008; Volmink, 1994). Disconnected from emotions or
morals, it is viewed as an “objective” arbiter of “truth,” as having no agenda of its own other than to
reflect the natural order of the world. In general, we do not challenge the power mathematics exerts
because we see its properties operating outside of humans—existing in patterns such as Fibonnaci
sequences in shells, seeds, flowers, and music; as fractals in trees, plants, snowflakes, and human vein
systems. These enduring phenomena are then recast as “truths” and reify mathematics’ place as superior
to all other disciplines or ways of viewing the world. Even the hard sciences (e.g., physics, chemistry)
are seen to rely upon mathematics in order to flourish. Perhaps as a result, we have come to view
mathematics as a sign of intelligence—those who understand it are inherently smarter (read superior) to
those who do not. Moreover, mathematics as a measure of intelligence is static. That is, some people
are mathematical (intelligent) while others are not. That is simply the way of the world.
With respect to education, mathematics exerts its power over individuals through a form of
“microaggression.” That is, particular ways of thinking are related with mathematics. Like Whiteness,
mathematics operates with unearned privilege in society. Its superiority in society and the natural world
is seen as normal, pure, even beautiful. Yet, such elevated status is somewhat arbitrary. We could
imagine a society where something other than mathematics conferred intelligence: for example, the
ability to be artistic, to relate well with others, or to view things holistically. All of these forms of
“intelligence” would structure society, its citizens, and their relationship to each other and our planet in
very different ways than they occur today.
One of the ways that mathematics dominates is by structuring what types of thinking are valued,
what is considered “the standard” to which we measure all things. Assigning higher value to those who
can reason and think abstractly outside of any real or experienced context, mathematics implicitly
suggests that those who cannot do this type of abstraction are inferior (Walshaw, 2004; Walkerdine,
1994). In fact, this phenomenon, referred to as “context dependent learners,” was assigned to Blacks
and Latin@s in the 1970s. In this sense, when it comes to schooling, mathematics can operate as a form
of microaggression, a repeated assault to those who value connection with others and one’s
environment, to those who need to see a reason for doing mathematics beyond getting a grade in school.
In fact, in many mathematics classrooms, students are expected to leave their emotions, their bodies,
their cultures, and their values outside the classroom walls, stripping them of a sense of wholeness. All
that seems to be needed for mathematics is a brain and an instrument to record—a pencil and paper, a
computer, a calculator. Even when students can clearly identify the mismatch between the mathematical
task at hand and the context from which it is supposedly extracted, their mathematics teachers often
become complicit with this form of microaggression and reply, “Just pretend.” And, yet, by privileging
abstraction, we deny ourselves the right to be compassionate, humane, and intimate.
Given that mathematics operates as a kind of proxy for intelligence, teacher candidates need to
recognize the lasting effects on students who are racialized as “other” or “inferior” by White
supremacist capitalist patriarchy. Such students include: girls, Blacks, Latin@s, American Indians,
recent immigrants, English learners, and students who come from working class families. These
students are disproportionately placed in low level mathematics courses; are not well represented in
advanced mathematics courses or on the mathematics team; and tend to score lower on tests of
standardized mathematics achievement, a scenario that is likely to worsen with newly released tests like
PARCC and the Smarter Balanced Test that are expected to have failure rates as high as 60 percent. As
a result of this process, certain students will not only be labeled as poor at math, they will be viewed
(and may view themselves) as less intelligent in society long into their adult lives.
In my mathematics methods courses, I ask teachers to reflect on their mathematical
autobiographies, not just to understand how they are positioned with respect to mathematics (and how
that may differ from their future students who might not have positive identities around doing
mathematics), but to ascertain what they think mathematics is. I ask them two general questions: 1)
“Think back to the first time you can remember doing mathematics. Who were you with? What were
you doing? How did you feel? And, how did you know you were doing mathematics?” and 2) Think
back to a time when someone else recognized you for doing mathematics. Who were you with? What
were you doing? How did you feel? And, how did they know you were doing mathematics?” From their
answers, we are able to launch into a discussion about who gets to decide what counts as mathematics
and how do our definitions of mathematics influence who identifies as mathematical as well as who is
recognized for doing mathematics. And, more importantly, they are able to start analyzing in what ways
they are complicit with a form of mathematics that is potentially oppressive (to themselves and/or
others). For many of them, mathematics is a noun, often involving words like axioms, logic, and
numbers. Almost all struggle to come up with an adequate definition, having never before been asked to
do so, even though they are mathematics majors. Similar to Whiteness, they had never faced any
consequences for not interrogating the very field and professional activity to which they were devoting
their lives.
On the other hand, if we define Whiteness as relating to Caucasian ancestry, mathematics is not
White. Most of the inhabitants of this planet are non-White and their ancestors (inhabitants of Egypt,
Mesopotamia, and Islam) contributed greatly to mathematical advances, as aforementioned. Even if we
ignore history and consider only the state of things today, we see that mathematics is practiced
throughout the world, in various forms that all relate. In that sense, mathematics is a verb, something
that is done by people. Alan Bishop (1988) developed a classification system to document the basic
forms of mathematics that are practiced by different people in different parts of the world. They
include: counting, locating, measuring, designing, playing, and explaining. In fact, many
mathematicians would agree that mathematics is a verb, not a noun. When asked what mathematics is,
they often respond, “It is what mathematicians do.” Seeing mathematics as a verb, anthropologists
(Eglash, 1999; Ascher, 2002) have extended Bishop’s work to show that, indeed, the whole world does
it. As such, mathematics is neither White in its historical sense nor in its modern sense.
By maintaining a view that mathematics is both White and not White, teacher candidates can
more effectively participate in a form of doing mathematics that they desire. That is, even while
understanding that there is a long and distorted history about mathematics and its place in society, they
can recognize they are part of a larger group of people on this planet who are “doing mathematics.” As
such, the mere act of doing it in ways that goes against White supremacist capitalist patriarchy is helping
to define what mathematics is. And, when teachers are able to see mathematics as a verb, as a living,
breathing thing that is in constant motion, then they can better position their students not as individuals
with misconceptions about or correct answers in mathematics (noun), but as authors and doers of
mathematics (Gutiérrez, 2012). Because mathematics cannot be done by itself, humans are always
helping shape what it is, what kinds of questions the activity can answer, and how doing it will help us
make sense of our reality (Gutiérrez & Dixon-Roman, 2011). Historically, the act of doing mathematics
has been more associated with supporting warfare and economics. That does not have to be our future.
Action & Coalition Building
“It’s all about me/It’s not all about me”
On the one hand, interrogating White supremacist capitalist patriarchy requires that I am
constantly reflecting on myself and the ways in which I might (unknowingly) participate in these
interlocking systems of oppression. In that sense, it’s all about me. Placing that responsibility
elsewhere (e.g., on others who have more power, more experience, or more claim to this work) is not
due to ignorance but a choice not to work on these issues. This process of fleeing from Nepantla is what
Gloria Anzaldúa would refer to as desconocimiento or a “refusal to know.” As a teacher, I need to be
prepared to raise issues of White supremacist capitalist patriarchy in both informal settings (e.g.,
interactions with people in school hallways, the parking lot, conversations over lunch) and formal
settings (e.g., classroom, school wide meetings, professional learning communities and conferences). In
order to do that, I must understand not only the systems of oppression I seek to dismantle, but my place
in them.
Elsewhere, I have discussed the dangers of philosophizing to the detriment of action and social
transformation (Gutiérrez, 2013b). That is, by adopting a postmodernist or poststructuralist perspective,
many individuals can become fascinated with the fact that nothing is real, that no value judgments can
be made, and they essentially become paralyzed from acting. Teacher candidates can end up in a cycle
of constant reflection about themselves and their place in systems of oppression to the point of not ever
knowing what, if anything, is the right thing to do about it. Yet, it is important for teachers to be able to
take a stand, to advocate for students who are Black, Latin@, immigrants, and/or English learners. As I
mentioned earlier, to the extent that teacher candidates learn about Whiteness, privilege, and White
supremacist capitalist patriarchy and are not called to action, it actually can serve as a form of
recentering Whiteness. We seek not just to understand but to transform White supremacist capitalist
patriarchy. Thinking our way towards progress or taking action as a single individual is not likely to
make any great impact on the powerful systems of oppression we face as teachers and teacher educators.
It is important to resist intellectualizing the struggle, and instead live it. Living it means action, such as
taking risks in our everyday work.
More than just “living” the struggle and taking risks as an individual, it is important to look for
ways to build coalitions with others (e.g., team teaching with people who are different from us,
developing partnerships with teachers who use creative insubordination on a regular basis, creating
communities in which we learn and can be held accountable to our beliefs, our students, and our
definitions of mathematics) so that we can be inspired to continue to participate in a larger movement.
In fact, history has taught us that progress usually occurs only through movements (e.g., Civil Rights
movement), when people come together to collectively resist systems of oppression and demand, often
through legal actions, that a new system be put into place. In that sense, it is not all about me.
Craig and Bonner seem to agree that introspection is an important part of interrogating
Whiteness. They claim,
we find it necessary to continuously look at our own positionalities, perspectives, and
living contradictions, especially as they relate to our identities as White MTEs and how
this interrogation might inform or hinder our goals. Engaging in this type of reflection
has allowed us to understand and be critical of our own cultural lenses and teaching
practices.
Later, they highlight how this approach of reflecting on prior experiences relates to assignments they
create for their teacher candidates: “We hope that our assignments provide our PSTs with an opportunity
to reflect on their prior experiences in terms of equity, access, and privilege and to develop sensitivity
for similar issues in their future practice. Yet, this whole process of reflecting seems to be the extent of
the action.
On the one hand, Craig and Bonner recognize that action is important. They assert, “…we
interrogate and notice our cultural backgrounds, challenge (and continue to challenge) our beliefs, and
take action in our practice…” However, the specifics of what it means to “take action” is not clear.
Bonner attempts to elaborate:
I began (and continue to) seek out new perspectives while deconstructing my Whiteness.
I began working closely with my advisor and others, who guided my thinking and work
in this area. She pushed my thinking about myself and my role in systems that oppress,
and by the end of my program my focus shifted to explicitly resisting the racism that is
inherent in schools and society, and has moved me towards autonomy… (p. 10)
From the description, it is not clear if she considers her action the “shift in thinking” or if she simply
failed to describe the specific actions that constituted “resisting racism.” I was left wondering.
Admittedly, Craig and Bonner note that because they only have 1 semester with their students,
they focus on the goals of noticing and challenging, and less on action. Even so, their notion of action
tends to be in the form of “re-noticing” or in actions that are directed to the classroom (e.g.,
implementing a mathematical problem that draws on the funds of knowledge of students they have
studied), not in engaging with others to dismantle systems of oppression. Again, their focus on racial
identity development with roots in psychology seems to privilege an individual rather than a collective
perspective.
As aforementioned, my approach to teaching privileges tensions. On the one hand, a large part
of addressing White supremacist capitalist patriarchy is the mirror test (It’s all about me); yet, the goal is
to reclaim the profession and that can only be done in solidarity with other professionals (It’s not all
about me). When teachers are able to hold both in mind, they can work from a place that better reflects
the reality in which we participate.
In discussing White supremacist capitalist patriarchy with teacher candidates, one film I find
especially helpful is Color of Fear, a discussion among men of different racial backgrounds reflecting on
White supremacist capitalist patriarchy. https://www.youtube.com/watch?v=vBSImagHK8c
Although this film was produced in 1994, many of the points are still very relevant today. In fact, one of
the prompts I use for this film is “What, if anything, from the conversation is still pertinent today?” In
addition, I probe for how this conversation can inform the stances and conversations we have in teaching
mathematics. For example, what kinds of things do we hear from our students, practicing teachers,
peers, friends, and family members that echo parts of the conversation? And, in what ways do we feel
comfortable in initiating greater dialogue? The variety of views from the White men in the film
highlights how “Whites” are not a monolithic group, shows some of the resistance tactics used by
Whites who feel defensive, and helps teacher candidates identify some of the actions of White allies.
The part of the conversation where people of color talk only to each other provides another level of
honesty and surfaces the ways their actions may unknowingly maintain White supremacist capitalist
patriarchy. This part of the film also helps add complexity to the phenomena and underscores the idea
that this work is not about one individual or one group of individuals solving the problem, but rather
involves being part of a larger movement.
Conclusion:
The ideas of double consciousness and nesting in Nepantla have long been the work of people of
color. The ability to see the world with contradictory lenses helps individuals deconstruct White
supremacist capitalist patriarchy as “normal” or “truth” and recognize their role in colluding with or
dismantling such supremacy. The point of identifying and deconstructing White supremacist capitalist
patriarchy is not to replace it with another form of supremacy, so that a new group is in power. Rather,
individuals who seek to deconstruct White supremacist capitalist patriarchy aim to dismantle all systems
of oppression. While many people of color grapple daily with the multiple and contradictory views and
identities they enact, they are not immune to maintaining White supremacist capitalist patriarchy. And,
while there are fewer incentives for Whites to interrogate Whiteness or dismantle oppression, the ability
to live in tensions is a stance that can be learned by others.
I have argued that more than just reflecting on the tensions and contradictions that arise in our
work as teachers and teacher educators, we must work to maintain those tensions, so as not to collapse
too easily into a state of resolution and false knowledge. Some benefits we gain when we maintain the
contradictions/tensions is that we continue to stay connected to each other. When we are not able to
make sense of our reality through only one lens, we are open to the views of others. There is a spiritual
greeting grounded in Mayan philosophy that suggests that all beings are connected. It is highlighted by
the saying En Lak’ech (You are the other me) to which the receiver responds with Ala K’in (I am the
other you). Seeing ourselves as hybrids, our identities as contradictory, is an important step in
maintaining a connection with others. Nesting in Nepantla also helps us as teachers and teacher
educators to develop a better familiarity with uncertainty and risk, a feature that is key to all teaching.
Moreover, researchers who study semiotics remind us that by continuing to hold two conflicting views
side by side (e.g., a new view that traverses but is part of an old view), we are more likely to generate
new knowledge. Maintaining the tensions and contradictions in our work is also necessary for all of the
everyday decisions that teachers make. For example, many teachers seek to create more student voice in
the classroom, to challenge what we think we know about students, and yet it is important to remember
that the very mechanisms we employ to “create student voice” can lead to essentializing students or
expecting them to be spokespeople for their group. The language of “Play the game/Change the game
highlights the ways in which even while seeking to dismantle systems of oppression, we are all still part
of those systems.
Epilogue
I feel fortunate to teach (and learn immensely from) a variety of students in my mathematics
methods courses. Some are students who have been marginalized in society and want to make the
mathematics learning experience a more humanized one for adolescents. Most are middle-class White
females who grew up in the suburbs and envision themselves teaching back in their home
neighborhoods once they graduate. Almost all of them excelled at mathematics while in high school,
though that feeling of success often ends abruptly once they hit upper level mathematics courses in
college. Many have gone 19-20 years having never had any real consequences for not reflecting upon
their history, their identities, or how individuals are racialized or positioned in society based upon their
perceived race, class, gender, religion, or sexuality. I have worked hard to help my teacher candidates
deconstruct society and the education system to see that the current version is but one of many we could
have (Freire, 1970). For me, that is the first step towards helping nurture a different, more humanized,
mathematics education forward. I also support my teacher candidates to construct identities that will
allow them to become informed advocates for their students, to take more risks that will benefit others.
Although it may sound like I have it all figured out. I do not. I have made many mistakes as a
mathematics teacher educator committed to social justice. For example, it took me several years to
recognize that mathematics teacher candidates cannot “drink through a fire hose” when it comes to
learning about issues of interlocking systems of oppression. Even though our time together is limited
during class, I now understand that there is a delicate balance between how much I can say and how
much I need to trust they will eventually say (with/to each other). On the one hand, I want them to
engage with tensions and contradictions, to not seek closure. On the other hand, I do not want that
process to lead them to forever question everything and never take a stand. After 20 years of this work,
I have a better sense of a direction in which I am heading, though I certainly do not have a destination in
mind. For now, I am happy to nest in Nepantla.
Bibliography
Anzaldúa, G. (1987). Borderlands/La Frontera: The new mestiza. San Francisco: Aunt Lute
Books.
Anzaldúa, G. and Keating, A. L. (2002). This bridge we call home: Radical visions for
transformation. New York: Routledge.
Ascher, M. (2002). Mathematics elsewhere: An exploration of ideas across cultures.
Princeton, NJ: Princeton University Press.
Ball, D. L. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1),
40-48.
Barrow, John. D. (1992). Pi in the Sky: Counting, Thinking, and Being. Oxford, London:
Clarendon Press.
Bartolomé, L. (1994). Beyond the methods fetish: Toward a humanizing pedagogy. Harvard
Educational Review, 64(2), 173-194.
Boaler, J. (1997). When even the winners are losers: Evaluating the experiences of ‘top set’
students. Journal of Curriculum Studies, 29(2), 165-182.
Chinnery, A. (2008). Revisiting “the master’s tools:” Challenging common sense in cross-
cultural teacher education. Equity & Excellence in Education, 41(4), 395-404.
Christensen, O. R., Skovsmose, O., and Yasukawa, K. (2008). The mathematical state of the
world—Explorations into the characteristics of mathematical descriptions. ALEXANDRIA
Revista de Educação em Ciência e Tecnologia, 1(1), 7790.
Connor, C. D. (2005). A people’s history of science: Miners, midwives, and low mechanicks.
New York: Nation Books.
D’Ambrosio, U. (1990). The role of mathematics education in building a democratic and just
society. For the Learning of Mathematics, 10, 2023.
D’Ambrosio, U. (2006). Ethnomathematics: Link between traditions and modernity. Rotterdam,
the Netherlands: Sense Publishing.
Dance, L. J., Gutiérrez, R., Hermes, M. (2010). More like jazz than classical: Reciprocal
interactions among educational researchers and respondents. Harvard Educational
Review. 80(3), 327-352.
Du Bois, W.E.B. (1994). The souls of Black folk. Chicago: Dover.
Du Bois, W. E. B. (1897). Strivings of the Negro people. The Atlantic. August 1, 1897.
Eglash, R. (1999). African fractals: Modern computing and indigenous design. Rutgers, NJ: Rutgers
University Press.
Fenning, P. & Rose, J. (2007). Overrepresentation of African American students in exclusionary
discipline: The role of school policy. Urban Education, 42(6), 536-559.
Freire, P. (1970). Pedagogy of the oppressed. New York: Herder & Herder.
Gutiérrez, R. (in preparation). Mathematics as microaggression.
Gutiérrez, R. (in preparation). Mathematics teaching as subversive activity.
Gutiérrez, R. (in press). Listening to Latin@ students. The Mathematics Teacher. Mahwah, NJ:
NCTM.
Gutiérrez, R. (2015). Risky business: Mathematics teachers using creative insubordination. A paper
to be presented at the annual meeting of the North American chapter of the Psychology of
Mathematics Education. East Lansing, MI.
Gutiérrez, R. (2013a). Why (urban) mathematics teachers need political knowledge. Journal of Urban
Mathematics Education, 6(2), 7-19.
Gutiérrez, R. (2013b). The sociopolitical turn in mathematics education. Journal for Research in
Mathematics Education, 44(1), 37-68.
Gutiérrez, R. (2013, c). Mathematics teachers using creative insubordination to advocate for
student understanding and robust mathematical identities. Proceedings of the Annual
Conference of Psychology of Mathematics Education North America. Chicago, IL.
Gutiérrez, R. (2012). Embracing "Nepantla:" Rethinking knowledge and its use in teaching. REDIMAT-
Journal of Research in Mathematics Education, 1(1), 29-56.
Gutiérrez, R. (2009). Embracing the inherent tensions in teaching mathematics from an equity stance.
Democracy and Education, 18(3), 9-16.
Gutiérrez, R. (2008). A "gap gazing" fetish in mathematics education? Problematizing research on the
achievement gap. Journal for Research in Mathematics Education. 39(4), 357-364.
Gutiérrez, R. and Dixon-Román, E. (2011). Beyond gap gazing: How can thinking about
education comprehensively help us (re)envision mathematics education? In Atweh, B.,
Graven, M., Secada, W., and Valero, P. (eds.), Mapping equity and quality in
mathematics education, (pp. 21-34). New York: Springer.
Gutiérrez, R. & Gregson, S. (2013, April). Mathematics Teachers and Creative Insubordination:
Taking a Stand in High-Poverty Schools. Selected paper presented at the Annual Meeting of the
American Educational Research Association. San Francisco, California. April, 2013.
Gutiérrez, R. & Irving, S. (2012). Student centered learning: Latin@s, Blacks, and mathematics.
A white paper commissioned by the Nellie Mae Foundation. Boston: Nellie Mae.
Available at: http://www.studentsatthecenter.org/topics/latinoa-and-black-students-and-
mathematics
Gutiérrez, R., Irving, S., & Gerardo, J. M. (2013, April). Mathematics, Marginalized Youth, and
Creative Insubordination: A Model for Preparing Teachers to Reclaim the Profession. Selected
paper presented at the Annual Meeting of the American Educational Research Association. San
Francisco, California.
Helms, J.E. (1990). Black and white racial identity: Theory, research, and practice. New York:
Greenwood Press.
hooks, b. (2004). The will to change: Men, masculinity, and love. Washington, DC: Washington
Square Press.
hooks, b. (2012). Writing beyond race: Living theory and practice. New York: Routledge.
Hyland, N. E. (2000). Threatening discourse: Cultural and contextual challenges in constructing
antiracist narrative and action in one elementary school. Unpublished doctoral dissertation.
University of Illinois at Urbana-Champaign. Urbana, IL.
Ignatiev, N. (1995). How the Irish became white. New York: Routledge.
Joseph, G. G. (2011). The crest of the peacock: Non-European roots of mathematics. Princeton, NJ:
Princeton University Press.
López, I. H. (1997). White by law: The legal construction of race. New York: New York University
Press.
López, I. H. (2004). Racism on trial: The Chicago fight for justice. Cambridge: Harvard University
Press.
Lortie, D. (1970). School teacher: A sociological study. Chicago: University of Chicago Press.
Maffie, J. Weaving the Aztec cosmos: The metaphysics of the 5th era. Downloaded on March 17, 2012
from http://www.mexicolore.co.uk/aztecs/home/aztec--Uphilosophy
McIntyre, A. (1997). Making meaning of whiteness: Exploring racial identity with white teachers.
Albany: SUNY Press.
Peterson, D. (2015). Thinking outside the boxes: The changing face of the US Census. Downloaded on
March 5, 2015 from http://www.las.illinois.edu/alumni/magazine/articles/2015/census/
Pollack, M. (2005). Colormute: Race talk dilemmas in an American school. Princeton, NJ: Princeton
University Press.
Skiba, R. J., Michael, R. S., Nardo, A. C., & Peterson, R. L. (2002). The color of discipline: Sources of
racial and gender proportionality in school punishment. The Urban Review, 34(4), 317-342.
Varenne, H., E. W. Gordon, and L. Lin. (2009). Theoretical perspectives on comprehensive education:
The way forward: Vol. 2. Perspectives on comprehensive education series. Lewiston: The
Edwin Mellen Press.
Volmink, J. (1994). Mathematics by all. In S. Lerman (Ed.), Cultural perspectives on the
mathematics classroom (pp. 51–67). Dordrecht, The Netherlands: Kluwer Academic.
Wager, A. A. & Stinson, D. W. (2012). Teaching mathematics for social justice: Conversations with
educators. Reston, VA: National Council of Teachers of Mathematics.
Walkerdine, V. (1994). Reasoning in a postmodern age. In P. Ernest (Ed.), Mathematics, education
and philosophy: An international perspective (pp. 61-75). Bristol, PA: Falmer.
Walshaw, M. (2004). Mathematics education within the postmodern. Greenwich, CT: Information
Age.
Warburton, T. T. (2014). Discourses influencing the teacher identity of secondary pre-service
mathematics teachers. Dissertation proposal. University of Utah. Salt Lake City, Utah.
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