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Equity and Cognitive Science

Here’s something I’m curious about. There are two different areas of mathematics education that have interested me recently. The first might be called the equity perspective. Here’s Rochelle Gutiérrez in The Sociopolitical Turn in Mathematics Education:

I use the term sociopolitical turn to reference a growing body of researchers and practitioners who seek to foreground the political and to engage in the tensions that surround that work. The sociopolitical turn signals the shift in theoretical perspectives that see knowledge, power, and identity as interwoven and arising from (and constituted within) social discourses. Adopting such a stance means uncovering the taken-for-granted rules and ways of operating that privilege some individuals and exclude others. Those who have taken the sociopolitical turn seek not just to better understand mathematics education in all of its social forms but to transform mathematics education in ways that privilege more socially just practices.

The second is the cognitive science perspective, which has been shared widely by the Learning Scientists and Dan Willingham. I’ve learned a ton about memory, cognition, and learning, and I’ve found cognitive science useful in better understanding the teaching in my classroom and thinking about how I structure activities to be consistent with cognitive research.

Melvin Peralta wrote in the spring about the importance of bringing both of these perspectives into classroom practice. They each have important insights for educators. But beyond learning from both perspectives, I wonder if I can learn more by putting ideas from the cognitive and sociopolitical perspectives into dialogue with each other. Here’s a first attempt at doing that.

I.

Memory is the residue of thought.

Dan Willingham

What’d you learn in class today?
Don’t walk fast, don’t speak loud, keep your hands to yourself, keep your head down.
Keep your eyes on your own paper, if you don’t know the answer, fill in “C”.
Always wear earbuds when you ride the bus alone,
If you feel like someone’s following you, pretend you’re on the phone.
A teacher never fails, only you do.
Every state in America, the greatest lessons, are the ones you don’t remember learning.

Brave New Voices, slam poem by the Los Angeles Team

We remember what we think about, and we remember more when that thinking is spaced over time. This cognitive principle is often invoked as a structure for effective studying, or as an argument for spaced practice to review topics that have been previously taught. What if we instead ask the question: What are some ideas that our students are thinking about, day after day and year after year, that might help us better understand what they actually learn in school? The young women who wrote the slam poem above (which I highly recommend watching in its entirety) might argue that the lessons students think about most often and spaced most consistently over time are about obedience, silence, and power. They are thinking, “school is a place where my voice is not important,” and “following rules without questioning is the best way to make it through the day,” and “certain people get to be in charge and that’s just the way it is.” Are these the lessons we want young people to take from school?

II.

Our working memories can only hold so much, and when our working memories are overwhelmed learning is harder. This is John Sweller’s Cognitive Load Theory The theory is often used to argue that inquiry learning cannot work because problem solving overloads the working memory of novices who don’t have enough knowledge about the problems that are meant to lead to learning. Students lose the forest for the trees as they get stuck on the particulars of a specific problem and struggle to step back and see broader connections.

But math problems are not the only thing that can consume working memory. What if we look to understand student identity through this lens?

“I’m always ready for that lady’s class and she gets me suspended because she doesn’t know what she’s doing. She sees what she wants to see.” As we talked more, I mentioned that the teacher said she never had her books with her for class. She responded that a friend shares her books with her and lends her something to write with whenever she needs it. For her, that made it obvious that she was prepared to learn. She then mentioned that she was always on time for class. “I’m always at the door when that bell rings. I’m always there.” The student saw herself as prepared and on time, but the teacher did not see the student the way she saw herself.

The point here is not to debate whether the teacher or the student was right or wrong; there isn’t a clear answer to that question. What’s important to note is that the teacher in this scenario had rendered the student’s self-image as “prepared and on time” invisible.

-Christopher Emdin, For White Folks Who Teach in the Hood…and the Rest of Y’all Too, p. 19

I can’t count the number of times I’ve made a decision in the moment and made a student feel like they are invisible, invalidating their best intentions. What is that student thinking about in class after an interaction that threatens their identity as a learner? How can they learn when their working memory is consumed with thoughts of our interaction and the disconnect between our interpretations of their place in the classroom?

III.

Abstract ideas can be vague and hard to grasp. Moreover, human memory is designed to remember concrete information better than abstract information.

Yana Weinstein & Megan Smith

I want every student to have equal access to high-level mathematics, and also for every student to feel empowered to pursue future mathematics and feel a sense of agency in their education. But that agency is an abstract idea; if a student doesn’t see images of people who share their identity doing mathematics, do they have access to the concrete examples to feel empowered?

At the Equity & Math Education panel at PCMI last week, KiMi Wilson argued that we have a responsibility to find examples of professionals who use mathematics and represent the identities of marginalized students to come into math classrooms and talk to students. Short of that, Annie Perkins has assembled information on dozens of mathematicians from a range of identities and ideas on how to share diverse role models with students in empowering ways. Telling students that they can learn mathematics is unlikely to be successful on its own for many students; sharing concrete examples of mathematicians who share their identities is much more likely to help students understand that they can be mathematicians as well.

IV.

I wonder if pursuing connections between these bodies of work is worthwhile. I’ve learned a ton from cognitive science, but I think it can also seem like a discipline that is distant from the realities of classrooms and students, providing recommendations that treat all students and all contexts the same. Can applying cognitive science to questions of equity help to bring more nuance to applications of cognitive science research? At the same time, perspectives on equity are often dismissed as “soft” or as distractions from the most important parts of teaching and learning. Can a dialogue between equity and cognitive science help to surface the importance of multiple perspectives in education research?

Positioning Students as Competent

Two thoughts on competence, reflecting on time at PCMI. First:

We’ve been thinking about Lani Horn’s book Motivated, and talking about the idea of competence. I had been thinking of competence as a student’s need to feel successful in doing mathematics. If students don’t feel like they are successful in doing math they are unlikely to engage in unfamiliar or challenging problems, take risks by sharing ideas, or persevere when learning feels hard.

We spent some time with Peg Cagle, and Peg offered a different take. She described competence as a student’s need to recognize their success in doing mathematics. I see this as an important shift. While it’s just language, the word recognize makes an assumption — that all students bring meaningful mathematical ideas and mathematical thinking skills to class. My job as an educator is to create structures and space to help students recognize those competencies. Horn offers a partial list of mathematical competencies that teachers can value beyond what is traditionally valued in math class — fast and accurate computation. Those broader competencies are:

  • making astute connections
  • seeing and describing patterns
  • developing clear representations
  • being systematic
  • extending ideas

Peg shared this image from her classroom as well:

Screenshot 2018-07-11 at 6.29.08 AM.png

I’m sure other educators could expand on these. The point is that there are lots of ways for students to be mathematically competent. If my goal is for them to feel  competent, I might work to prop up their confidence or self-esteem without changing any structures in my classroom. If, instead, my goal is to help students recognize the ways they are mathematically competent, I am obligated to find ways to surface and highlight broader competencies that create avenues for every student to recognize their successes. Those are two very different classrooms; the second is much more responsive to the needs of particular students, and develops a much richer idea of what it means to do mathematics.

Second idea. In talking about competence yesterday, we also talked about the challenges of grades. What does it mean to value broader competencies like extending ideas when we are obligated to put a letter grade on a transcript at the end of the term? Those grades seem to be all many students care about. Do grades erase any work we do to assign competence in broader ways? I can’t realistically improve at more than one or two areas of my practice at a time. In the context of schools unwilling to change grading policies, would I be smart to put my effort somewhere else?

A Thought Experiment on Tracking

Lots of talk on tracking in the math world right now, and I’ve enjoyed following along with the comments on this recent NCTM President’s Message from Robert Berry and this blog post by Michael Pershan, as well as the conversation on Twitter (for instance, here).

In the comments linked above, many people make an argument along the lines of, “but what about the gifted/smart/advanced students?” Tracking is the status quo, and these are the students who many perceive would be affected by a change. They argue that ending tracking will reduce opportunity for a certain group of students, labeled as more able than others. They argue that these students will be less challenged, will love math less, and will struggle to be engaged in the typical heterogeneous class. For more detail, check out the comments and conversation in the links above — there are many compelling arguments, from the perspectives of educators, parents, and former students.

Here’s a thought experiment. What if, instead of a world where tracking is the norm and NCTM is advocating to end it, we imagine a world where there is no tracking, and someone is advocating to institute grouping students into classes by perceived ability? What might people say if heterogeneous classes were the status quo, and we argued to change that?

Here’s an argument I might make:

What about the students who won’t be selected for a higher track? They’ll be pushed into low-level classes taught by less qualified teachers, they’ll interpret tracking as a message that they are less “smart” (likely based on standardized tests), and they’ll be segregated based on those messages, undermining community as entire classes come to believe they’re not mathematically capable. Given the way that academic ability is currently assessed, tracking will create a system of de facto segregation based on race and class, exacerbating differential access to the type of education that young people need to be full citizens in their country. And as tracking spreads, opportunity will be hoarded by families who know how to manipulate the system and buy advantages for their children, whether through private tutoring or pressure on their schools. All of this will limit the mathematical trajectories of many students, often before they’ve hit puberty.

In this alternate world, where tracking is a change to the status quo, what would you advocate for to better support all students?

Deficit Thinking and Creative Insubordination

I’ve been on a bit of a kick recently writing about the difference between asset-oriented and deficit-oriented approaches to teaching, informed by ideas from Lani Horn and Javier Garcia. I’ve enjoyed trying to better understand what an asset orientation looks like in different contexts, and trying to train myself to better see my students’ potential. I wrote yesterday about how talking about the impact of students’ parents can be a form of deficit thinking, and Melvin Peralta offered this nugget on Twitter:

Melvin got me thinking — while I’ve spent a ton of time trying to figure out what an asset orientation looks like in practice and articulating the shifts I want to make in my teaching, I haven’t done much thinking about why teachers take deficit perspectives in the first place.

The answer seems obvious. Teachers work in schools that are designed in large part to rank and sort students, and follow traditions of reducing student thinking to a number on a piece of paper quantifying what they know and don’t know, the points students earned and the points they’ve lost. Teachers live in a culture that values competition over community, where success is often measured by the failure of someone else. Teachers attended school themselves, and in most cases were particularly successful at playing the game and earning points and distinctions to stand out from other students. And teachers often enter schools with a goal of supporting students toward a vision of success that reflects our own experiences. I know all of these things are true for me. They contribute to a mindset that listens for wrong answers and mistakes in order to fix them, labels students to explain their “underachievement,” and endlessly quantifies and sorts students rather than humanizing them.

I think my perspective on parents might be unhelpful. Holding teachers to a particular standard when the institutions we work in erode any successes seems hypocritical. But how can teachers respond to the imperfections of schools? Rochelle Gutierrez writes articulately about how we might approach this through a strategy of “Creative Insubordination” (page 58, here):

In choosing to use Creative Insubordination, we are refusing the status quo when it is not in the best interest of our students. This means questioning some of the typical norms in mathematics teaching and learning. An important step in this work is first deconstructing what is going on around us, making the “normal” seem abnormal. For example, do we notice that the students in our calculus classes do not represent the demographics of our school? Only then can we imagine and plan for a different possible future where that representation is present.

Teaching mathematics involves negotiating one’s practice with colleagues, parents, administrators, students, and at times, community members. Choosing to refuse the status quo is an important option for maintaining our sense of morals, especially given the fact that we will never please all of the aforementioned constituents at the same time. Having political clarity on why we are doing the things we do is important (Beauboeuf-Lafontant, 1999).

Gutierrez offers useful strategies in her piece for resisting structures that are harmful for students, but in many schools this kind of change seems hopeless, and teachers already feel unfairly maligned for failures of students that feel out of their control. I wonder what conditions might help teachers feel a sense of agency in their work in imperfect institutions, helping us do our best with the resources we have while also staying optimistic in our ability to make change for future students.

Parents

I often hear educators ascribe student behaviors, almost always negative ones, to the student’s parents. “He’s gonna keep acting that way if his parents don’t stop coddling him.” “She talks like that because she’s copying her mother.” I have two core beliefs that guide my thinking around parents:

  1. I’m not a parent, and I have no right to judge a parent or assume I know how to raise a child better than they do. I don’t understand how hard it is and I don’t understand the particular experiences that influence parenting decisions. Even if I were a parent, I would conjecture that the idiosyncrasies of individual children over years would leave me little basis to judge another parent.
  2. It’s easy to blame behavior on parenting, but reflecting on students I’ve known, I’ve known incredible students who seem (from my perspective) to have subpar parents, and I’ve known students who have struggled enormously who seem to have loving, caring, and hardworking parents. I’m unlikely to know the exact causes of an individual student’s behavior, and blaming parents is at best an oversimplification and at worst an excuse not to help a student who needs more support.

I don’t meant to minimize the impact of abuse and neglect; educators have a serious responsibility to report these things and their impacts are tragic. Instead, I’m interested in the everyday conversations where educators ascribe behaviors to parenting decisions or personalities or the home environment. I see this as a type of deficit thinking. Students have no control over the family they are raised by, and I have never heard an educator say, “this student is struggling because of bad parenting, and knowing that helps us intervene in more helpful ways.” Blaming parents is a red herring; it’s a distraction from figuring out how to actually help every student succeed. My argument is not that parenting is meaningless; I have enormous respect for the hard work families do and I’m sure parenting does influence that person a child becomes. But from the perspective of a school and in the context of a classroom, teachers are far more likely to blame “bad” parents than praise “good” ones, and I see this blame as an excuse and a distraction from creating spaces where we work to learn how every student can reach their potential.

Metacognition and Identity

I want my students to learn metacognition while solving a problem or reasoning about a concept. For me, this means students can work toward a solution and simultaneously step back to make connections with other ideas, monitor their strategies, and decide whether their answers make sense.

Lani Horn writes in Motivated:

The cultural power of mathematical smartness makes math class a minefield of social risk. For example, students often fear that any visible signs of struggle not only implicate their precarious understanding of the topic at hand but also compromise their general sense of competence. In this way, a single mistake can be (wrongly) interpreted as a sign of general intellectual weakness. The high stakes attached to mistakes bring together the psychological and social dimensions of competence: in the cost-benefit analysis of social risk, nothing seems more costly than a highly public error and the resulting judgment from one’s teachers and peers (p. 60).

One important element of metacognition is a willingness to recognize and learn from mistakes, but many (most?) students experience school as a place to avoid failure, rather than to learn from it. Here is an observation from John Holt in How Children Fail on the strategies students use to minimize the consequences of failure:

Kids are expert at finding such strategies. They can always find ways to hedge, to cover their bets. Not long ago, in room period, we were working with a balance beam. A wooden arm or beam is marked off at regular intervals and balanced on a pivot at its midpoint. The beam can be locked in a balanced position with a peg. We put a weight at a chosen point on one side of the beam, then give the student another weight, perhaps the same, perhaps heavier, perhaps lighter, which he is to place on the other side of the beam so that, when the beam is unlocked, it will stay in the balanced position. When a student has placed the weight, the other members of his group say, in turn, whether they think the beam will balance or not.

One day it was Emily’s turn to place the weight. After much thought, she placed it wrongly. One by one, the members of the “group” said that they thought it would not balance. As each one spoke, she had less and less confidence in her choice. Finally, when they had all spoken and she had to unlock the beam, she looked around and said brightly, “I don’t think it’s going to balance either, personally.” Written words cannot convey the tone of her voice: she had completely dissociated herself from that foolish person (whoever it was) who had placed the weight on such a ridiculous spot. When she pulled the peg and the beam swung wildly, she almost seemed to feel vindicated (p. 14).

Most interactions in class do not illustrate so clearly an unwillingness to think metacognitively, but I would conjecture this happens all the time in my classroom. I have often thought of metacognition as a skill; if I tell students to be metacognitive, ask them questions requiring them to practice components of metacognition, and explain to them the importance of monitoring their own thinking, they will come to think metacognitively on their own. I think this misses an important piece. Many students arrive to math class without a sense of competence, feeling tenuous in their position and without a strong identity as capable mathematics learners. Identity is the foundation; without a belief in their ability to be competent in math class, students are likely to experience fear and defensiveness that prevents any possibility of metacognition. The experience of years in schools can actually help students gain skills that operate in the opposite direction; strategies to avoid thinking, to avoid feeling stupid, to avoid taking risks, and to foreclose any opportunities to think about their own thinking.

I wonder what structures might both minimize the counterproductive strategies students develop, while also helping students to feel like they can learn from mistakes in math class and feel that they can be their authentic selves and use those experiences to become stronger mathematicians.

Here’s another observation from John Holt, during a lesson on categorizing words as nouns, verbs, and adjectives:

The teacher, whose specialty, by the way, was English, had told these children that a verb is a word of action–which is not always true. One of the words she asked was “dream.” She was thinking of the noun, and apparently did not remember that “dream” can as easily be a verb. One little boy, making a pure guess, said it was a verb. Here the teacher, to be helpful, contributed one of those “explanations” that are so much more hindrance than help. She said, “But a verb has to have action; can you give me a sentence, using ‘dream,’ that has action?” The child thought a bit, and said, “I had a dream about the Trojan War.” Now it’s pretty hard to get much more action than that. But the teacher told him he was wrong, and he sat silent, with an utterly baffled and frightened expression on his face. She was so busy thinking about what she wanted him to say, she was so obsessed with that right answer hidden in her mind, that she could not think about what he was really saying and thinking, could not see that his reasoning was logical and correct, and that the mistake was not his but hers (p. 16).

Stepping back from student metacognition for a moment, I wonder how often I do things like this, letting my predetermined ideas of “right” and “wrong” dictate a lesson rather than student thinking. I also wonder the extent to which I hold an identity as a learner of teaching; to what extent am I able to see my mistakes and learn from them? Metacognition is for teachers too; how can I create that commitment for myself?

Seeing Brilliance

Since watching Danny Bernard Martin’s NCTM session, “Taking a Knee in Mathematics Education,” I have been reflecting on my role as a white educator. The first school I worked at, the vast majority of my students were people of color. My current school is majority white. Yet in both contexts, I can only ignore race in the classroom to the detriment of students of color. This piece is my best attempt to reconcile my role as a white educator of students of color with the realities of race in America. 

I. Intention

I recently read Killers of the Flower Moon: The Osage Murders and the Birth of the FBI. While the events took place nearly a century ago, I found the narrative of Killers of the Flower Moon to echo the broader narrative of race in America in ways I hope I can learn from.

The Osage Nation were one of many indigenous peoples forcibly removed from their homelands to less desirable territory in Oklahoma. The Osage, however, had the good fortune of discovering large oil reserves on the land they were moved to. Profits from the sale of mineral leases were distributed to the Osage in the form of “headrights” that were passed down through families, and annual income from an individual headright was in the thousands of dollars for several decades, peaking above $13,000 (more than $100,000 in today’s economy). Then, in the 1920s, murders and suspicious deaths of Osage rapidly increased. The book focuses on the family of Osage Mollie Burkhart; Mollie loses her mother, two sisters, brother-in-law, and cousin in quick succession, and was being poisoned herself. J. Edgar Hoover’s Bureau of Investigation, which later became the FBI, began an investigation into the murders. The FBI discovered the Ernest Burkhart, Mollie’s husband and a white man, and his uncle William Hale, had orchestrated a plot to funnel headrights in the family to Mollie before killing her and inheriting them all together. Ernest Burkhart and William Hale were each convicted for their role in the murders.

This is a terrible story of white greed and the plunder of wealth from people of color. But the story didn’t end there, and the next turn was what really stuck with me.

The Osage were considered wards of the federal government, and were not considered competent to make their own decisions with the money they made from mineral leases on their land. Each Osage had a white “guardian” to manage their finances and approve any financial decisions they made. This led to graft and corruption in the community — white guardians and lawyers to administer the guardianships profited enormously off of the Osage, but the corruption did not end there. The period during the murders of Mollie Burkhart’s family was called the “Reign of Terror.” Ernest Burkhart and William Hale’s trials made the national news, and the convictions helped to establish J. Edgar Hoover’s fledgling Bureau of Investigation as a permanent American institution. Yet dozens more Osage died mysteriously during that time, and the vast majority of those murders were never investigated. The murders began years before Mollie Burkhart’s family was targeted, and continued for a decade after. In many cases, white men would establish guardianships over as many as a dozen Osage, and many of these Osage died mysteriously, in some cases almost all of the individuals whose finances were controlled by a single guardian. Bodies went missing and autopsies were skipped, as the same white doctors and white-owned funeral company always seemed to be there to explain away the deaths.

What was originally labeled a conspiracy seemed actually to be common practice, and the FBI investigation seemed a token gesture, a way of getting national attention to an ambitious bureaucrat trying to consolidate his own power rather than justice for the Osage.

Killers of the Flower Moon is a grim portrait of the ways that white people have hoarded wealth and power in America. But more than that, it was a reminder of exactly how that plunder happens. Some media narratives might portray racism as the actions of a few bad apples, or the result of societal norms that have since been changed. Killers of the Flower Moon reveals that the racism that might have seemed horrific and unusual was actually routine and accepted. And when an oppressed people asked for justice, they learned that justice was a chess piece in a white person’s game, rather than a sincere effort to right the plunder of people of color.

I believe that this narrative is at the heart of what has made America. Ta-Nehisi Coates has documented this same intentional plunder through discriminatory housing policy and practice, as policies at the federal, state, and local level prevent Black families from accumulating wealth through home ownership while creating system to do the opposite for white families. Nikole Hannah-Jones has documented the intention behind the continued segregation and hoarding of resources in our school system, as white families work to keep their children separate from children of color. This intention continues today. To grapple with racism in America is to acknowledge that racism is not a product of the past or an unfortunate accident of history or the result of the actions of a few. Racism is a system designed and perpetuated to strip wealth and dignity from those who are not in power. It is intentional, it is ubiquitous, and most importantly it has been intentionally hidden from the eyes and minds of white people.

Many white people get uncomfortable talking about racism. I know I do. We are likely to claim that we have nothing to do with racism, to play down the impacts we have not worked to understand, and to frame racism as a past that we need to move forward from. I believe that, to come to terms with being white in America, and to come to terms with being a white educator of students of color, I need to name that racism exists because of the intentions and actions of white people, over centuries and continuing today.

II. Action

The first thing I need to understand is that racism is not an accident of history or an isolated consequence of some anonymous “bad people.” But once I see the impact of racism on my students and the ways that we have been socialized to accept inequities in education, my fist instinct is to say, “well what can I do to change it?” That’s the second thing I need to understand — that there is no simple “action step” or easy change I can make in my classroom to solve racism. In fact, the instinct to want a concrete action step that helps me feel better about the realities of race in classrooms is another way that whiteness asserts itself and prevents the dialogue from moving forward. Here is Danny Martin in a 2009 paper:

A fourth way that race and racialized inequality is resisted, particularly in the context of mathematics teaching and learning, is through what I call solution on demand. I have witnessed this on several occasions and often experience it when I am asked to speak with teachers and administrators regarding mathematics achievement and persistence among African American students. Despite my insistence on the complexity of these issues, I am inevitably asked some version of the following: “What you have said is fine, but tell me, specifically, what I should do today when I go back to my school or classroom to work more successfully with African students?” In most cases, this is a sincere request. However, because these audiences are initially unaware of the degree to which I foreground race in my research, demanding an immediate and simple solution once they discover this can also be seen as a strategy used to hastily get past race and racism. Such a demand not only trivializes the complexities of race, racism, and racialization but also the experiences of those affected. In essence, it is a way to retreat from race and resists the realities of racism by reducing the harms to simple problems with simple solutions. My hesitancy to provide a specific answers is not meant to suggest that no solutions exist. But top-down, externally generated solutions that are not responsive to the needs and conditions of the context in question are unlikely to have a meaningful effect.

And in the question-and-answer portion of his recent NCTM talk, when asked a question along these lines, Danny Martin responded:

Step number 1, step 0 even, would be to hear me, first of all, to just hear me, open ears, open heart, let it soak in, it may not be today it may be tomorrow it may be a week from now, it may be a month from then but hear me. What am I saying, why am I saying it? I think that’s step 1, what sense are you making of it. Follow up, if you have questions about something I said, certainly ask for clarification so we can begin a conversation. In terms of the pragmatics of what do I do when I go back to work: obviously I can’t tell any particular person what they should do because I don’t know the context, I don’t know the children, I don’t want to essentialize whiteness or white people, black people, blackness. But maybe step 1 after step 0 is sort of the internal work, the self-reflective work. One simple question is if you go back into a classroom with black children in it, you have to ask yourself, “why am I here? Why am I here?”

Insisting on action can be a tool of the oppressor. I know I’ve walked out of equity-oriented sessions at conferences and heard well-meaning white folks say, or said myself, “I just don’t know what she wants me to do about this…” or “that was interesting, but I wish he gave us an action step.” I was in a local meeting filled mostly with white people talking about immigration, not long after Donald Trump was elected. The room was really excited about action — setting up sanctuary locations, asking the local Latinx community how we can help, and more. One woman at that meeting shared the perspective that it’s not always the job of white folks to jump in and try to fix things. We need space for the humble work as well. Maybe what the local community needs is not for us to jump into action, but to be willing to show up and peel potatoes so that those who have been marginalized can do their work.

That internal work is me peeling potatoes. I do hope that I can hear this reality and make change, but at the same time there is an important space to go slow and work to really hear what is being said and reflect on my role and my position, in the past and in the future.

III. Tension

Acting and not acting are both actions; nothing is neutral

-Imani Goffney

There’s a fundamental tension here. I need to resist the instinct for neat and tidy action steps, yet at the same time inaction is a choice that can influence my students as easily as action. And these actions or inactions are bound up in the everyday acts of teaching — while I’m doing this internal work, I still have students in my classroom. Here is Deborah Ball, unpacking a few moments of an interaction between black girls Toni and Aniyah, stepping back to consider the context the two girls live in and the subtleties of the decisions teachers make in the moment. In the moment Ball is considering, Aniyah shared her thinking on a problem with the class, and Toni laughed and asked why she chose the answer she did. Ball is considering how to respond.

So we know from this report that came out last year, Girlhood Interrupted: The Erasure of Black Girls’ Childhood, that discipline is disproportionately inflicted upon black girls, and here you can see for example that while black girls account for less than one in six girls in school they comprise over half of the multiple suspensions whereas white girls are half of the girls in schools and suffer only one-fifth of the multiple suspensions, and there’s more detail there [on a slide]. So how does that happen, how does that actually happen? Let’s try to think about that. So in the report what we understand is that these are for subjective judgments. These are for not visible actions, these are things that teachers have to interpret, like deciding that someone is disruptive or deciding that someone might be bullying , and you can imagine that Toni might be read by a teacher as bullying Aniyah, or that she might be read as disruptive, or somehow not attentive or not engaged. So it’s not that hard to imagine how Toni could easily be asked to step away from the group, to not talk, or maybe even be sent out in the hall and if she’s out in the hall she isn’t even learning, she’s also been told that she’s not valuable, and the rest of the class doesn’t benefit from her work. This is serious, and these are all I want to emphasize in the discretion of the teacher. These are not about bringing a gun to school, these are about how she’s being read and interpreted. So let’s think about what it would take to disrupt the patterns that fill the discretionary spaces that make it likely a black girl like Toni is marginalized.

Part of Ball’s answer in this situation is to take as axiomatic the brilliance of black girls — to enter the interaction as a teacher assuming that these two girls are brilliant, that their contributions have value, and responding in ways that work both to humanize the students and to draw out what they have to offer the class.

This leads me to another tension. I need to look at all students as brilliant and see my role as drawing out that brilliance, yet at the same time know the societal context that the students are coming from, and know that we are swimming upstream against forces that are working intentionally to prevent that brilliance from coming to light. This is why I need to be conscious of the context from which students of color, among other marginalized groups, enter my classroom. I want to look at all students as brilliant, and create a space where every student can be brilliant in my class. I need to double down on my belief in the brilliance of students of color specifically because of the forces working to keep that brilliance from surfacing.

If we expect to prepare both students and future teachers for a more participatory democracy, a focus on tensions in teaching from an equity stance is one place to start.

This quote from a paper by Rochelle Gutierrez is one I keep coming back to. Embracing these tensions is my answer to the question of action. My goal is not to come up with a neat and tidy action step to address the racism outside of and within my classroom. Instead, my goal is to create a space where I can embrace the inherent tensions in this equity stance, and use those tensions as opportunities to continue to learn from interactions in my classroom.

Gutierrez writes elsewhere about “The Mirror Test.” If I look in the mirror and ask myself if I am doing what I set out to do in teaching, what would I say? I want to practice the central value of surfacing the brilliance in every student, and working to be aware of the forces that seek to undermine that brilliance for certain students. And I want to practice that value by seeking out tensions inherent in teaching from an equity stance that don’t have easy answers, and that I need to navigate to actualize the brilliance of every student.

There’s no neat list of those tensions either, but here are two that are on my mind right now:

  • Students arrive to my class with different levels of preparation. I have to work every day to hold every student to high expectations and know that they can engage in cognitively demanding mathematics, yet also put in place supports and scaffolds to build a bridge from where students are to where I want them to go. And, despite the brilliance of my students, in some cases I need to put a lot of work into building that bridge and helping them reach ambitious goals.
  • I have an obligation to teach certain standards, and in many ways helping students reach the standards of the education system as it exists will empower them with the agency to see their own brilliance in the future. At the same time, the education system is not designed to draw out the brilliance of every student; it is designed to sort and rank and bestow distinction on some at the expense of others. I need to work within a broken system, while also working to give students the knowledge and tools to dismantle it.

One essential piece of looking at equity through the lens of tension is humility. It means stepping back from my goal of being the best teacher for every student and acknowledging that I don’t have the skills or the knowledge to do that right now. It means being willing to embrace the tensions in coming up short, and looking at my lessons as a work in progress and seizing on shortcomings as an opportunity to learn from my students’ perspectives and get a little better next time. Recognizing these tensions is my version of peeling potatoes, it’s my internal work, it’s my process of education to make better decisions in those discretionary spaces where action or inaction can uphold or disrupt oppression.

I don’t have a neat and tidy ending for this piece either. I am a work in progress. But in order to make progress as a white teacher in America, I see these three pieces as central. Recognizing the intention behind racism and plunder, knowing that my instinct for action is often unproductive, and being willing to do my internal work, recognizing the inherent tensions in teaching toward equity.