Wednesday, June 9, 2021

Anti-Racist Math Instruction

This pamphlet, titled A Pathway to Equitable Math Instruction/Dismantling Racism in Mathematics Instruction, is the weirdest thing I have read this year.

It contains, on the one hand, a lot of good advice about teaching. For example, one section asks teachers to consider how they were taught math and not just to replicate it, but to think seriously about what was good and what was bad and ask whether their students might need a different approach.

Another section encourages constant interaction with the students to find out how they are progressing. Which is great. 

But here is the weird part: this is framed in terms of dismantling systematic racism and avoiding "powerhoarding," which is a characteristic of white supremacy. Apparently asking your students every day how well you taught is a way to fight white supremacy. Like this:

White supremacy culture shows up in math classrooms when...
Students are tracked (into courses/pathways and within the classroom).

Provide students with opportunities to give feedback to teachers about the classroom and instruction.

• Verbal Example: Fist to five, How well do you understand what we talked about today? Fist to five, How well did I teach this today?

• Classroom Activity: Exit tickets or surveys that ask students to identify how well teachers taught, what helped them learn, what got in the way of their learning, etc.

My daughter had to tell me what "fist to five" means – turns out this is asking someone to give you a rating from zero to five by holding up fingers – but otherwise what we are doing here is to take a perfectly standard problem in pedagogy, how to figure out how your students are doing and respond to that, and insist that it is really about racism and antiracism.

I discovered this pamphlet because David Brooks mocked it for talking up ethnomathematics, a concept he finds absurd. The word "ethnomathematics" is used these days in two different, mutually exclusive senses. First, it means the mathematics of non-western peoples, like the Aztecs or the ancient Egyptians. The pamphlet makes only a small nod in that direction, asking teachers to let students know that cultures around the world have math. Fine. Second, it means making mathematics relevant to people who live in barrios or tough urban neighborhoods or any other non-white, non-suburban community. Our pamphlet thinks this is very important. But, and this is the thing I want to write about, the vision of what this might mean is wrapped up with old arguments about math instruction in ways that simply make no sense to me.

An entirely typical section goes like this:

White supremacy culture shows up in math classrooms when...
Independent practice is valued over teamwork or collaboration.

While there is some value in students being able to complete work independently, when this is the only or most common avenue for learning or practicing, it reinforces individualism and the notion that I’m the only one. This does not give value to collectivism and community understanding, and fosters conditions for competition and individual success, which perpetuates the idea that if a student is failing it is because they are not trying hard enough or that they don’t care.
Co-construct knowledge in the classroom.

• Verbal Example: Let’s get into partners and do a thinkpair-share. We will incorporate everyone’s ideas and try to synthesize them.

• Classroom Activity: Have students create mathematical definitions in their own words in groups, and bring the groups together to coconstruct mathematical definitions as a class.

My response to this is that educators have been debating the relative merits of group vs. individual learning for 2500 years, give or take a few centuries. Why is individual learning racist, group learning anti-racist? It has become an article of belief in certain circles that white culture is individualistic, while African American and Hispanic culture places more emphasis on the community, and here we see that translated into classroom strategy. But does that really make any sense?

Personally I hated all group activities in school, which probably explains why I ended up such a monster.

Here's another interesting section:

White supremacy culture shows up in math classrooms when...
There is a greater focus on getting the "right" answer than understanding concepts and reasoning.

Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict. Some math problems may have more than one right answer and some may not have a solution at all, depending on the content and the context. And when the focus is only on getting the right answer, the complexity.

How much attention math teachers should pay to getting the right answer vs. understanding the method is also an ancient argument. Math reformers have been trying over my whole lifetime to shift the focus from getting relatively simple answers correct to understanding mathematics on a deeper level. They have mostly failed. This has many causes, of which the two most important are that most US math teachers are not very good at teaching a deep conceptual understanding of math, and that students don't give a damn.

What does any of this have to do with racism and anti-racism?

White supremacy culture shows up in math classrooms when...
Rigor is expressed only in difficulty.

Too often in math, we limit the definition of rigor to difficulty, rather than its full complexity including thoroughness; exhaustiveness; interdisciplinary; and balancing conceptual understanding, procedural skills and fluency, and application. This allows math teachers to shy away from complex problems and tasks and instead streamline teaching like we are spoon-feeding, in fear that students can’t do the work—and reinforcing right to comfort and quantity over quality. This discomfort with emotion and feelings (quantity over quality) leads to the sentiment “Math makes people feel stupid and it hurts to feel stupid,” and rather than addressing the implications behind that statement, we instead make the content easier so that students are more likely to understand. This is highly problematic because it assumes that students can’t rather than giving them the opportunity to engage with rigorous mathematics.

Start with more complex math problems and scaffold as necessary.

Verbal Example: If we wanted to build a rocket, what are all the things we might need to know before we get started? Along the way, we decided that we want the rocket to reach the moon. What do we need to consider now?

Classroom Activity: When solving equations, start with the most complex problem, generate ideas for how to solve it, and use the simpler equations as examples to support those ideas.
I studied math past calculus, and I have been a teacher for 30 years, and I am not at all sure what any of this means or what it would look like in practice.

But this is my favorite section:

How do I dismantle power structures in the classroom?

White supremacy culture shows up in math classrooms when...
Participation structures reinforce dominant ways of being.

Classrooms are often microcosms of the world around us and reinforce dominant (or white) ways of being. For example, small groups of students receive the teacher’s attention throughout instruction and a few students are typically called on to participate in class discussions, reinforcing notions of perfectionism. The patterns of students who fall into those categories often mirror societal norms. Another common participation structure is pairing students as helper and helpee. This reinforces paternalism and other power structures that identify students as either being good or bad at math (also either/or thinking). Also, requiring students to raise their hand before speaking can reinforce paternalism and powerhoarding, in addition to breaking the process of thinking, learning, and communicating. Create multiple ways of participating that honor myriad ways of thinking and being.

• Verbal Example: For this section, feel free to work alone, in pairs, trios, or quads (let them choose).

• Classroom Activity: Community circles or storytelling circles, incorporating dance, music, song, call and response, and other cultural ways of communicating.

Sure, storytelling circles, whatever. 

What if the kids all divide into groups in a way that leaves the class geek without any partner at all? If the teacher intervenes and forces him into a group, is that powerhoarding?

But here's the real question: why are we forcing students to study math at all? Did anybody ask the students if they wanted to study math? What if we did, and they said no? Wouldn't forcing them to take math anyway be powerhoarding? 

The assumptions behind this pamphlet – that education is important, schools are good, everyone should understand math, that we want minorities to be equally represented in STEM fields –are the assumptions of western, middle class society. They are the values of bourgeois discipline that have I have been writing about. In the terms of this pamphlet's authors, they are white supremacy. I think that is entirely the wrong framing, since there are millions of white people who hate all this as much as anyone with brown skin does. But in their terms, insisting that students learn math is exactly the thing they are protesting against.

On the one hand, our authors want minority students to get the best math instruction they can, and they seem to think (though they never say this) that right now many minority students do poorly in math because of bad instruction from racist teachers who don't care. I am entirely on board with that; let's have good teachers who care. But, their idea of good math instruction is not in any way neutral. It embraces several educational theories that are all controversial: that group exercises are better than individual learning, that it is better to understand math concepts than to get the problem "right," etc. They do not bother to defend their views except by saying that they are antiracist, and the other side racist. They offer absolutely no reason whatsoever why we should believe that. Nor do they offer any evidence that minority students taught this way do better, and it is not clear how they would, since they think standardized tests are white supremacy.

And to get back my main point: as a critique of western, bourgeois society – what they call white supremacy – this fails utterly because it is based in the most fundamental way on the exact assumptions of the society they want to critique.


David said...

This is a very interesting essay. On a very broad level, it's another indication of the gulf between leftists/the woke and centrist liberals. Centrist liberals are very much wedded to bourgeois discipline, social order, and the ideal of up and out of poverty for everyone (whereas the left/woke want to preserve that communitarian buzz they perceive in poor non-white communities). At the same time, even the left/woke are ambivalent about how much they want to challenge bourgeois discipline; the logic of their positions might indicate doing away with school altogether, as you seem to suggest, but only the hardest of the hard left are prepared to embrace that sort of thing (and, on that level, the hard left and the hard right have more in common with each other than either has with the center--as has been pointed out many times, here and elsewhere).

David said...

I will say also that I share John's dislike of group work. One of my main complaints about contemporary teaching is the overemphasis, as I see it, on group work, breakout rooms on zoom, and so on. I never give group assignments, and I discourage students from working together. I want them to develop their individual capacities to read, think, understand, and comment. To me, there's nothing like struggling alone through a difficult text. I'm not much of a "lean in" meritocrat or high achiever, but I've never been into that almost oceanic (or even Borg-like) collectivism that some people admire and enjoy. Then again, I've never been into group membership and group rituals either.

szopen said...

This reminds me the old joke about how one geezer in early 90s wanted to learn about hacking, so he borrowed the only available books in library about computers, translated from Russian, and so he learned a lot about Lenin.