Talking about race, class, gender, sexual orientation – stuff like that – in relation to math class feels like tricky territory. Race, class, gender, sexual orientation, language, physical ability, religion — they shouldn’t matter for student achievement. Does focusing on social identities in thinking about math class help or hurt students who are outside of the mainstream?
I think it’s really important to be aware of and responsive to students’ outside-of-math-class cultures and experiences. Here’s why. I want all my students to work as mathematicians in my class. I believe that all students have a playground in their brain for shapes and quantities, that all students can wonder, observe, conjecture, explore, refine, reason, explain… And I also believe that all my students are pretty novice about these things. I have to be able to listen to them and hear them as mathematical thinkers, even when their expressions are very, very novice — and therefore different from what I’m used to hearing.
Students’ outside-of-math-class experiences change the “accent” in which they speak math. Not necessarily their actual accent (though some of our students have accents or speak math in a different language than we do!) but more the way they think and express their thinking.
We don’t realize we all have accents. We think of people with accents that are strongly different than our own as being “weird” “different” “cool” “special” — and rarely think of ourselves as being people with accents (unless we have an accent that’s different from the people around us so it gets pointed out to us a lot).
I have a hard time recognizing my students doing math and being mathematicians when I am distracted by their “accent,” and I’m more distracted by it the more different it is from how I conjecture about, reason about, and explain quantities and shapes. In fact, I don’t always realize I have an accent — I believe I’m fluent in math and speak the universal language of math. Which makes what my students are saying and thinking sound “weird” “special” and even wrong.
Here are some concrete examples that I’ve read about or experienced:
- Dealing with uncertainty and the issue of right/wrong — different cultures, and in the US, different economic classes, have different ways of thinking about uncertainty, especially when it comes to uncertainty in school. In some cultures (for example, the latte-sipping liberal elite!) school is a place to learn to argue, to poke holes in accepted ideas, to get troubled and cause trouble. In other cultures school is a place to learn the right way to behave, talk, etc. School is your ticket into proper society… so encountering uncertainty, challenging authority, poking holes, etc. is bad news. This doesn’t mean that students whose cultures relate differently to authority and knowing should be told what to do and made to just memorize procedures… but it does mean that they’ll engage differently with the challenge of checking on their own whether a solution is correct, that they will need explicit coaching & parameters around times that they are debating the relative merits of different arguments when there is a teacher in the room who could be the voice of correctness but is choosing not to be.
- Written vs. oral communication — like everything, there is as much variation among individuals of the same “culture” as there is between cultures on this… but… that said: the role of writing vs. talking is different in different cultures. In some cultures the word on the page has a different kind of authority than the spoken word. In some cultures reading and writing is more of a communal, oral exercise where people talk about what they’re reading or writing as they read and write it. In some cultures girls are brought up to be more reserved, to not blurt — and so they may find it easier to use writing to marshall their thoughts before speaking. In some cultures, you talk things out before you put anything down on paper. So a “think-pair-share” task where students write silently and then share orally may go awesome in one classroom and bomb in another, because the students in the other classroom would have to “talk-think-write” to be successful on the same task.
- Consensus building & arguments — this one I’m more out on a limb about. I don’t know the research and have only read anecdotes but… it seems to me like one thing that happens in math class is there’s a tension between knowing things because you’ve deduced them through rigorous logic, knowing things because you have faith in the person telling them to you, and knowing things because they seem right inductively. Back in the Dolciani days, in theory everything was deduced through rigorous logic, and in practice a lot was taken on faith from the teacher. Student-led investigations these days in theory begin with intuition and inductive reasoning (wow, in all these examples, making a triangle just knowing the side lengths guaranteed that my triangle was exactly the same as yours) and end with rigorous deduction (that will always be true because I can prove there will always be a rigid transformation that maps the three sides onto their corresponding sides and since rigid transformations preserve shape and angle measure, all the corresponding parts will be the same). In practice, I think a fair number of investigations build up students intuition and inductive reasoning, but then the conclusion that this always works is taken on faith again. And it seems to me that there’s a cultural piece at work here. What is the way to win an argument in students’ out-of-math culture? Convincing others? How? By logic? By coercion? By force of personality? By showing lots of examples? By offering counter-arguments? Which is more important — being right or everyone agreeing? If students’ out-of-school experience is that agreeing is important, and that it’s not polite to bring a counter-argument if everyone else agrees, then where does that leave them in math class? How do we honor their experience of argument and also help them participate in doing math, as mathematicians?
It’s so, so important to me to meet mathematicians and math teachers from many cultures, and hear them talk about their experiences with school mathematics, their children’s experiences in school mathematics, and their students’ experiences with school mathematics, to help me hear my own accent.
As a white, American, mostly East Coast, mostly male, mostly middle-class person, I am so used to argumentation and picking things apart and valuing logic and trying to see “why does that work?” and “will that always work?”, and doing that kind of argument everywhere from the dinner table to friends’ houses that when I don’t see those same “accents” in my students I think they aren’t mathematical. I don’t see my students’ use of different kinds of mathematical knowing as they use their spatial intuition (not my strength) and can just “see” why something works, let alone when they decide to agree on a conclusion that doesn’t follow deductively because it preserves the feelings of everyone in the group (even if some of them “know” it doesn’t work). I don’t hear the mathematics in my students’ accents so I don’t know how to support them to be accountable to the math even as they’re being accountable to their group, or accountable to their lived experience of the world.
So… if you have a different perspective about your students’ math, about your own mathematical habits of mind, if you come from a culture where school math is a little different, where arguments happen differently, where authority and rightness are interpreted differently… I want to talk to you at TMC14, and I want to talk to you explicitly about your background and experience and how it’s made a difference in your math classroom!