I still think sometimes about the ideas behind this old post of mine. I was wondering which distribution I should strive for in my teaching:
I’m still not sure I have a clear answer. But another layer I’m thinking about is how a linear measure of “student learning” oversimplifies how I want to support students. Content knowledge is one thing, but students who have struggled in math class in the past often have negative beliefs about themselves and about their learning. Those beliefs do a lot to undermine learning in the long term. If students show up to class believing that they’re bad at math and math class is pointless they’re likely to continue having a hard time.
One distribution to think about is which students learn the most — is it the students who have done well in math classes in the past, or students who have had a hard time? A second distribution is how I influence student beliefs and dispositions about their own learning. This is an area where I want to prioritize students who have struggled in the past.
I can try to facilitate those beliefs a few different ways. One is having a constant barometer of how successful students feel. If students feel like they are constantly getting things wrong they are likely to internalize that as a part of their identity in math class. If I can start class with tasks that are accessible to every student and scaffold success in challenging work I can help more students to develop positive beliefs. I want to have a barometer on success for all students but pay particular attention to students whose beliefs I want to influence the most.
A second strategy is assigning competence. When I ask a student to share a great idea or a new connection I am publicly signaling that student’s competence. It’s often only a few high-achieving students in a class who regularly have their ideas highlighted. I can keep a special eye out for high-quality work from students who often struggle. It’s important not to tokenize or compromise; students can see through me when I’m celebrating someone without good reason. But when students do great work I want to celebrate it, and I want to prioritize celebrating students who I know often struggle.
I’d love to think more about other dimensions of what I hope students take away from my class. It’s easy to generalize about a group of students — “they learned this” or “they didn’t learn that” — but there’s a wide range elided by those statements. I want to get better at thinking about and acting on that complexity in ways that support all students.