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.
Memory is the residue of thought.
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?
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?
Abstract ideas can be vague and hard to grasp. Moreover, human memory is designed to remember concrete information better than abstract information.
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.
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?