“We do not learn from experience… we learn from reflecting on experience.”
My teaching has come to focus more and more on purposeful practice — kids doing math, thinking deliberately about how the math they are doing connects to broader mathematical ideas, and getting feedback on that thinking.
But when I think back to my teachers who made a meaningful impact on me, I don’t think of teachers who did a great job structuring everyday practice in class. Maybe that’s a paradigm that’s worth changing. I would love my students to look back on my class as one where they both learned a ton of math, and learned about how their brain learns math best.
But my favorite teachers were those who inspired me to continue learning, to challenge myself, to see what I was capable of and push my boundaries. That seems like a slightly different goal than building students’ knowledge of mathematics.
John Dewey said that we learn from reflecting on experience. Kids learn math in my class when they spend that time doing math and reflecting on the math they are doing. But what if the most meaningful experiences in school are those that students can’t stop thinking about after class, the next week, the next month, and the next year?
I’m not sure if I’m providing those experiences for students. And I’m not sure how to do it better. In many ways I’ve become a more “traditional” teacher in the last year. I’ve become more purposeful in the ways I use class time, and more ruthless in things I’m willing to cut if they don’t contribute to kids learning math. I’ve grown what I think is a healthy disdain for projects that seem to have more fluff than substance, that don’t connect directly to my learning goals for students.
I wonder what a curriculum would look like that was structured around students’ beliefs and dispositions toward math, with the goal that students are still reflecting on their mathematical experiences years later. I’m skeptical it’s too vastly different than what I do now, but it’s something worth thinking about this summer.