My Substitute Teaching Was Saved by a Student's Wrong Answer
I was a substitute teacher Monday this week here in Oakland, CA, and it was mostly a humbling experience. The students in my classes hadn’t had a regular math teacher all year—just a rotating sequence of guest teachers like me, all trying to maintain continuity with one another. It was also the day after November break. I came in like 🌈 HAPPY MATH MAN 🌈 and the kids mostly sent me packing.
The brightest spot of the day was when a student offered a wrong answer. I went from his desk to the front of the room and said to everyone, "Octavio has a really brilliant wrong answer I have to share with you."
I don’t know if it was the words “brilliant” and “wrong” right next to each other or if it was the urgency in my voice, but that line visibly scrambled the circuitry of several kids, including the student I named. But tell me this isn't a brilliant and wrong answer:
We were working on Stacking Cups. The student saw that 5 cups was 15 centimeters tall and calculated that 10 cups would be 30 centimeters tall. But it isn’t. It’s 22 centimeters tall.
From the front of the room, I trusted a bunch of strangers and some of them seemed to trust me to help all of us figure out why an answer that seemed very correct was actually incorrect. We figured out why, and afterwards, we talked about a version of the situation where, had we stacked cups differently, Octavio's answer would have been correct.
Kids are watching what we do and how we teach, more than the words we say or the posters we put on the wall. A Pathway to Equitable Math Instruction:
Though math teachers often tout the phrase “mistakes are expected, respected, inspected, and corrected,” their practices don’t always align. Teachers often treat mistakes as problems by equating them with wrongness, rather than treating them as opportunities for learning—which reinforces the ideas of perfectionism (that students shouldn’t make mistakes) and paternalism (teachers or other experts can and should correct mistakes).
As an exercise in developing a pedagogy of generosity towards student thinking, I highly recommend taking any math question and asking yourself (perhaps with colleagues) "What will be the most common wrong answer to this question? How is it brilliant? What can I do with it next?"
Start yourself with this one I posted to Twitter yesterday where 14% of students who answered it all had the same wrong and brilliant answer.
Several of the responses Twitter teachers proposed were so generous to students, so curious about their thinking, and so attentive to important mathematical ideas, they gave me a literal emotional reaction.
Give the exercise a try and let me know what it does for you.
What Else?
3D printed chocolate Platonic solids. You could pick any three words from that sentence and I’d insta-click.
Anna Weltman is a fantastic author of interesting and accessible math books (I have a special place on my shelf for This is Not a Maths Book) and she has a new one out.
Twitter teachers are going wild for this Desmos-ified homage to Green Globs from Rajeev Raizada.
Libardo Valencia describes how he used the Desmos Art Contest (on now!) with his students.
I'm 100% sure you know people or students who would enjoy Mathigon's December Puzzle Calendar.