If we want to work toward more equitable math instruction, we need another way to think about “misconceptions,” since they often lead to deficit thinking about students.
Dr. Rochelle Gutiérrez offers this powerful idea that guides my work:
Ouch! How humbling to think that we aren’t the all-powerful keepers of mathematical truth. But once I get past my initial discomfort, this becomes a tool for centering student thinking.
For example, a student was solving the problem “4 people equally share 10 brownies. If they share all the brownies, how much brownie does each person get?”
With a “misconception” lens we might see:
- This is a division problem but the student didn’t write 11 divided by 4
- The student wrote 3 instead of the correct answer 2 1/2
With a “conception” lens we might see:
- The representation matches the action of the problem (dividing) and gives enough detail for us to understand their work quickly
- Student knows dividing a whole number into 2 equal pieces is called “cutting in half”
- “3” as an answer makes sense if we’re counting the number of brownie pieces each person gets
3 is only a “misconception” when we expect students to come to our view that the answer must be given as a fraction (2 1/12). We miss the CONCEPTION that we can count and name the number of pieces one person receives.
The lens of “conceptions” allows us us to lead with curiosity: “How did you get 3?” or (pointing to the halves) “Tell me what happened here.”
So, next time you come across “student misconceptions,” I urge you to look for and utilize “student conceptions” instead.