What is a best mistake?

We have been playing around with the prompt “What is the best mistake?” in Algebra I lately. Today we did another similar exercise where I gave them two flawed solutions to a homework problem and the prompt “Which is the best mistake?”

Like in past iterations, students buzzed about what that means, and I was predictably quiet save for my warning that they have 60 seconds to formulate an argument.

Anyone in this field will tell you that a good answer is one with a solid reasoning, a good warrant. I heard a few that I liked. The best argument all day–all year so far–was when a student said “#1 is the best mistake because it is a mistake I would make.”

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