Two Wrongs and a Right

Thoughtful analysis of mistakes is a great way to develop and deepen mathematical understanding. Ever since I stumbled across Michael’s Pershan’s Math Mistakes website, I’ve been looking for ways to incorporate more error analysis into my classroom and department.

two-wrongs

One practice I’ve been using for years is Assessment Corrections, where students identify, correct, and reflect on recent assessment mistakes. (Here’s the form I use to guide the process.)

One practice I’ve wanted to use but never followed through on is starting math department meetings with a five-minute discussion of a mistake from one of our students.

Whatever the format, I’m convinced that my own teaching practice would benefit from an increase in thoughtful error analysis. I suspect the same is true for many other teachers. And since developing new habits is difficult, I’ve been considering how to incorporate math-mistakes-style reflection into my classroom through simple, repeatable routines.

Two Truths and a Lie, Math Style

Here’s what I’ve come up with:

  1. Display three solutions to a problem. Ideally, include photos of original student work. If that’s not possible for some reason, photos of teacher-written solutions on post-it notes or index cards will do the trick. So will typed-out solutions.
  2. Facilitate student reflection and discussion. There is much to be gained from each of the following: individual student reflection, discussion in pairs or small groups, and whole-group discussion. Whatever format (or combination) you choose, lead students to think about the assumptions behind each mistake, whether there are fragments of correctness in a given mistake, and how they might help a classmate who was prone to such a mistake.

Looking Ahead

I’m excited to use this approach more often in my classes throughout the rest of the semester. Will it be perfect? Probably not. I can imagine some errors that simply won’t fit in this side-by-side-by-side format. And I’m uncertain whether a projected slide is as useful as a paper handout, or if I should lean toward the latter. Even with these lingering questions, I do know this: This routine has the potential to add considerable value to my classroom, as it provides students with repeated opportunities to develop their sense-making and argument constructing/critiquing abilities. And if I had to rank the CCSS Standards for Mathematical Practice in order of importance, it’s likely I would place those two (SMP 1 and SMP 3) at the top.

Questions

How do you incorporate thoughtful discussion of math mistakes into your classroom or department? Do you have ideas for how to make my “two wrongs and a right” approach better? Drop a line in the comments below.

Comments 3

  1. Thanks for posting on error analysis. Ironically, this is a topic of upcoming conference sessions for me within the next year. I think your two truths and lie could be a fun activity to try out.

  2. I really like this idea! Do you suggest students only orally discuss the issues with classmates or do you believe it is also beneficial for them to write down notes on the differences in their own words for their notes (or as an assignment)? If the latter, how much time would you allow?

  3. chmila: I typically had students share aloud with a partner, then we would share out with the whole class. But I think having students write down a few observations before sharing could also be very powerful.

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