November 20, 2013 by ray_emily
It’s been a minute since I’ve come up with something I really felt compelled to share here, so… guess this is a big day.
This year, my kids have math blogs – which they seem to be digging, which makes me very happy. I’m aiming to have them post about 10 times this year to write about how they are making use of mathematical habits (thanks, Bryan Meyer), among other things.
This week, I had two goals: I wanted my students to do some error analysis pertaining to fraction operations, and I wanted them to do some for-real reflecting about their understanding of fraction operations. Essentially, I hoped to cement student understanding of addition, subtraction, and fraction ‘basics’ before jumping into multiplying and dividing after Thanksgiving break.
I threw together this sheet:
And then this one:
The conversations that ensued were great. (Students discussed in groups, and then we shared out as a class, prior to any writing on that second worksheet.) I loved hearing kids verbalize their conceptual understanding of fraction operations as they remarked upon what Jane, Peter and Sam did correctly and incorrectly. Additionally, my students seemed to take great pride in being able to locate the patterns. (If you haven’t closely analyzed the first sheet: Jane, Peter and Sam each have unique misunderstandings that reoccur in the three problems that they complete.)
I was pretty pleased with the writing prompts, too—which ask kids to think about and propose theories for WHY Jane, Peter, and Sam made these mistakes. (Thanks for the inspiration, Michael Pershan!) So often, when I attempt to get kids analyzing wrong answers, they tell me, “Oh, it was just a careless mistake,” or, “That was a computational error – I need to slow down.” I heard nothing of the sort today, which made me happy happy happy.
Each student will author two blog posts as a result of this activity (alas, each student must choose to neglect either Jane, Peter, or Sam). I’m hoping for good results and good dialogue in the comments.
One improvement I’d like to make, next time, would be to use real student work, in actual student handwriting. If you have other suggestions, I’d love to hear them. I’m hoping to recycle this activity in the future.
PS – Come to think of it, this activity is kind of like an updated, much-improved version of another activity I wrote about here.