A Mathematical Gallery Walk

"Writing in math class" has long been a topic of discussion. Like many, many other topics of discussion it is an aspect of my teaching practice that is undergoing transformation.

It started with "write your answer in a complete sentence."

Mary bought 2 dozen apples.

THAT was writing in math class?!? Yep, pretty much.

My transformation probably began with Laying the Foundation training. I was introduced to what was expected of students' writing on Advanced Placement tests. And I began to expect more of my students' explanations. (For the record, they hated it.)

Then we began administering the ACT Aspire as our spring test; there's an entire "Justification/Explanation" section of the scoring. And our students are not scoring as well in that area as we would like.

I determined this year to focus on students' mathematical writing. In the past I would be thrilled if students could tell me ANYthing when asked to explain their work. Now I want to focus on those explanations being thorough and precise and using correct mathematical language.

I knew I wanted students to read and evaluate each others' writing as part of our work on justification/explanation, but I was unsure how to do it. Our instructional coach mentioned a gallery walk in one of our department meetings, and I realized that was the approach I wanted to take. I found this post to help me organize the gallery walk for my classroom.

Completed Gallery Walk

I split my Algebra 1 students into groups and gave each group a multi-step equation to solve. On chart paper, they had to show their solution and explain how they solved the equation. Then the groups rotated through each problem, making notes (via post-it) of what they liked about the explanation and any suggestions or questions they had about the explanation. When groups returned to their own problem, they revised their explanation.

Solving a problem and writing the explanation

Making post-it note suggestions

For my first attempt at a gallery walk, I think it was very successful. Students have to be taught how to critique each other's work, but that is also a Mathematical Practice standard, and all-in-all they did pretty well. Each class - unprompted - was able to pick an explanation that they thought was well-done. One class picked up on a explanation that was a bit wordy and made suggestions for making it more concise.

My goal is to incorporate more gallery walks throughout the year.

One issue I face when working on student explanations is TIME. It is hard for me to take time to work on writing and justification when there is so much math to cover. But I'm learning to work it in where I can. I am trying to put at least one thing on every test that requires students to explain in words. On the equations test, it was an error analysis problem. After the tests were graded, I made a warm-up for each class that included snapshots of actual student answers to the error analysis problem from that class. We discussed what was good about each response and elements of each response that should be included in the "ideal" response. Then I had students rewrite the "describe the error Carlos made and explain what he should have done correctly" part of the problem. I got some impressive rewrites!

As with everything else in my classroom, writing/justifying/explaining is a work in progress. Seeing student progress in that area is exciting and motivating.