I decided to apply this learning in my math program this week.
First, I had my students watch another group of similar-aged students work through and share their solutions to a math problem involving addition of multi-digit numbers. I invited them to just notice whatever they wanted to pay attention to, and to subsequently make up some comparative sentences (as my class is extremely ESL, I provided some contextual vocabulary scaffolding; see this blog post for examples).
The next day, we watched the video of the same students we had observed the day before, but this time I asked my students to focus specifically on how the students in the other class communicated their thinking. In particular, I asked them to write down (as they were watching the video) what, specifically, the students in the other class said or did while they were explaining their thinking.
As we watched, I stopped the video several times to model think-alouds (“Oh, look, they are pointing to their diagram while they explain their answer to the teacher!” and, “Oh, I hear them using signal words to organize their explanation – did you hear that? She just used the word ‘first’ to tell what she did first while solving the problem!”)
At the end of this viewing, I asked students to share 2-3 ideas from their whiteboards with a neighbour. Then we discussed all the things we noticed, as a group, and compiled a list of criteria for successful communication in math.
I posted the list prominently in the room so that the students and I could easily refer to it as needed. I then invited students to solve a math problem, independently, and communicate their solution on a piece of paper, ensuring they had done all the great things from our co-constructed criteria list before submitting their work.
Although not all of the students shared a comprehensively explained solution on their paper, I was quite amazed at how many of them got “the right answer” mathematically. Many students who had been struggling with the math unit during the preceding few weeks where able to accurately solve the problem (it was a multi-digit subtraction problem). It was as though watching other students communicate effectively, and dissecting what it was that made them effective communicators, had helped my own students to think through a problem, even if they did not actually explain the process they used to solve it in great detail on the page.
I am looking forward to upcoming lessons, where we will refer back to the criteria in order to assess how well we are communicating our mathematical thinking while problem-solving. Although our next unit is measurement, the criteria we constructed together are applicable cross-strand, and we will continue to focus on communicating.