In her post-lesson reflection, Mia shares that her students don’t always perceive the noise level of the classroom in the same way that she does. Many of her students may be more comfortable with a higher classroom sound volume than Mia is.
In considering her students’ work, Mia describes the challenges in having young students convincing each other of their strategies and talking about proof, noting a “big leap” with one particular student in defending her thinking. Mia shares her own openness to students’ ways of solving, using the word stories they were working on and categorizing the stories by the kind of problem they are: put-together or take-apart.
This lesson is contextualized in the arc of the school year and to my students’ overall shift in “unraveling the mysteries” of mathematical thinking. I like connecting students with each other because while they can often see a mathematically correct response, they can’t always yet explain why it is correct.
I’m really explicitly creating partnerships, or what I think of as academic “matchmaking,” based on three criteria:
1) students who have the same answer and the same strategy. This matchmaking has the lowest burden of “matching” in both language and mathematical thinking. It’s like “convince yourself,” because you already are in total agreement with this person; you’re just getting a chance to practice the precision of language (SMP 6: Attend to precision) to support what you did.
2) students who have the same answer but a different strategy. This match requires more precise language of comparing/contrasting/connecting ideas and strategies to understand why two different ways could come to the same answer. It’s like “convince a friend,” because this person is inclined to agree with you, you both obviously think something is the same here.
3) students who have different answers. This match requires the greatest level of argumentation and precision of language, because it’s really about trying to change somebody’s mind to your way of thinking. This is like “convince a skeptic.”
More than the correct answer, I’m interested in my students understanding why a particular strategy works and why another strategy wouldn’t.
I try not to stop them when they’re wrong, because I don’t stop them when they’re right. Every time I stop them, I’m signaling that I know something they don’t, and I don’t want my students to guess what I want them to say, as opposed to engaging in describing and defending their strategies. It’s more valuable for them to observe another student counting with precision in a different way, giving them a greater cognitive load to assess their own strategy or approach.