Here is a transcript from part of a classroom discussion.

Student: “So, I think.. well we believe, we noticed that expression number two combines with vision number B because it’s parenthesis

xplus two, right?So all the visions and all the squares are repeated three times because it’s being multiplied by three. And so thexI believe, well we believe, would be the rectangle and the squares would be the two.”

What do you think is being discussed in this example? It’s impossible to understand this conversation without a visual representation. So, let’s look at the task the students are talking about.

Now, consider the same questions. What mathematics is being discussed?

Let’s look at the task again but with some annotation meant to draw students’ attention to the salient details of the explanation.

Now imagine the conversation. What is being discussed? What strategy is being shared?

Here is a generalizable principle: if one doesn’t have a visual way for students to track a conversation, one should assume they cannot.