#13. Listening in math

Posted on September 4th, 2014

From the Institute for Learning, this is Victoria Bill.

In previous podcasts, I talked about the importance of students making sense and sharing their mathematical reasoning, as well as the use of precise mathematical language. Without careful listening, none of this is possible.

When we think about Accountable Talk®, we think about something everyone does quite naturally—speak—and then we think about deploying talk for particular classroom purposes. But what about something else we do naturally-listening? It's obvious that students can't respond to one another unless they listen. Teachers, too, benefit by listening carefully to students' discussions. Teachers gather valuable information that helps them make teaching decisions.

Let's consider this example of 4th grade students working on an apparently simple multiplication comparison word problem. So visualize this problem.

Imagine a rubber band is 6 cm. long at first. Then it is stretched to be 18 cm. long. How many times as long is the rubber band once it is stretched as it was at first?

The teacher walks around the classroom, listening in to students' small group discussions. Most of the students in the class give the incorrect response—12 cm. long because, they claim, the rubber band started at 6 cm. and was stretched 12 cm. more to arrive at 18 cm. in length. They've answered the wrong question. They've answered how much longer instead of how many times longer.

A few students say, "The rubber band is three times longer than it was originally." They say this because they solved 6 cm. x 3 = 18 cm.

By listening in, the teacher learns that only a few of the 4th grade students are thinking about the situational problem as they should—multiplicatively. Now the teacher can prepare the next phase of the lesson accordingly. The teacher invites students to represent the correct multiplicative visual showing 3 iterations of a rubber band that is 6 cm. in length. This visual will help students understand that the prompt, "How many times as long is the rubber band now as it was as originally?" is a comparative question that asks them to compare the final iteration of 18 cm. with the initial amount of 6 cm. The teacher presses students to compare this prompt to the question that they actually answered: "How much longer is the rubber band now than it was at first?" Imagine what the students will say when comparing the two prompts with each other.

There's as big a payoff to listening to students. It is an in-the-moment means of formative assessment that helps teachers immediately adjust instruction to support student learning.

Victoria Bill

Victoria Bill is the Chair of the Institute for Learning's mathematics Disciplinary Literacy Team.

More information on Victoria Bill.