When Students Talk About Mathematics

What happens when students talk mathematics? How are they able to convey their understanding to Ms. Barney--and what feedback does she give on how to improve their explanations?

Marilyn Burns, our favorite math guru, has several suggestions for why students should do more talking in mathematics classrooms:

 

  • Burns maintains that students should have to explain their reasoning because it's insufficient and shortsighted to rely on quick, right answers as indications of students' mathematical power. She suggests that during math lessons, probe students' thinking when they respond. Ask: Why do you think that? Why does that make sense? Convince us. Prove it. Does anyone have a different way to think about the problem? Does anyone have another explanation?
  • Burns contends that students are forced to organize their ideas when they are asked to explain their thinking. They have the opportunity to develop and extend their understanding. Teachers are accustomed to asking students to explain their thinking when their responses are incorrect. It's important, however, to ask children to explain their reasoning at all times.

In this and the next two pages, we're going to try to peer into the minds of the students. (Don't worry--no students were harmed in the making of these video clips.)

Our goal? To gain insight into the level of student understanding. Let's begin with our first student. As you listen to the explanation, consider whether the student has organized ideas in order to offer this explanation.