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Promoting Discussion in Mathematics Classby Terri Dew
We all know how much students love to talk, but getting them to talk about mathematics instead of soccer, their weekend plans, or last night’s football game can be a difficult task. To make this happen, we have to create a classroom climate that promotes discussion of mathematical ideas. Discussion of mathematics often depends on the type of questions asked by the teacher. By asking good questions of our students, we are able to elicit deeper thought about mathematics and, in turn, deeper understanding of mathematics concepts.Asking good questions is much easier than it seems. Here are a few questions to ask during math class that will promote student thinking and discussion about mathematics:
- How did you know to do that?
- Why did you decide to add those numbers?
- Did anyone solve the problem in a different way?
- Did anyone else solve the problem like Josh did?
- Why does that work?
- Does that always work?
- Why did you decide to do it that way?
- Does that seem like a reasonable answer?
- Can someone paraphrase what Candy just said?
- Do you agree or disagree with what Candy just said? Why?
How we ask our questions is as important as what we ask. Often, we get in the habit of either calling on students who have their hands raised or calling a student’s name and then asking the question. Either of these methods indicates to the rest of the class that it is not important to pay attention. If you don’t raise your hand, you don’t have to answer. If the teacher doesn’t call on you first, then you don’t have to answer. A more effective way to ask questions is to pose the question, pause for five seconds to give the students time to think about the answer, then call on a student whether their hand is raised or not! This may take some practice for students to learn to not call out the answers. In the beginning, it may help to state “I’m going to ask you a question and I want you to all think about it. Don’t answer out loud until I call on you.” Another option is to give everyone a chance to think about the answer and then discuss it with a partner before you call on one student to answer. This gives every student the responsibility to think about the answer to the question and share their ideas with someone else.
Providing adequate wait time is imperative if you want to foster good mathematical discussions in your classroom. There are three kinds of wait time to use to get your students thinking and talking about math. First, wait at least five seconds after you ask a question before you expect a response from students. This gives them time to think about the answer to the question. Second, wait at least five seconds after a student responds. This provides time for the student to add to their response if they think of additional ideas and allows time for other students to process what they have said. Third, provide wait time for yourself before responding to questions students ask. This gives you time to think about their question and indicates to them that you think their question is important.
Once a student responds, there are a few guidelines to follow if you want to create a climate of mathematical discussion. First, do not repeat the student’s response for the rest of the class. If you do, the students will learn that they don’t have to listen to each other because you will repeat the important parts for them. A strategy to use instead is to have another student paraphrase the idea of the first student. Encourage students to respond to one another by asking questions such as “What do the rest of you think about Jodie’s idea? Did anyone else solve the problem Jodie’s way? Did anyone do it a different way?” Eventually, students will refer to methods by the names of the classmate who introduced it to the class—“I did it Robert’s way this time.”
Over time, these strategies will build a community of mathematical thinkers who value discussion and respect the opinions of others. Be careful, good classroom discussions do not happen in one day or even one week! Be patient and consistent in the use of these questioning and discussion strategies and you will be rewarded with students who have a deep understand of mathematics and are able to communicate their understanding to others!
