Strategies for encouraging student discussion, explaining, and argumentation about mathematics

Question

How do we get students to see their own explanations as valuable to their learning?

For instance, talking can help a student uncover misconceptions that might otherwise remain unexplored until much later. Students can also benefit from examining the misconceptions of their peers.

The act of participating reinforces how valuable students' contributions are. With feedback from an instructor, they can also see how mathematical their contributions are.

However, students often express a belief that a good math class is one where the teacher or book gives good explanations, rather than one that requires students to explain.

What type of activity in the classroom have you seen that helps students express their mathematical thinking, and helps show it as valuable?

Answer 1

I will try, though I am a biologist. The main difference between your question and the one linked in the comments seems to be that you want students to realize that articulating mathematics leads to better learning of mathematics. Not just being willing to answer questions, but talking.

I would recommend a technique that can be done with either clickers or a paper "quiz." I'll present it as a clicker technique, but the same things can be done with a short 3-5 question quiz.

1. Pose a somewhat difficult clicker problem, expected accuracy at perhaps around 60%.
2. Students work independently and submit answer via clicker.
3. Students are then encouraged to discuss in pairs or small groups of three. They are allowed to resubmit a new answer.
4. Students are then given an isomorphic question (same concept, slightly different presentation), and asked to independently solve and submit again.
5. Instructor points out that student answers overall have improved- indicating that talking about mathematics helps organize thinking and uncovers confusions.

A paper in Science using this technique shows that students who miss the first question but are given the opportunity to discuss and then answer an isomorphic question improve more than students who do not discuss (reference below, open-source).

You would still have to do the sell, of course. Students tend to avoid expending extra calories when possible and will hope to avoid serious thinking during class. But with practice (and exam questions similar to the clicker questions), motivation will rise. It's more fun to be an instructor too - students talking! about the subject!

Smith, M. K., Wood, W. B., Adams, W. K., Wieman, C., Knight, J. K., Guild, N., & Su, T. T. (2009). Why peer discussion improves student performance on in-class concept questions. Science, 323(5910), 122-124.