A Tutorial Exercise

Post date: Apr 21, 2017 9:59:56 AM

For this post I thought I would described an exercise I went through in tutorials a while back, and my thoughts on it.

Before the tutorial, I prepared 6 mathematical statements which the students should be able to determine are true or false. During the tutorial, I handed out the 6 statement at random, one per student, and told them to determine whether it was true or false. If they think the statement is true, they needed to try and prove it, if false, they should find a counterexample. I gave them five minutes to work on their own. Afterwards, I paired them up and ask them to explain to each other the statement they got given, the conclusion they came up with, and to discuss any details they are not sure about. Again I gave them five minutes before bringing the whole class together. In turn, I asked each student to explain their partner's statement and solution.

This exercise ran on a few levels. First, the statements were designed to engage the students with definitions and theorems they had just covered in the lecture, hence deepening their understanding. Second, they practise their listening skills as they had to explain to the class what their partner told them. This had the side effect of practising their mathematical communication. I saw a few students who started talking to their partner with details missing, but worked out the details as they explained their ideas. This introduced them to some of the benefits of working with someone else, even if they do not understand what you are doing. Finally, a benefit I did not anticipate is class discussions. In a few tutorials, they were some pairs that could not decide whether the statement they were given was true or false. I turned these into class discussion, and often the class was split in two, with both side having an idea of why their side was right, but not being able to prove it. This meant we could discuss several theorems and definitions, and why do they or don't they apply in this situation.

Overall, I think this is a good exercise to run from time to time. It helps the student acquire a few skills useful for their learning, as well as help them understand new mathematical content. The only downside is the preparation time. It is rather difficult coming up with enough statements which are not too hard for the students, relevant enough, and doesn't take too long to solve. This said, as I have several tutor groups, I could use the same preparation for all of them, and I have kept the statements for future years.