Student teachers' reflections on their learning process through collaborative problem solving in geometry

摘要

This paper reports research that focuses on student teachers' reflections on their learning process in a collaborative problem-solving context. One group of students with limited mathematical backgrounds worked on two problems in geometry without teacher intervention. We focus on two episodes from the group dialogues. In the first episode (section 5) the students basically reflect on two key issues. The first reflection is related to the concern of making problem-solving tasks too difficult in general while the second reflection has to do with the concern of participation in the solution process. The students discuss how they can give hints or introduce particular ideas before presenting a solution in order to stimulate colleague participation, thus promoting the understanding of the solution process. The second episode (section 6) illustrates the reflection of students on their preparation as future teachers of mathematics. They emphasise that the experience of getting stuck with a problem may help them to better understand the frustration pupils experience while working on unfamiliar problems in classroom. Based on the experience of getting stuck, the students reflect on how they could motivate themselves as well as pupils to work on mathematical problems. They suggest that a good strategy is to start working on an easier problem. If they succeed in coming up with a solution to that problem, they think that it is then more stimulating to proceed to a difficult one.