The journey or the destination? An investigation into the beliefs of pre-service post-primary mathematics teachers regarding problem-solving

It has been widely reported that the affective domain is an important contributor to problem-solving behaviour among students. Cognitive resources available to students are related to the students’ beliefs around what they consider useful in learning maths (Schoenfeld, 1983).  Problem-solving holds a key position in both Junior Cycle and Senior Cycle curricula in Ireland. Given that much research has shown that the teachers’ beliefs about problem-solving play an integral role in building positive attitudes to problem solving among their students, it is essential to investigate the beliefs of prospective mathematics teachers. The aim of this study was to investigate the affective domain of pre-service post-primary mathematics teachers in Ireland. This study was conducted in a university setting and involved the implementation of both quantitative and qualitative measures; the existing Indiana Mathematical Belief Scale (IMB), and open-ended questionnaires. Participants in the survey were enrolled in a module on mathematical problem solving. The open-ended questionnaire asked participants to describe how they felt at different stages during their attempt to solve a mathematical problem. This was then analysed using an inductive approach. A statistical analysis of the IMB (n=151) showed that students strongly believed that an increase in effort can have a positive influence on mathematical ability. However, it was concerning to find that students believe that problem-solving involves learning step-by-step procedures. Another positive finding of the IMB was that students strongly value the understanding of mathematical concepts over memorization of procedures. In contradiction to this, it was found through the analysis of the open-ended questionnaire that students had a greater focus on achieving an answer rather than on the problem-solving process. We discuss the implications for the design of the module, which seeks to support the development of the capacities required for the successful teaching of mathematical problem solving.