Dispositional Reactions and Knowledge Invoked in Mathematical Problem Posing: Case Study of Three Undergraduate Students

This study was designed to examine how three undergraduate students enrolled in a developmental mathematics course interpreted and engaged with problem-posing tasks, the problems they posed and the knowledge the posed problems potentially invoked. All three students commented on the value of problem posing, as problem posing invited them to see the entirety of the problem situation and understand it. In addition, the students had a positive disposition towards posing mathematical problems, particularly with respect to the novelty of problem-posing activities and the creativity that such activities afford. It was also found that the students could pose problems with the potential to evoke a variety of linear, quadratic and exponential relationships. The findings of this study suggest the feasibility of using problem posing to engage undergraduate students in developmental mathematics courses in order to create opportunities for them to develop their mathematical understanding. This study is exploratory in nature and the paper ends with a discussion of a few directions for future studies.