Posing mathematically worthwhile problems: developing the problem-posing skills of prospective teachers

Abstract

Problem solving is a key priority in school mathematics. Central to the valuable role played by problem solving is the quality of the problems posed. While we recognize the features of good problems and how to support learners in solving problems, less is known about the ways in which prospective teachers’ (PTs) conceptions of what constitutes a ‘good’ problem develop within the confines of an Initial Teacher Education program. This study explored the effect of engagement in a mathematics education course on the problem-posing skills of 415 prospective primary teachers. A 3-week instructional unit consisting of a series of lectures and tutorials on problem solving and problem posing was implemented. A questionnaire examining participants’ understandings of and ability to pose problems was administered prior to and following instruction. Results reveal that participation brought improvements in conceptions of what constituted a good problem and in the ability to pose good problems (targeted at grades 1–4). Initial problems generally were arithmetic, required one step to solve and had only one correct solution. Following the instructional unit, attention was paid to designing problems that had the potential of multiple strategy use, multiple possible correct solutions, multiple modes of representation and the incorporation of extraneous information. Despite these improvements, the complexities of problem posing and the challenges that persist for PTs in posing good problems are evidenced. Recommendations are made for the enhancement of problem-posing experiences, most notably developing skills in identifying mathematically worthwhile problems from a selection of problems or in reformulating given problems to make them better, that support PTs in developing the knowledge and understandings required to pose mathematically worthwhile problems.