Developing problem posing in a mathematics classroom

抄録

This is an exploratory study of 18 grade 9 students working on two problem-posing tasks involving the quadratic function. There are a variety of problem-posing strategies used by students, including the use of associated sub-topics, using the quadratic formula as a guide, working backwards, and adopting a trial-and-error approach. The free-posing task seems to help students to bring out more variety of sub-topics that they can connect, perhaps reflecting some confidence for such type of task. This is less so in the semi-structured task. It also appears that the number of sub-topics used is not dependent on student achievement type. Some implications for teaching and for teachers are also discussed. Specifically in the context of differentiated instruction in a classroom, problem posing activities can be one strategy to engage students. The findings of this exploratory study have the potential to add to the body of local knowledge about how problemposing instructions can be engendered in the classroom to bring about deeper classroom engagement in mathematics.