A Discursively Oriented Conceptualization of Mathematical Problem Solving

Abstract

This chapter suggests a discursively oriented conceptualization of mathematical problem solving and then illustrates the conceptualization by putting it in use for rethinking results of two past studies on problem solving. In the first study, a practice of developing and using heuristic discourse was facilitated in two eighth-grade classes during a 5-month period. This practice positively affected problem-solving heuristic literacy and aptitudes of those students who were identified as “weak” at the beginning of the intervention. In the second study, effort was made to incorporate aesthetic discourse in problem-solving discussions in three middle-school classes during 8-month period. The effort resulted in gradual change of sociomathematical norms and development of positive attitude to mathematics in one of the participating classes. The chapter concludes by discussion of the promise of the proposed conceptualization for practice.