Experimental study for design of computational learning support to enhance problem posing

Abstract

In the learning of problem posing, even though it is difficult for learners to generate diverse problems by associating and combining various situations expressed in problem texts and mathematical structures of solutions, they must do so. To design supporting methods for expanding the variety of problems, it is crucial to understand the types of problems that learners have difficulty in posing, and to draw crucial elements to facilitate diverse problem posing. We conducted an experimental investigation to obtain the empirical data of the variety of mathematical word problems posed by novice participants. The results indicated that the participants posed only a few problems that had situations identical to and solutions different from given base problems. It was also revealed that the problems constructed by the participants based on their own ideas were relatively simple and inappropriate. These results suggest that idea generation support for constructing solution structures of problems is effective in expanding the variety of problem posing.