An Experimental Study on Support for Leaning of Problem Posing as a Production Task

Abstract

In learning of problem posing, it is important but difficult for learners to generate diverse problems by associating and combining various situations expressed in problem texts and mathematical structures of solutions. 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 participants were asked to pose new problems from given examples. The experimental results indicated that the participants posed only a few problems that had situations identical to and solutions different from the examples. It was also revealed that problems that the participants constructed based on their own ideas had relatively simple and inappropriate solution structures. Those results suggest that idea generation support for constructing solution structures of problems is effective in expanding the variety of problem posing. According to these findings, we discussed approaches to support the learning of problem posing.