Study on the Effects of Learning Examples through Production in Problem Posing

Abstract

Problem posing is identified as an important activity in mathematics education. Although it is difficult for novice learners to pose diverse problems, they must do so. Such novices particularly have difficulty in appropriately composing mathematical structures of solutions when posing new problems. This paper discussed and experimentally studied an approach to support learning of problem posing as a production task. We designed support for learning by imitation of examples, in which learners reproduce problems presented as examples. That is expected to facilitate learners’ understanding ideas used in generation of the examples, and to stimulate new idea generation in learners’ own problem posing. We then verified the effects of learning an example through imitation, with the results indicating that learning by imitation can facilitate adaptation of ideas used in an example into learners' problem posing, whereas it cannot necessarily facilitate appropriate problem posing when they try to diversify.