Experimental Study on Failures in Composing Solution Structures in Mathematical Problem Problems

Abstract

Problem posing is identified as an important activity in mathematics education and a critical skill to be acquired. Several studies implemented support systems for learning of problem posing which aid novice learners in successfully posing appropriate problems. However, such learners may not necessarily success in posing appropriate problems without the support. Toward further support for novice learners in acquiring problem posing as a mathematical skill, we have to understand failures occurring in problem posing by novice learners. This study experimentally investigated problem posing by novices and empirically described their failures. In our investigation, participants were engaged in a learning task to study an example by reproducing it and a novel generation task to pose their own problems, with the results indicating that some participants composed problems whose texts and solutions were inconsistent in the learning task.