The effects of self-explanation training on students' problem solving in high-school mathematics

The performance of a group of grade 9 mathematics students trained to use a self-explanation procedure during study of a new theorem in geometry was compared with that of students who used their usual study procedures. The processing activities used by the students during the study session and those used in a subsequent problem-solving test were observed. The focus of analysis on both occasions was on the knowledge access, knowledge generation, management and elaboration activities used by students. The self-explanation group showed more frequent use of each type of activity and also obtained higher scores on the problem-solving test. The difference in post-test performance of the groups was greatest on a set of far-transfer items. These items required the students to extend their use of the newly learned theorem to problem types that were substantially different from those presented in the original study material. Of particular note was the carryover effect of self-explanation training to students' processing in the subsequent problem-solving session. The relationships among the processing activities, students' beliefs, prior knowledge and post-test performance were examined using a partial least-squares path analysis procedure. Use of the self-explanation method had an indirect effect on performance, this effect being mediated by associated knowledge access and knowledge generation activity. There was no direct effect of method on performance. The strongest predictor of performance was the level of knowledge generation activity during which students showed evidence of making novel connections, either within the newly presented study material or between parts of that material and their existing geometry knowledge. In the final path model derived from the analysis of student performance, the students' prior knowledge measure had both a weak direct on their problem-solving performance and an effect on that performance that was mediated by relationships with the knowledge access and knowledge generation variables in the model.