The transfer of learning has been the subject of much scientific inquiry in the social sciences. However, mathematics education research has given little attention to a subclass called backward transfer, which is when learning about new concepts influences learners' ways of reasoning about previously encountered concepts. This study examined when…

Experts' perceptions of mathematical problem structures were compared with students' perceptions before and after a course on mathematical problem solving. After the course the students perceived problem relatedness more like the experts, indicating that criteria for problem perception shift as a person's knowledge bases become more richly…

The starting point for this study was the resistant nature of prior knowledge in conceptual change from natural numbers to rational numbers observed in our previous study. Thus, in this study the effects of deliberately teaching the abstraction of the density of numbers on the number line was tested in a quasi-experimental study at the beginning…