Learning from worked-examples in mathematics: students relate procedures to principles

Abstract

This article discusses the relevance of the worked-example effect for mathematics education. This effect refers to the finding that, in initial cognitive skill acquisition, students profit more from studying worked examples as compared to solving problems. One reason for the effectiveness of worked examples is that the students get the opportunity to interrelate principles (e.g., mathematical theorems) with multiple problem cases. A knowledge structure in which principles and multiple problem cases are represented in an interconnected way is a very good pre-condition for transfer. Several potential objections against worked examples from a mathematics education perspective are discussed (e.g., worked examples do not address typical student errors) by referring primarily to our own studies. We also propose further research exploring whether the powerful method of learning from worked-examples can be adapted to and used in other, presently intensively discussed areas of mathematics education (e.g., fostering skills of mathematical modelling). Finally, recommendations for mathematics education are outlined.