Interleaving Effects in Mathematics: Comparing interleaving, blocking and exposition strategies for teaching secondary school pupils how to classify mathematical images

Abstract

‘Interleaving’ is a strategy that has become increasingly popular in secondary school mathematics teaching over recent years. It is often defined as being the opposite of another strategy called ‘blocking’, with blocking referring to when content from different categories is grouped together by type (e.g., AAAABBBBCCCCDDDD) and interleaving referring to when different categories are mixed together (ABCDABCDABCD). Some research has investigated the potential benefits of interleaving for revision during mathematics practice assignments; other research has investigated its benefits for inductively learning how to classify images into categories. Based on findings from this research, recommendations in professional literature advise teachers to use interleaving more often during mathematics lessons. However, this thesis proposes two problems with this: the conditions in which interleaving effects have previously been found in research are not authentic to school-based mathematics learning; and that blocking and interleaving are not the only two strategies available to teachers and pupils.

The aim of the research in this thesis has been to investigate whether interleaving effects found in the inductive learning strand of research also apply to category learning in secondary school mathematics, while also comparing blocking and interleaving with a third alternative strategy: learning through exposition. The empirical research took the form of three randomised controlled trials involving secondary school pupils learning to classify mathematical images into categories. The results found no main effects of any study conditions on participants’ accuracy during the classification tests in any of the three experiments. These findings led to considerations about the differences between the types of categories that are learned about in mathematics and the types of categories that have been used in research where interleaving effects have previously been found. The thesis concludes by reflecting on the difficulties and discrepancies that can occur when transferring findings from laboratory-based research into classroom-based practice.