The Role of Representations in Growth of Understanding in Pattern-Finding Tasks

The major aim of this paper is to report on a study of the relationship between students ’ external representations of a mathematical concept and growth of understanding. Using the context of pattern-finding activities, we investigated the relationship between participants ’ levels of understanding using the Pirie-Kieran Model and of the type of representation used at each level. Our findings suggest that there is an association between participants ’ levels of understanding and the types of representations used. Further, teachers and researchers might assess students’ understandings of a particular mathematical concept through questions or tasks that elicit representing a concept in an alternate form