The role of the context for pupils’ choice of solution strategies and representations when working with combinatorial problems

Abstract

This paper reports on a study based on two classroom sessions in a Norwegian school where pupils in Grade 4 (age 9) worked on two combinatorial problems. Data were collected by video-recording two pairs of pupils collaborating in each session, as well as a whole-class session at the end of the second session. The pupils’ written work during the sessions was also collected as data. The classroom sessions were designed based on principles from the Theory of Didactical Situations. Data were analysed using a dialogical approach and based on theory for multiplicative structures and semiotic representations. The study shows that the pupils’ solution strategies and choice of representations in the two problems differed considerably, despite the mathematical similarity of the problems. The aim of the paper is to inquire into how the context in which the problems were set could influence the pupils’ strategies and choice of representations in the solution process, and to what extent the context also could influence whether the pupils recognised the situations as multiplicative