The effects of different modes of representation on problem solving: Two experimental programs

Abstract

This paper explores the effects of two experimental programs on the development of arithmetic problem solving (APS) ability by 6-9 year-old pupils. The programs stimulated flexible interpretation and use of a plurality of representations in the context of APS with emphasis on a particular mode: informational picture or number line. An a priori model has been validated for all the pupils, suggesting that different modes of representation of the problems influence APS performance, irrespective of the kind of instruction they have received. Data analysis also revealed the beneficial effects of both programs applied not only to the tasks in the representation that was emphasized in each program, but also to the tasks represented in other modes, indicating their success in the general development of APS ability.