Third grade students’ multimodal mathematical reasoning when collaboratively solving combinatorial problems in small groups

Abstract

The aim of this study is to investigate Norwegian primary school students’ multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8–9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as count-all and grouping. These approaches were characterized by the students’ use of inscriptions that displayed all combinations and inscriptions that did not display all combinations. Moreover, the students used gestures such as pointing and sliding. The students’ multimodal reasoning was characterized by the ways their utterances, inscriptions, and gestures emerged and supplemented each other. The students’ pointing gestures mediated the intended mathematical meaning solely when combined with inscriptions displaying all possible combinations. Sliding gestures, on the other hand, did mediate the intended mathematical meaning when their inscriptions were not displaying all possible combinations. In this latter case, the shortcomings of their inscriptions were complemented and compensated by the sliding gestures. The students’ multimodal mathematical reasoning made explicit their combinatorial thinking, mediated the intended mathematical meaning, and facilitated their solving of the given combinatorial problems.