Heuristics and semantic spaces for the analysis of students’ work in mathematical problem solving

In this research, our objective is to characterize the problem-solving procedures of primary and lower secondary students when they solve problems in real class conditions. To do so, we rely first on the concept of heuristics. As this term is very polysemic, we exploit the definition proposed by Rott (2014) to develop a coding manual and thus analyze students’ procedures. Then, we interpret the results of these analyses in a qualitative way by mobilizing the concept of semantic space (Poitrenaud, 1998). This detailed analysis of students’ procedures is made possible by collecting audiovisual data as close as possible to the students’ work using an action camera mounted on the students’ heads. We thus succeed in highlighting three different investigation profiles that we have named explorer, butterfly, and prospector. Our first results tend to show a correlation with these profiles and the success in problem-solving, yet this would need more investigation.