From everyday problem to a mathematical solution: Understanding student reasoning by identifying their chain of reference

This paper investigates a group of students’ reasoning in an inquiry-oriented and open mathematical investigation developed as a part of a large-scale intervention. We focus on the role of manipulatives, articulations, and representations in collaborative mathematical reasoning among grade 5 students. In this analysis, we apply the idea of the chain of reference from the studies of Bruno Latour (1999) to the exploration, generation, and formalization of scientific knowledge. This framework allows us to combine knowledge from mathematics education about language and representations, manipulatives, and reasoning in a way that allows us to follow the material traces of students’ mathematical reasoning and hence discuss the possibilities, limitations, and pedagogical consequences of the application of Latour’s (1999) framework.