The object-tool duality in mathematical modelling. A framework to analyze students’ appropriation of Sankey diagrams to model dynamic processes

Abstract

Students often do not experience the relevance of learning mathematics. This paper reports on an exploratory case study, in which a class of grade 8 students (n=35) was introduced to Sankey diagrams. The aim was to explore to what extent these students could appropriate Sankey diagrams, meaning: they could describe these as objects in themselves and they could use them to model and visualize phenomena relevant to them. Based on Cultural-Historical Activity Theory, we developed an analytical construct defined as the object-tool duality, coordinating mathematics as a set of objects and as a set of tools. The analysis of students’ answers showed that they could use these diagrams as tools to visualize phenomena. When asked to describe the object, all mentioned the tool-side. So, in their appropriation the tool-side came before the object-side. Our contribution is that teaching the tool-side of mathematics before the object-side may increase students’ sense of the relevance of mathematics, which is a topic to develop for future research.

Keywords

• Appropriation
• mathematical modelling
• object-tool duality
• relevance (of mathematics)
• Sankey diagrams