Things Kids Think With: The Role of the Physical Properties of Mathematical Tools in Children's Learning in the Context of Addition of Fractions

Abstract

This research was designed to examine the role of the physical properties of the mathematical tools, in children’s learning in the context of adding two fractions. My two research questions were: (1) How does the feedback from the mathematical tools play a mediating role between the physical actions of the child with respect to the mathematical affordances of the tools and the child’s thinking about and learning and knowing of solving addition of fractions problems? And (2) What role is played by mathematical tools in the emergence of a Zone of Proximal Development during the child’s solving of addition of fractions problems? To address these questions, I interviewed 13 grade 7 students in Ottawa, Ontario, in groups of two and in three rounds of 30-minute interviews per group. The results showed that the physical properties of the tools play a role in how children perceived the mathematical affordances of the tool, attached mathematical meaning to the tools, created mathematical artefacts and solved the addition of fractions problems. Moreover, the findings show that in children’s interactions with mathematical tools, at times, the Zone of Proximal Development (ZPD) emerged, with the guidance provided by the tools. I conclude that children’s interaction with the tools provided them the possibility of learning newer forms of reflections, expressions and actions in relation to adding two fractions. This learning was a result of a complex and intertwined relationship between the immediate physical properties and affordances of the tool, the traces of the thoughts of the designer of the tools, as well as the children’s previous knowing of fractions. With this study, I extend the Vygotskian notion of the more knowledgeable other within the ZPD to include not only agents (children and adults) but also tools.