Moving towards understanding: Reasoning about graphs in primary mathematics education

Abstract

The PhD study described in this thesis focuses on stimulating fifth-grade students’ reasoning with motion graphs, as an approach to incorporate higher-order thinking (HOT) in mathematics activities in primary school. The graphing of motion – including both graph interpretation and graph construction activities – is rarely addressed in mathematics textbooks, although there is ample evidence that students at this age can deal with representations in which motion data are visualized. Students’ reasoning about motion graphs could potentially benefit from the incorporation of bodily experiences during graph-related activities. The idea that bodily experiences – including touching, gesturing, perception, and moving one’s whole body – are relevant to the field of mathematics, can be positioned within contemporary work on embodied cognition. The research presented in this thesis mainly focuses on the evaluation of a learning environment consisting of a six-lesson teaching sequence incorporating embodied activities related to graphing – both graph interpretation and graph construction – using motion-detecting graphing technology. In this respect, we bring together – and build upon – previous work done within the field of mathematics and science education as well as previous work done within the field of embodied cognition and investigate how both research strands combined might be a fruitful way to develop students’ reasoning about graphs of motion. The first aim of the research presented in this PhD thesis is investigating whether and to what extent mathematical activities in the domain of graphing motion are prone to elicit students’ HOT. The second aim is investigating the foundational role of bodily experiences, as concrete activities, for cognition and mathematical activity by taking into account opportunities the incorporation of bodily experiences offer to support the learning of mathematical concepts, and more specifically, reasoning about motion graphs. A third and final aim of this PhD thesis is whether HOT stimulated within the domain of graphing motion has the potential to foster high levels of reasoning in another mathematics domain, namely the domain of linear equations, providing further insight in the extent to which HOT can be regarded domain-specific, domain-general, or both.