Mathematical Tool Fluency: Learning Mathematics via Touch-based Technology

Recent advances in the study of mathematics embodiment have given rise to renewed interest in how mathematical learning relates to our bodily actions and the sensorimotor system. In this dissertation, I explore the embodiment of mathematics learning with a particular focus on the relationship among gestures, hand and finger movements, and the use of mathematical tools. The theoretical lens of perceptuomotor integration enabled me to articulate mathematics learning through the development of tool fluency within a non-dualistic view of mathematical tools. The dissertation is structured as three stand-alone descriptive case studies that adopt Husserl’s phenomenological attitude in analysing participants’ lived experience while using mathematical tools. Drawing on the work of Nemirovsky, one of the main intentions is to provide a thick description of learners’ perceptual and motor activities, which may result in the emergence of perceptuomotor integration in Husserlian experiential time. The results provide evidence for a high degree of gestural and bodily engagement while learning, communicating, and playing with mathematical tools. For example, in the first study, we discuss the process of learning cardinality for a young child in the context of mathematical explorations with a multimodal iPad application named TouchCounts. We identifying the development of ‘finger-touching’ action while the child is playing with it. In the second study, I present and discuss the notions of ‘active sensation’ and ‘tactile perception,’ in the context of a blind undergraduate student explaining the behaviour of a rational function. In the third study, which involves a prospective teacher identifying types of geometric transformation in a touchscreen geometry software (Geometer's Sketchpad (GSP) on iPad), I identify new modes of Arzarello’s active interactions. Identifying, analysing, and exploring different modes of interactions with touchscreen-based mathematical tools leads me to propose a new methodological approach for analysing video data. This methodological approach enabled me to catalogue interactions in order to monitor and assess the emergence of mathematics expertise while the learner interacted with the mathematical tool.