for the learning of mathematics

an international journal of mathematics education

Melissa Rodd - Vol. 30 Num. 3 (2010)
 Geometrical visualisation – epistemic and emotional


A well-documented experience of students of elementary Euclidean geometry is ‘seeing’ a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed, critiqued and adapted from a perspective that positions potential knowers as being part of a physical, social and cultural geometric environment. Specifically, the philosophical argument reviewed uses as a premise that human ‘dispositions’ include neurological propensities to perceive spatial forms and thus visual perception is potentially a route to knowing geometrical theorems. Using tasks and reports from mathematics education, it is argued that such dispositions are affect laden. Thus visualisation of geometrical theorems is entwined with emotion. This results in a paradox – geometrical knowledge is both objective (epistemic) and subjective (emotional). This paradox is resolved by using ecological realism that rests on the idea that knowledge is environmentally relational.