Dynamic geometry: An agent for the reunification of algebra and geometry

Abstract

This paper investigates the degree of separation or unity between the algebraic and geometric modes of thought of students in tertiary education. Case studies indicate that as a student is inducted into the use of algebra the insightful and visual components of geometrical and graphical modes of thought are sidelined. Based on Vygotsky’s taxonomy of the psychogenesis of cultural forms of behaviour, I suggest that this separation occurs because the algebraic methods remain fixed at a naïve or algorithmic stage. The algebraic concepts may fail to be internalised because the stage of instrumental functioning of algebra as a ‘tool’ or ‘method’ of geometry is not successfully transitioned.  I suggest that this stage of instrumental functioning may be stimulated by using dynamic geometry programs to promote the formation of images in conjunction with algebraic representations in problem solving. In this way the modes of thought in algebra and geometry in mathematics may be reunified.