Versatile Learning & the Computer

The activities that are prized in mathematics are usually symbolic and logical. Far less often do we emphasize the visual and holistic. In this paper we discuss the use of the computer to encourage a more versatile approach to learning involving both types of mental activity. Empirical evidence is drawn from three studies: the relationship between equations and the graphs of straight lines [Blackett 1987], the introduction of the gradient of a more general function in the initial stages of the calculus [Tall 1986a] and the introduction of algebraic symbolism [Thomas 1988]. In each case we find that traditional approaches lead to a narrow symbolic interpretation, yet the use of the computer gives a visual framework for the mental manipulation of higher order concepts. Many researchers have identified two distinct learning strategies (see, for example, Brumby 1982). The first style has been labelled analytic or serialist, whilst the second has been called global, holist or intuitive. The essential characteristics of the two learning styles have been listed as: