Learning mathematics through computer-based visualization

Abstract

Learning mathematics through computer-based visualization Since the beginning of the 90s there has been an increasing use of computers for enhancing learning in mathematics in Sweden and abroad. Methods and aims have varied. The tools used have mainly involved computer algebras (Maple, Mathematica, Derive, etc). The most recent additions are advanced graph-displaying calculators that have partly taken over some of the use of computers in this context. One important result from the various experiments has been the use of plotting functions to improve understanding of various mathematical concepts by studying function graphs. In this project we have gone a stage further in visualizing mathematics: The understanding of mathematical methods and concepts often involves seeing structures in mathematical models, formulae and expressions. This understanding is often the starting point for selecting and applying a method of calculation. Often it is just the teacher who sees these structures, at least initially. The students?conception of structure often comes much later. The intention behind this project is to utilize computer-based visualization techniques to demonstrate and consolidate structures and courses of events, which otherwise are just talked about in teaching situations. Modern visualization methods not only support a more intuitive conception of the objects, they can also contribute to an interactive learning environment. In this way we hope to enhance the students? conception and understanding of central mathematical concepts. We have emphasized components of mathematical expressions by colors, patterns, shapes, by a change in the typesetting or by linking the expression to a graphical representation and by pop-up menus. We thus have to link the components of the mathematical expression to the user interface. In this paper we will describe our method and results through some examples in integration by parts, substitution and the function concept. It is possible to follow the work at http://www.itn.liu.se/~oweka/MADAVI/