Learning mathematics
through computerbased visualization
Owe Kagesten
oweka@itn.liu.se
Department of Science and Technology
Link?ing University
Sweden
Abstract
Learning mathematics through computerbased 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 graphdisplaying 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 computerbased
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 popup
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/
