Visualizing Higher Level Mathematical Concepts Using Computer Graphics

The computer is going to revolutionize mathematical education, not least with its ability to calculate quickly and display moving graphics. These facilities have been utilized in interactive programs to demonstrate the ideas in differentiation and integration, evolving new dynamic concept images. Theoretical background The work described in this paper is the result of a happy accident of history. Over a number of years mathematics educators have studied the concept imagery generated by students when learning the calculus and now microcomputers have become available which can draw moving pictures to provide powerful cognitive support for this imagery. Though by no means a total solution, it is hoped that interactive work on the computer can give fruitful insight into the calculus that is potentially more meaningful. The research of Orton (1979) confirmed that a group of students taught by current methods in the U. K. had great difficulty with a number of ideas in the calculus requiring relational understanding. These included the idea of rate of change between two points on a graph with all the possible signs involved, the notion of the derivative as a limit, the idea of the area as the limit of a sum and the meaning of