Reform calculus - yesterday, today, and tomorrow. (English)

N. Z. J. Math. 32, Suppl., 89-95 (2003).

Reform movements in mathematics have been with us for almost as long as civilisation itself. The parody of Heraclitus (circa 500 BC) "the only thing that remains constant is change itself", reminds us that the ways we do and teach mathematics will continue to be reformed. It is crucial, and probably inevitable, that this reform will lead us forwards, not backwards. The current calculus reform ideas are a response to the profound influences of computing technology in the mathematical toolkit of mathematicians, scientists, technologists, teachers, and students. Along with other reforms, calculus reform enables us to do mathematics differently with subsequent changes in the pedagogy of the way mathematics is learned. In this paper, an attempt is made to view the current state of calculus reform as the outcome of a long history of the development of mathematical concepts, technologies, clever ideas, and smart teaching methods. The historical development of algebraic techniques has had a major influence on these changes, and the way we model and solve problems in the future will require ongoing developments in algebraic structures and the way we do algebra. We may yet see more powerful icon-based algebras. Some forecasts are made in this direction. (Authorâ€™s abstract)