Technology and Calculus

Of all the areas in mathematics, Calculus has received the most interest and investment in the use of Technology. Initiatives around the world have introduced a range of innovative approaches from programming numerical algorithms in various languages, use of graphic software to explore calculus concepts, and on to fully featured computer algebra systems such as Mathematica, Maple, Derive, Theorist, and Mathcad. The innovations arose for a wide range of reasons—some because a traditional approach to calculus was considered fundamentally unsatisfactory for many students, others because ‘technology is available, so we should use it.’ Most had a pragmatic approach, trying out new ideas to see if they worked. Some began with a theory that formulated how the enterprise should work, others formulated their theories in the light of successive years of experience. Technology brought with it new market-driven factors in which large companies cooperated with educators to develop new tools. The first round of materials were in a competitive situation, often with the main objective to get the materials adopted. The first years were high on hype and low on facts about the true success of the new ideas. The system was complex, and the wider effects of the changes would take several years to become apparent. Opinions were many, informed observations few. Over recent years, evaluations of reforms and research into learning of calculus have begun to provide some answers. Our main aim is to focus on the research on the use of technology in teaching calculus and to report what it has to say to the community of mathematicians, educators, curriculum builders, and administrators. We include an analysis of the conceptual learning of calculus to put the research results in perspective. Our report addresses the wide range of students with different needs and aspirations who take calculus, the views of mathematicians, and the needs of society in this changing technological age. In an article addressed to the mathematical community, Schoenfeld (2000) formulated some broad principles about the mathematics education research enterprise. He emphasized that there are no ‘theorems’ in mathematics education that can be used to build up a theory in the way that is familiar to mathematicians, but there are issues of replicability, explanative power, and predictive power that can be of value in reflecting on teaching and learning mathematics. One must keep these issues in mind when considering the results from research.