Technology and Calculus

Abstract

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, to use of graphic software to explore calculus concepts, to fully featured computer algebra systems such as Mathematica (Wolfram Research, 2005), Maple (Maplesoft, 2005), Derive (Texas Instruments, 2005), Theorist (no longer available, replaced by Livemath, 2005) and Mathcad (Mathsoft, 2005). 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 early years of using technology in calculus were characterized by hopeful enthusiasm and based on little documentation of 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.