Challenging the Traditional Sequence of Teaching Introductory Calculus

Abstract

Despite considerable research with students of calculus, rate, and hence derivative, remain difficult concepts to teach and learn. The demonstrated lack of conceptual understanding of introductory calculus limits its usefulness in related areas. Since rate is such a troublesome concept, this study piloted reversing the usual presentation of introductory calculus to begin with area and integration, rather than rate and derivative. Two classes of first-year university students taking introductory calculus were selected to pilot the effect of changing the sequence; one class was a control group and the other class followed the reversed sequence. Advances in technology, especially computer algebra systems (CASs) may facilitate new ways of studying mathematics. In this study, handheld CASs were used to support students’ thinking as they grappled with the concepts of introductory calculus. The use of CASs enabled consideration of symbolic patterns and numerical integration leading to a deeper conceptual understanding of integration. The easy access to the multiple representations of functions provided by CASs facilitated an exploration of rate where each representation highlighted different aspects of rate resulting in deeper conceptual understanding of differentiation.