Calculus at A-level and its understanding

Abstract

It is my contention that in the teaching of calculus at A level we have, all too often, been producing an understanding of calculus—and, implicitly, a view of mathematics—that is distorted and unrealistic. I am glad of the chance to air these criticisms in this contribution to the debate about the future of sixth form mathematics. (In this article, “sixth form” is synonymous with A level, whether studied at school or college.) Nevertheless, as I maintain later, the changes now being wrought in sixth form mathematics generally may well prove beneficial.

What does it mean for a student to understand the first-year calculus? Perspectives of 24 experts

“…Debate over what students should know and be able to do upon completion of the first-year calculus has been disputatious for over a century (Bressoud, 1992;Douglas, 1986;Ford, 1910;Hobbs & Relf, 1997;Kaput, 1997;Kleiner, 2001;MacDuffee, 1947;Maher, 1991;Maltbie, 1900;Munroe, 1958;Osgood, 1907;Renz, 1986;Tucker, 1999;Woods, 1929). Inability to arrive at consensus on essential learning points has been reported across the mathematical community (Ganter, 2001;Tucker, 1999;Zorn, 1991) with some questioning whether consensus is possible or even appropriate and others asserting its necessity.…”