Differential Calculus: Concepts and Notation

This paper suggests that many students with A-level Mathematics, and even with a degree in Mathematics or a related subject, do not have an understanding of the basic principles of calculus. It considers advice given in books about the teaching of calculus in the last sixty years and describes the approach used in three textbooks in current use. Attention is drawn to the lack of a conceptual basis in the common core syllabus at A-level and some suggestions are made for improvements.