This book is for people who teach calculus – and especially for people who teach student teachers, who will in turn teach calculus. The calculus considered is elementary calculus of a single variable. The book interweaves ideas for teaching with calculus content and provides a reader-friendly overview of research on learning and teaching calculus along with questions on educational and mathematical discussion topics.

Written by a group of international authors with extensive experience in teaching and research on learning/teaching calculus both at the school and university levels, the book offers a variety of approaches to the teaching of calculus so that you can decide the approach for you. Topics covered include

• A history of calculus and how calculus differs over countries today
• Making sense of limits and continuity, differentiation, integration and the fundamental theorem of calculus (chapters on these areas form the bulk of the book)
• The ordering of calculus concepts (should limits come first?)
• Applications of calculus (including differential equations)

The final chapter looks beyond elementary calculus. Recurring themes across chapters include whether to take a limit or a differential/infinitesimal approach to calculus and the use of digital technology in the learning and teaching of calculus. This book is essential reading for mathematics teacher trainers everywhere.