1st Edition

The Learning and Teaching of Calculus Ideas, Insights and Activities

    304 Pages 149 B/W Illustrations
    by Routledge

    304 Pages 149 B/W Illustrations
    by Routledge

    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.

    Series foreword

    1 – Introduction

    2 – Calculus across time and over countries

    3 – Making sense of limits and continuity

    4 – Making sense of differentiation

    5 – Integration and the fundamental theorem of calculus

    6 – Interlude: The ordering of chapters 3, 4 and 5

    7 – Calculus applications: differential equations and integration

    8 – Beyond elementary calculus



    John Monaghan is a professor at the University of Agder, Norway and an emeritus professor at the University of Leeds, UK. He has taught in schools and universities, and the learning and teaching of calculus has been a research interest throughout his career.

    Robert Ely is a professor of mathematics education at the University of Idaho, United States. He studies the reasoning of students with infinitesimals, integrals, variables, and argumentation, and he is particularly interested in the perspectives that history can bring to such reasoning.

    Márcia M.F. Pinto is Associate Professor at a public university in Brazil. She has experience teaching mathematics to prospective teachers, mathematicians and engineers and co-authoring textbooks for distance learning courses on calculus.

    Mike Thomas is Professor Emeritus in the Mathematics Department at Auckland University, New Zealand. His research explores advanced mathematical thinking at school and university, including the role of representations, versatility and digital technology.

    Back cover quotes:

    ‘I highly recommend this book. You will undoubtably be inspired and awed at the beauty of the ideas presented.’ Chris Rasmussen

    ‘The most impressive aspect of this book is that the authors cover so much ground without taking a stance on any of the controversies they so carefully explain.’ Pat Thompson

    ‘When we teach calculus, we need to know about differential and infinitesimal ways to understand calculus … how calculus ideas evolved over time … calculus curricula around the world … calculus education research … alternatives to the classic order … calculus in solving real-world problems … [this book] does quite a bit of all of that.’ Elena Nardi