The Learning and Teaching of 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.

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

Index