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List of contents
1. What Didactics is and why it is important; 2.What is calculus?; 3. Foundational mathematical understandings and ways of thinking for the calculus (understandings students should have to study calculus); 4. Limits and Approximations; 5. Rate of Change, Accumulation, and the Fundamental Theorem of Calculus; 6.Chain rule and Implicit Differentiation; 7. The Fundamental Theorem of Calculus revisited; 8. Integration and the concept of differential; 9. A Foundation for Advanced Mathematical Topics; 10. Teaching, Learning, and Curriculum
About the author
Patrick Thompson is Professor of Mathematics Education at Arizona State University. He is current editor of the journal Research in Mathematics Education and a former associate editor of Cognition and Instruction.
Guershon Harel is Professor of Mathematics Education at the University of California at San Diego, but studied for his Masters and PhD degrees at Ben-Gurion University Israel. Since 2008 he has run ‘Math for America Summer Institute for Teachers’ in San Diego.
He has worked extensively with US math teachers and also published numerous research articles and scholarly books.
Michael O. J. Thomas is Professor of Mathematics at the University of Auckland. He practiced as a Maths Teacher in the UK for twenty years and received his PhD in Mathmatics from the University of Warwick in 1988. He has gone on to publish nearly 200 academic articles and book chapters.
Summary
The Teaching and Learning of Calculus offers a fresh perspective on the challenges and difficulties of effectively engaging students. The authors argue convincingly that many of the difficulties in learning calculus result from ways students understand, or fail to understand, fundamental mathematical concepts in primary and early secondary school and offer alternative ways of understanding and thinking about early mathematics concepts that have natural extensions to learning calculus.
Areas covered include:-
What is calculus?
Foundational mathematical understandings
Concepts of calculus, including limits and approximations, rate of change and accumulation
Integration and implicit differentiation
Teaching, learning and curriculum
Throughout the text the authors show that teaching often fails because many calculus concepts are taught in a way that makes it difficult for students to connect ideas that they study in calculus with ideas that they already have—thus leading students to lean on memorization as a way to cope with instruction that makes little sense to them.
This important book proposes new ways of thinking about the ideas of calculus that will guide maths researchers, teachers and teacher educators in rethinking maths instruction.
The authors conclude by describing the ways in which many current practices in calculus curriculum and instruction are anathemas to high quality learning. They argue for a particular style of integrated active intellectual engagement that students must experience and important conceptual ideas with which students must engage if they are to build coherent, long lasting understandings of calculus that will support using it in other disciplines and supply a base for future mathematical learning.
IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of advanced textbooks for teacher education which aims to advance the teaching of maths by integrating mathematics content teaching with the broader research and theoretical base of mathematics education.
