Dreams of Calculus, Softcover reprint of the original 1st ed. 2004 Perspectives on Mathematics Education

The purpose of this book is to stimulate a much needed debate on ma- ematics education reform. We do not claim that we present anything near the whole truth, and that there are not many other points of view. We thus invite to debate and urge other people to express their views. As scientists we believe that it is our duty to present our own standpoints and conc- sions as clearly as possible, to open for scrutiny and discussion, rather than ambiguous politically correct views, which are di?cult to question. This book may be viewed as an introduction to our mathematics e- cation reform project Body&Soul based on a synthesis of Body (com- tational mathematics) and Soul (analytical mathematics). We do make a case for computational mathematics, which is the new world of mathem- ics opened by the computer, now waiting to enter mathematics education. But we do also propose a synthesis of this new world, with the kernel being computational algorithms, and the traditional world of analytical ma- ematics, with analytical formulas as the kernel. In fact, algorithms are expressed using analytical formulas before being translated into computer code, and good analytical formulas are necessary for understanding and insight.

I Perspectives.- 1 Introduction.- 2 What? How? For Whom? Why?.- 3 A Brief History of Mathematics Education.- 4 What is Mathematics?.- 5 Virtual Reality and the Matrix.- 6 Mountain Climbing.- 7 Scientific Revolutions.- 8 Education is Based on Science.- 9 The Unreasonable Effectiveness of Mathematics the Natural Sciences?.- 10 Do We live in “The Best of Worlds”?.- 11 The Reasonable Effectiveness Computational Mathematics.- 12 Jazz/Pop/Folk vs. Classical Music.- 13 The Right to Not Know.- 14 An Agenda.- II Essence.- 15 A Very Short Calculus Course.- 16 The Solar System.- 17 Turbulence and the Clay Prize.- 18 Do Mathematicians Quarrel?.- III Appendix.- A Comments on the Directives of the Mathematics Delegation.- A.1 The Directives.- A.2 Comments.- A.3 A Sum Up.- B Preface to Body&Soul.- C Public Debate.

A first-class debate book on the crucial issues of current mathematics teaching Includes supplementary material: sn.pub/extras