In this post, we will see the book The Teaching of Mathematics by A. Ya. Khinchin.

About the book

Khinchin was a teacher-genius before his time and a mathematician of outstanding calibre. The main contents of this book are four articles written by A. Ya. Khinchin for Russian mathematics teachers. 101 pages are devoted to four articles written between 1938 and 1949 by Khinchin (who died in 1959), the remainder of the book to biographical notes and an appendix on mathematics teaching in the Soviet school.

One of the best sections is the one on the concept of limit. The author traces the historical development of the limit concept to determine which approach is best suited for the schools.

In his first article on basic concepts, Professor Khinchin stresses the basic importance of teaching so as not to conflict with later learning. He favors simplification, but never falsification. He advocates precise language

The second article on Mathematical Definitions is excellent and should be read by high school teachers. The discussion of the difference between a definition and a description and when it is desirable to present each is particularly good. It is refreshing that a mathematician of Khinchin’s standing had such understanding of teaching problems.

Some absolute gems of advice and insight to consider if you are in education. Though written 80 years back the ideas of Khinchin are very relevant now.

The book was edited by B. V. Gnedenko and was translated from Russian by W. Cochrane and D. Vere-Jones. The book was published in 1968.

Credits to original uploader.

You can get the book here.

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Contents

Introduction by Ian N. Sneddon vii
Translators’ Foreword ix

B. V. Gnedenko

Introduction to the Russian edition xiii
Note for the English edition xx

A. Ya. Khinchin

Basic Concepts of Mathematics in the Secondary Schools 1
Section 1 The Concept of Number 1
Section 2 The Concept of Limit 20
Section 3 The Concept of Functional Dependence 31
Mathematical Definitions in the Secondary Schools 44
On Formalism in School Mathematics Teaching 60
On the Educative Effect of Mathematics Lessons 77

Appendix 1

B. V. Gnedenko and A. I. Markushevich 102
A. Ya. Khinchin: A Biographical Sketch 113
Bibliography of Publications 115

Appendix 2

D. Vere-Jones
Mathematics Teaching and the Soviet School 117

List of General References 165

Popular Lectures in Mathematics: Edited by I. N. Sneddon 166

Topics in Mathematics: Edited by A. L. Putnam and I. Wirszup 167