The Teaching Of Mathematics | A. Ya. Khinchin

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 firstarticle on basic concepts, Professor Khinchin stresses the basic importance of teaching so as not to conflictwith 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.