This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the American mathematics educator have been translated from the Russian and appear in this series for the first time in English. The aim of this series is to acquaint mathematics educators and teachers with directions, ideas, and accomplishments in the psychology of mathematical instruction in the Soviet Union. The authors have done a philosophical and psychological analysis of the special problems of teaching mathematics to children. They first create a psychological construct, then develop techniques that follow. The six chapter titles are: The Psychological and Didactic Principles of Teaching Arithmetic; The Introduction of Numbers, Counting, and the Arithmetical Operations; Instruction in Mental and Written Calculation; Teaching Problem Solving; Geometry in the Primary Grades; and Different Kinds of Pupils and How to Approach Them in Arithmetic Instruction. (MK)