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. This series should assist in opening up avenues of investigation to those who are interested in broadening the foundations of their profession. The seven studies found in this volume are: An Experiment in the Psychological Analysis of Algebraic Errors; Pupils' Comprehension of Geometric Proofs; Elements of the Historical Approach in Teaching Mathematics; Overcoming Students' Errors in the Independent Solution of Arithmetic Problems; Stimulating Student Activity in the Study of Functional Relationships; Psychological Grounds for Extensive Use of Unsolvable Problems; and Psychological Characteristics of Pupils' Assimilation of the Concept of a Function. (Author/MK)