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…

This report consists of five separate papers. The first is an extensive review of the "state of the art" in computer simulation and artificial intelligence. This review states that artificial intelligence and computer simulation have accomplished a great deal, with particular attention to findings relevant to psychology. The second paper is an…

A discussion of differential equations is accompanied by an analysis of two situations whose solutions require differential equations. A computer program is given that will solve these equations. (MP)

Discussed is the problem of finding the volume common to two intersecting right circular cylinders. (MP)

It is advocated that introductory calculus texts should present topics in a manner that is understandable to students without necessarily sacrificing rigour. Illustrative examples are given of a conversational approach to problem solving. (Author/MN)

This paper considers the aspect of heuristic teaching in which theorems are introduced in the form of problems and the proofs of these theorems as solutions to problems. The traditional treatment along with an illustration of a heuristic approach is discussed for each of several well-known theorems. (MN)

The often-neglected strategy of looking back is discussed, with an example. Considering what-if-not is described with generalizations of the problem. (MNS)

The focus is on the problem-solving strategy "write an equation." Other topics to develop problem-solving skills are included. (MNS)

Solving a problem using the work-backward strategy is discussed, with tips on other facets of problem solving. (MNS)

An example is noted in which a given problem is reformulated and extended. The problem solving includes discussion and dispute, plus the recognition that different approaches are both possible and desirable, is thus demonstrated. (MNS)

This book is a year-long program of daily exercises in problem solving for 2nd and 3rd grade students that presents 144 lessons, each with seven problems. The problems cover number sense, computation, measurements, geometry, problem solving, and patterns. The material is presented in a sequential fashion with concepts repeated and expanded, and…

An experimental calculus class was instructed by inquiry-style presentation incorporating heuristic problem-solving strategies. A control class was also instructed using an inquiry style, but with no emphasis on heuristics. Based on interviews, it is suggested that heuristic-oriented instruction can be an effective mode of teaching problem…

Decision exercises using a finite state machine and replacement systems are described in this second of two articles. For the first article, see MT No. 62, March, 1973, pp. 50-55. (DT)

General verbal problem solving techniques and a modified wanted-given technique were compared. Fifth graders using either of these two techniques did not score higher than control groups. Those using the wanted-given technique used correct procedures significantly more often. (DT)