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…

A model of conceptual change, adapted from Posner, is presented. It includes both the replacement of an existing concept (conceptual exchange), and the incorporation of a new concept (conceptual capture). Conceptual exchange occurs only when an existing concept is dissatisfying and a new concept is intelligible, initially plausible, and fruitful.…

TO VERIFY A PREVIOUSLY OBSERVED DEVELOPMENTAL INVERSION IN PROBLEM-SOLVING ABILITY AND TO EXPLORE PROBLEM-SOLVING STRATEGIES, RESEARCHERS GAVE A SET OF SEQUENTIAL-PATTERN RECOGNITION TESTS TO 316 CHILDREN, REPRESENTING NURSERY SCHOOL THROUGH SIXTH GRADE. EACH TEST CONSISTED OF FINDING TOKENS PLACED BEHIND 5 DOORS IN A PREDETERMINED PATTERN. THE…

ACCORDING TO PIAGET, THE CONCEPT OF CONSERVATION IS A PREREQUISITE TO MATHEMATICAL UNDERSTANDING. THIS STUDY SOUGHT TO DETERMINE WHETHER THE ABILITY OF FIRST GRADE CHILDREN TO SOLVE ADDITION PROBLEMS WAS DEPENDENT ON THEIR MASTERY OF CONSERVATION OF NUMEROUSNESS. SECONDARY PURPOSES WERE TO INVESTIGATE THE EFFECT IN PROBLEM STATEMENTS OF (1)…

ELEMENTARY SCHOOL PUPILS' ABILITY TO USE EVIDENCE FROM SCIENTIFIC INSTRUMENTS WAS DETERMINED. THE 320 PUPILS FROM GRADES ONE THROUGH SIX WERE PLACED IN DECISION-MAKING SITUATIONS REQUIRING THEM TO USE EVIDENCE FROM A PLATFORM BALANCE OR GRADUATED CYLINDER. PUPILS WERE REQUIRED TO DIFFERENTIATE BETWEEN MASSES OR VOLUMES OF PAIRS OF OBJECTS. THE…

This research furthers our understanding of the relationship between an organismic factor, "cognitive style," and performance on concept learning and information processing tasks. These results, obtained from students in grades six, eight, and 10, indicate that not only do "high analytical" type students perform better on this…

Verbal protocols were collected from math-anxious and math-comfortable college students while they solved algebra problems. These protocols were then examined for differences in problem-solving processes. Differences occurred in the use of two basic strategies: generating values and symbolic transformations. Math-anxious students generated more…

This study extended over two academic years and involved six biology teachers and 199 students in nine slow-learner classes in four high schools. Classroom interaction was observed and recorded, then analyzed using the Flanders System of Interaction Analysis. Teachers were assigned specific roles of maintaining a definite interaction pattern or of…

A series of exploratory studies and three experiments dealing with conceptual rule learning are reported in this paper. Discussants related the results to subject matter fields and to educational research and development. Four groups of subjects, five to twelve years old, solved six rule learning problems. It was concluded that younger children…

The present study examines the role of conceptual tempo on creativity and problem solving. It was hypothesized that reflective children would do well on tasks involving an evaluation component, while impulsive children would do well on typical creativity tasks. Measures of creativity, assessing fluency, flexibility, and originality, as well as…

Vocalizing and nonvocalizing pairs and individuals solved four three-attribute conjunctive problems. In terms of overall effectiveness, vocalizing pairs were superior; individuals vocalizing to a confederate, individuals vocalizing to the experimenter, and nonvocalizing individuals were intermediate, in that order; and nonvocalizing pairs were…

Examples from almanacs are used to provide real-life problems that involve estimating, computing, and thinking. (MP)

Data show that disadvantaged students can be taught problem-solving strategies in mathematics and can reach a level of mastery in mathematical thinking that is not expected from their performance on I.Q. tests. (MP)

Students often fail to apply knowledge and skills learned in one context to other situations. Although the implicit assumption in educational practice has been that transfer takes care of itself, a knowledge of the mechanisms of transfer can enable educators to help their students integrate general and local knowledge. (TE)

Explores how a set of possible student misconceptions about solving a complex problem can be used in computer-based intelligent tutoring systems and in computer-based exercise and test generation. Topics discussed include expert systems, misconception covers, discrimination trees, methods of acquiring the set of misconceptions, and protocol…