The author interprets several mathematical concepts as groupings using Piaget's definition. He also discusses (briefly) the implications for primary education. (SD)

The cognitive processes involved in the human ability to understand and use positional notation (i.e., place-value) were investigated in a series of psychological experiments. Although the tasks used in all studies were very simple, usually only requiring the tested individual to identify the larger of two numbers as quickly as possible, a number…

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 study investigated the effect of initial instruction on the processes children use to solve basic addition and subtraction verbal problems. Prior to instruction and following a 2-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different models of addition…

EARLY FORMS OF NUMERICAL REASONING WERE INVESTIGATED BY EXAMINING THE ROLE OF A SET OF VARIABLES IN THE DEVELOPMENT OF CONSERVATION OF NUMBER. CONSERVATION OF NUMBER WAS DEFINED AS THE RECOGNITION THAT THE NUMBER OF OBJECTS CONSTITUTES AN AGGREGATE WHICH IS NOT CHANGED MERELY BY REARRANGING THEM. EXPERIMENT ONE WAS CONDUCTED WITH CHILDREN FROM…

This is part two of a two-part SMSG algebra text for ninth-grade students. The text was written for those students whose mathematical talent is underdeveloped. Chapter topics include the real numbers, addition of real numbers, multiplication of real numbers, properties of order, and subtraction and division for real numbers. (MP)

This is part three of a three-part manual for teachers using SMSG high school text materials. Each chapter contains a commentary on the text, answers to the exercises, and a set of illustrative test questions. Chapter topics include: (1) the system of vectors; (2) polar form of complex numbers; (3) sequences and series; (4) permutations; (5)…

This mathematics data bank of generic objectives was developed as the major element of an implementation of Comprehensive Achievement Monitoring in the Individualized and Personalized Adult Basic Education Program of the Canadore College (North Bay, Ontario) Continuing Education Division. The bank contains approximately 900 objectives organized…

Chapters 4-5 of the special materials written for low achieving students in grades 7-8 by SMSG deal with number theory and the properties of the integers. Included for each chapter are pretest exercises, a self-test, instructional lessons and exercises, and a chapter test. (CT)