Article addressed itself to the question of relationships between the cognitive styles of subjects and their use of certain solution strategies on a concept attainment task in mathematics. (Author/RK)

Several ideas for activities related to statistical concepts and the methods of using probability to analyze situations are presented. (SD)

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

Data from three separate experiments were employed. College undergraduates were taught laws of logarithms by means of the same lesson material, and received the same twenty-item posttest after they were instructed under one of three learner control conditions. In the complete learner control condition, students chose both the sequence and number…

The question of how Piaget selects mathematical concepts for his theory is addressed as a problem which may have contributed to a misinterpretation of the relevance of conservation studies for mathematics education. A new form of pseudo-conservation is discussed in which nonconservers of length are able to pick out strips of equal length from an…

This student discussion guide is intended to accompany "Discovery in Mathematics," a text for teachers. This guide is a part of the developing curriculum program that helps students to organize their mathematical experiences in the early school years. The materials in this booklet deal mainly with fundamental arithmetic and algebraic…

A model for learning and teaching mathematics is described which focuses on the relationships between mathematical concepts, the psychology of the learner, and instruction. The model distinguishes between figural and operational concepts and the types of abstraction (simple vs. reflective) needed to comprehend these concepts, that is, to…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…

This paper reports results of two retention studies. In each, tests were given some time after instruction to a class of students whose initial level of performance was quite high. Results of these studies are summarized in terms of evidence related to the following questions: (1) to what extent are performances immediately following learning…

This report describes research conducted regarding the development of a precise scientific language called the "Set-Function" Language (SFL) which was formulated in terms of sets and functions. The SFL retains many of the basic aspects of cognitive formulations but also provides more rigor than most of the other scientific languages. The SFL…

This booklet has been written for elementary school teachers as an introductory survey of the real number system. The topics which are developed include the number line, infinite decimals, density, rational numbers, repeating decimals, irrational numbers, approximation, and operations on the real numbers. (RS)

These materials were developed as a practical response to some of the recommendations of the 1963 Cambridge Conference on School Mathematics (CCSM). Experimental sessions are described in detail in this report. In the Estabrook Elementary School, Lexington, Massachusetts, first grade children (1964-65 Academic Year) concentrated on material…

This study interprets and evaluates elementary mathematics research literature and current teaching practice. The list contains three related documents: (11-A) gives answers from research on elementary mathematics. It is the authors synthesis and interpretation of research findings in question-and-answer format; (11-B) offers generalizations and…