This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the two most original creations of the human spirit; (2) mathematics of music; (3) numbers and the music of the east…

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the golden section; (2) the geometry of the pentagon and the golden section; (3) meet Mr. Tau; and (4) the golden…

This is an SMSG elementary school text for second-grade students. The development of mathematical ideas in the text is grounded in appropriate experiences with things from the physical world and the immediate environment. Chapter topics include: (1) sets and numbers; (2) addition and subtraction; (3) sets of points; (4) linear measurement; (5)…

This is part two of a two-part SMSG elementary school text for fifth-grade students. The content is aimed at the development of some of the fundamental concepts of mathematics such as number, numeration, the operations of arithmetic, and intuitive geometry. Chapter topics include addition and subtraction of rational numbers, measurement of angles,…

Six tests were constructed, four on a pictorial level and two on a symbolic level, to measure the performance of fourth-, fifth-, and sixth-grade children, in three different ability groups, on problems concerning ratios or fractions. Two variables were of interest in the four tests on a pictorial level: (a) "equal" ratio situations vs.…

This guide is to assist teachers with motivational ideas for teaching elementary school mathematics. The items included are a wide variety of games (paper and pencil, verbal, and physical), jingles, contests, teaching devices, and thought provoking exercises. Suggestions for selection of mathematical games are offered. The devices are used to…

This report presents a more detailed elaboration and discussion of the mathematical content of the central concepts which have been designated as the Mathematical Strands of the Mathematics Curriculum for grades K-8. In Part I of the report there is a discussion of the pedagogical philosophy which the committee felt was to have an importance equal…

The intent of this paper is to suggest and illustrate how electronic hand-held calculators, especially non-programmable ones with limited data-storage capacity, can be used to advantage by students in one particular aspect of work with polynomial functions. The basic mathematical background upon which calculator application is built is summarized.…

Explorations involving the use of mini electronic calculators in connection with mathematics instruction were conducted with two fifth-grade classes, two second-grade classes, and one third-grade class. Explorations are being continued with third-grade classes (last year's second grade classes). Selected activities and related materials are…

The main purpose of this study was the exploration of the relationship between first graders' performance on traditional readiness measures and their performance on an instrument based on Piagetian tasks. All correlations among the predictive indices considered were significant (p less than .01), as were the correlations of these measures with…

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 functionl-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

This text is the fourth of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This text begins with a brief discussion of quadratic equations which motivates the…

Included are the standard topics presented in the undergraduate and/or graduate course on methods of teaching mathematics in elementary education. Chapter 1 describes the historical development of learning theories, including Piaget's. Chapter 2 contains a biographical sketch of Piaget and an explanation of his theory of cognitive development.…

This book emphasizes the importance of teaching mathematics in a meaningful way. It is designed for elementary school teachers who are interested in why and how certain mathematical concepts and skills work. Topics discussed include: numbers and numerals; sets and sentences; the teaching of addition, subtraction, multiplication and division in the…

To investigate the efficacy of a training procedure designed to facilitate the attainment of the mathematical concept of number conservation, 43 children from grades 1 and 2 were tested for their ability to conserve. Some of the pupils were found to be nonconservers; some, transitional conservers; and some, conservers. Pupils of the first two…