Presented is an elementary approach to areas, columns and other mathematical concepts usually treated in calculus. The approach is based on the idea of average and this concept is utilized throughout the report. In the beginning the average (arithmetic mean) of a set of numbers is considered and two properties of the average which often simplify…

This is part of a student text which was written with the aim of reflecting the thinking of The Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for mathematics. The instructional materials were developed for teaching geometry in the secondary schools. This document is chapter six and titled Motions and…

This report represents a survey of some of the school mathematics contests which are conducted in the United States. The report is based on information obtained from fifty-nine national, state, regional, and local level contests. National contests are described separately. Brief accounts of certain school mathematics contests, the extent of such…

This book is a reissue of the second edition which appeared in 1940. It has the distinction of being the first vintage mathematical work published in the NCTM series "Classics in Mathematics Education." The text includes a biography of Pythagoras and an account of historical data pertaining to his proposition. The remainder of the book shows 370…

This booklet is a collection of the papers presented at a joint session of the Mathematical Association of America and the National Council of Teachers of Mathematics during the fiftieth annual meeting of the MAA. These papers were presented under the headings of "Geometry and School Mathematics,""High School Geometry," and…

The uses of the textbook made by the teacher in daily and long-range planning, the uses by the student in daily study and review, and interactive uses between teacher and student relating to homework assignments and reading of the text were investigated. Thirty-six teachers were selected randomly from among those teaching geometry and second-year…

The purpose of the study was to determine if instruction in aspects of sentential logic significantly influenced the growth of logical thinking abilities of junior-high-school students. One hundred fifty-seven students enrolled in seventh-, eighth-, and ninth-grade general mathematics classes participated. The Cornell Conditional Reasoning Test…

The teacher's guide for the first unit of this SMSG series covers the two chapters on elementary geometry and on functions. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives are stated, and a time…

The teacher's guide for the seventh unit of this SMSG series covers the introductory chapter on perpendiculars and parallels and the chapter on similarity. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral…

The teacher's guide to Unit 9 covers the second chapter on perpendiculars and parallels in this SMSG series and the chapter on coordinate geometry. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives…

The teacher's guide for Unit 10 of this SMSG series covers the chapter on problem solving and the chapter on solution sets of mathematical sentences. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives…

The first chapter in the twelfth unit of this SMSG series deals with the following topics involving quadratic functions: parabolas, translations of the parabola, completing the square, solving quadratic equations, "falling body" functions, and the use of quadratics in solving other equations. The chapter on statistics discusses…

This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…

The author presents material suitable for use by teachers of gifted students in the junior or senior year of high school. The mathematics presented includes mathematical induction, the binomial expansion, number theory and Pascal's triangle. The author weaves much of the history of mathematics into the materials. Included are student tests and…

Reported are the results of a correlational study designed to investigate sex differences in various correlates of attitude and achievement in mathematics. Biographical inventories consisting of 90 or 97 true-false statements were constructed to assess mathematical attitude. The inventories were administered to eighth grade, college freshmen, and…