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) Srinivasa Ramanujan; (2) Minkowski; (3) Stefan Banach; (4) Alfred North Whitehead; (5) Waclaw Sierpinski; and (6) J.…

This report is a continuation of a study conducted at the University of Wisconsin during the spring of 1967. The previous study, Technical Report #38, succeeded in teaching conservation of numerousness to small groups of kindergarten children, in a middle-class community. The purpose of the present study was to determine if the typical classroom…

This is Part 1 of the second course in a series which focuses on building fundamental mathematical structures. Topics considered in this book include: an introduction to mathematical logic and mathematical proof, a continuation of the study of groups, an introduction to axiomatic affine geometry, fields, the real number system, and coordinate…

Topics included in Part 2 of Course II are: real functions; descriptive statistics; transformations in the plane; length, area, and volume; combinatorics; and mass points. The chapter on real functions includes a discussion of properties of functions, composition of functions, inverses of functions and other topics. The chapter on descriptive…

It is extremely difficult to extend in a natural way the concepts developed in high school geometry to motivate the concepts of trigonometry. To solve this difficultry, the author defines "sensed angles" as ordered pairs of rays and makes appropriate definitions which yield the familiar angle properties of plane geometry. He then shows how this…

Behavioral differences between school superintendents who achieve their positions through promotion in the home district (place bound) and those who achieve their positions through movement from one school system to another (career bound) were analyzed by means of interviews with 61 superintendents in one county. The study examined the rate of…

The 1959 Royaumont seminar "New Thinking in School Mathematics," having agreed on the need for modernization, recommended that a second group of experts work out detailed synopses of the entire subject matter of secondary school mathematics. This book is the report of the second seminar and contains the Dubrovnik Program which stimulated…

This is the ninth in a series of ten self-contained units designed for use by students in ninth grade general mathematics classes. This unit is divided into six sections dealing with different concepts involving positive and negative numbers. Some concepts presented include positive and negative integers, addition and subtraction, multiplication,…

This is the sixth in a series of ten self-contained units designed for use by students in ninth grade general mathematics classes. This unit is divided into eight sections dealing with different types of mathematical thinking. Some topics presented include functions, permutations and combinations, symmetry, inductive thinking, and logic. Though…

This publication is part of a series of guides written by Pennsylvania's Department of Public Instruction and is designed to present some of the unifying concepts in mathematics to elementary teachers. This pamphlet discusses the commutative, associative, and closure properties for addition and multiplication of whole numbers, and the distributive…

The purpose of the study was to compare the effectiveness of instruction using modern mathematics materials to instruction using traditional materials. Arithmetic achievement comparisons of sixth and eighth grade groups for the 1968-69 school year were made with their counterparts for the 1964-65 school year. Five schools were included. Subtests…

Reported are research projects questioning the effectiveness of inservice teacher training and the effects of various mathematical curricula on student learning. (GW)

Reviews the use of diagrams in presenting new materials as a reflection of the growing generality of mathematics education in England. Social needs, mathematical research, learning theories, school population, and technology are given as reasons for rapid change in mathematics education. Available from: 18 Campden Grove, London, W8 4JG, England.…

The "old math" and "new math" are compared on the basis of their goals and objectives. The authors argue that revision in curriculum and in research related to mathematics education is necessary, and provide several suggestions for directing change. This journal is available by writing to: Search, State University of New York, 99 Washington…

The history of mathematics curriculum revision since 1900 is described, the present day school mathematics situation is analyzed, and suggestions for a two-track mathematics program are given. (DT)