Patterns in an array of numerals are analyzed; suggestions are given for guided discovery activities leading to a discussion of the properties of identity, closure, commutativity, inverses, and associativity. (DT)

Discussed are some applications of Euler's Formula N plus F minus E equals Z, where N, F, and E are respectively the number of vertices, faces, and edges of a planar figure. In particular, the Four-Color Problem is proved for the special case of five countries. (CT)

Defends new math by stating that most new math programs were never correctly implemented, that scores on the Scholastic Aptitude Tests and other aptitude tests were lower not only in math but in verbal ability as well, and that math concepts have not been learned in either new math or traditional curricula. (CS)

The author discusses the recent history of mathematics education. He argues that the curricular reforms of the 1950's and 60's are too important to discard, and that, rather than discard these programs, mathematics educators should remedy their defects. (SD)

The concept of function is central to the teaching and learning of mathematics. As a mathematical notion, the concept of function is fundamental, yet powerful, and is a unifying theme that is found running throughout most branches of mathematics. Until quite recently, when it came to the elementary transcendental functions it was commonly…

In this paper we present three cases of instructional design that illustrates both horizontal didactising, the activity of using already established principles to design instruction, and vertical didactising the activity of developing new tools and principles for instructional design. The first case illustrates horizontal didactising by…

The recommendations of the National Advisory Board on Mathematics Education are summarized. After an 18-month study period, this board concluded that mathematics programs offered in various schools are quite diverse. Recommendations concern use of calculators, testing, and the teaching of statistics as well as other subjects. (SD)

Arguing for a mathematics curriculum based on pure mathematics, the author suggests that applications be used for motivational purposes. (SD)

Mathematical processes involve both rigorous logical thinking and creativity. The difficulty with the new math seems to lie with its apparent reliance on logic alone. It is important to stress intuition and guessing as well as deduction in order to make mathematics better understood. (SD)

AN EVALUATION WAS CONDUCTED TO ANSWER THREE QUESTIONS--(1) HOW MUCH DID ELEMENTATY SCHOOL TEACHERS WHO VIEWED INSTRUCTIONAL TELECASTS ON MODERN MATHEMATICS KNOW ABOUT THE NEWER MATHEMATICAL CONCEPTS BEFORE THE SERIES OF PROGRAMS BEGAN, AND WHAT WERE THEIR ATTITUDES, (2) HOW MUCH DID THE TEACHERS KNOW, AND HOW MUCH WERE THEIR ATTITUDES CHANGED…

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) Laplace; (2) Carl Friedrich Gauss; (3) Wolfgang and Johann Bolyai; (4) Evariste Galois; and (5) Josiah Willard Gibbs.…