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) axioms in algebra; (2) the foundations of algebra; and (3) noncommutative algebra. (MP)

This manual was designed for use with the first of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

The author discusses the impact of mathematical developments around the turn of the century, and historical concerns and development of mathematics education. This article is a continuation of SE 515 504. (SD)

Rational points in the plane were defined as points having both coordinated rational. Students solved several problems linking rational points with lines, circles, and other geometric figures. (SD)

Use of graphs in studying greatest common divisors, least common multiples, and other concepts can illustrate patterns related to the definitions of these concepts. (SD)

Presents a covariation approach to learning exponential and logarithmic functions based on a primitive multiplicative operation labeled splitting that is not repeated addition. Suggests that students need the opportunity to build a number system from splitting structures and their geometric forms. (30 references) (MKR)

The teaching of negative numbers poses problems at the school level. A historical account of the intellectual difficulties in the evolution of negative numbers and a method of viewing negative numbers as an extension of the number system to help overcome these difficulties are presented. (MDH)

Presents an activity using fractal cards--eye-catching pop-up cards--by applying simple iterative processes to single sheets of paper. This activity incorporates the concepts of measurement, number systems, sequences, series, limits, recursion, iteration, self-similarity, and fractional dimensions. Contains 12 references. (ASK)

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…

A series of questions can be posed and resolved in the process of teaching that the decimal expansions of rationals are terminating or repeating. (SD)

Patterns emerging when two-digit numbers in various bases are operated on by squaring and summing the digits. (SD)

The purpose of this report is to make a tentative contribution to the knowledge of students' understanding of the significance of numerical information. The article relates to a study made by the author. (Author/MK)

Discusses how American and Canadian Indians created mathematical connections and the first numeration systems used north of Mexico. A listing of various tribes, their locations, and how their simple or complex methods of computing may have originated from establishing a correspondence between different parts of the body and quantities they wished…

This outline is for a pre-algebra course designed to prepare students for algebra or to satisfy a one-year mathematics requirement. A key purpose is to present a practical mathematical experience. A detailed outline is given with a suggested time allotment for each chapter. A discussion of each topic follows with teaching suggestions and examples.…

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include the decimal system, exponential notation, base seven, and the binary and duodecimal…