Almost 50 years ago, Arthur Coxford and I developed a high school geometry course in which geometric transformations were fundamental to the mathematical development. Properties of reflections and size changes (dilations) were taken as postulates and used to deduce properties of symmetric figures, the traditional theorems of triangle congruence…

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

In this article, a continuation of SE 513 148, the author presents seven additional applications of group theory to high school mathematics. These applications can be used, not only to illustrate the group concept, but also to extend the development of ideas in the high school curriculum. (SD)

Derivations of elementary trigonometric identities involving constants (namely, particular values of the sine function) are presented. (MK)

The possibility of non-transitivity of preference choices is discussed. One example each from voting and from sports demonstrate some conditions where transitivity does not hold. Suggestions are made for using this type of problem in the classroom. (LS)

This two-volume set is a self-help student text designed as an alternative to the standard algebra text. Each lesson is introduced by and centered around an application of the topic under discussion. For each lesson, questions are given covering the reading, testing understanding of the reading, and for discussion. Some sections contain questions…

The author argues against some topics included in the standard high school mathematics curriculum, including traditional algebraic word problems, trinomial factoring, complicated fractional expressions, and some geometric theorems and proofs. (MP)

Documents some of the changes that have taken place in secondary school mathematics curriculum. Examines the reasons for the changes in thinking that have brought applications of mathematics from a position of relative nonexistence in the 1960s to one of major importance in the 1990s. (GR)

A series of interesting mathematical applications for the greatest integer function are presented. (JT)

Enrichment activities that teach about geometry as they instruct in geometry are given for some significant topics. The facets of geometry included are tessellations, round robin tournaments, geometric theorems on triangles, and connections between geometry and complex numbers. (MNS)

The Van Hiele level theory offers an explanation and a remedy for student difficulty with higher-order cognitive processes required for success in secondary school geometry. This document reports results of a study which involved about 2700 students in 13 high schools, selected to provide broad representation of community socio-economics in the…

Responds to Crowley's and Wilson's articles on the reliability of the van Hiele Geometry Test. Discusses the issue of the difficulty of trying to maximize content validity while minimizing measurement error. (YP)

Argues that first-year algebra should be taught in eighth grade. Outlines an algebra course that could provide average students with a working kowledge of algebra. Proposes that this would require students to have experiences with variables, equations, formulas, and graphs during previous years of study. (TW)

The aim of this project was to develop a curriculum for first-year algebra students to provide a wide range of applications of mathematics. This type of application would permit students to understand how algebraic symbolism develops out of natural needs. A pilot draft of the materials was field-tested during the 1974-75 school year, revised, and…