Why and how to teach about the real numbers as a complete ordered field is discussed. (MNS)

Properties of the arithmetic mean and the geometric mean are discussed, with an analogy between additive multiplicative averages. Drawing analogies between symbols and relations is proposed as a way of strengthening students' understanding and enriching the study of elementary statistics. (MNS)

This explanation of finding functions includes comments on how to help students move from finding specific solutions to determining generalized solutions. (MNS)

Study of circular transformation and its associated properties is proposed as review and reinforcement of familiar concepts and for developing broader understanding of transformations. Inversion on a circle is discussed in some detail. (MNS)

A definition of convexity with six conditions is discussed and illustrated. (MNS)

A study of a class of numbers called 'Good numbers' can provide students with many opportunities for investigation, conjecture, and proof. Definitions and proofs are presented along with suggested questions. (MNS)

The historical origin of star-polygons is noted and the mathematics of them presented, with illustrations. Seven theorems are included, as well as a computer program designed to classify star-polygons. (MNS)

Described is the geometry of the antenna, particularly the reflective properties of the parabola and hyperbola, which determine the microwave path and concentrate the weak incoming energy. (MNS)

Representation of integers in various bases is explored, with a proof. (MNS)

Two methods for solving matrix equations are discussed. Both operate entirely on a matrix level. (MNS)

How min-max problems can be solved with trigonometry and without calculus is described. (MNS)

This paper discusses some of the factors which have to be considered in constructing an adequate description of the understanding of mathematics. It examines three models of understanding which have appeared during the last three years. (Author/MK)

This learning module is designed to enable teachers to help children further develop their concepts of the meaning of numbers in our number system (including concepts of quanity, one-to-one correspondence, number order, before-after, greater than-equal to-less than, number patterns, and the structure of our number system). The module contains a…

Part I of this guide develops sets and set operations: listing and describing sets, characteristics of sets, universal empty sets, unions and intersections of sets, properties under set operations, differences and complements of sets, Venn diagram interpretations, set notation, ordered pairs, Cartesian products, and equivalent sets. Part II deals…

Exploring the numerical nature of quadratic equations is the focus of this article. Small solutions, the general case, and a detailed analysis are each presented. (MNS)