The author gives a method for involving students in developing and verifying elementary number theory hypotheses by studying areas and perimeters of primitive pythagorean triangles. (MN)

A mathematical card game, based on the actual card game, is described for providing practice with positive and negative numbers. (JT)

The opportunity for students to develop formulas that involve tangent lines to a circle and the Pythagorean Theorem and to use approximation and common sense is provided in a suggested distance-to-horizon problem. (MN)

The concept of even and odd integers is explored through the use of fractions. (JT)

The good and bad points of Euclidean geometry and transformation geometry are briefly surveyed with emphasis on the teachability of Euclidean geometry and the mathematics of transformation geometry. (MN)

The author examines certain areas of confusion which arise in the teaching of linear equations for lines. (SD)

Several approaches to the teaching of matrices are discussed. (SD)

Several examples through which the Klein 4-group can be introduced are offered. (SD)

Presented is a sequence of ruler and compass constructions which are connected with the triangle. (SD)

The British schools are moving toward a single comprehensive examination for the Certificate of Secondary Education (CSE). The current CSE syllabus and examinations are outlined and criticized. (SD)

Two transcripts of children exploring and solving problems presented by computer programs are given. The transcripts show the insight that occured. (MNS)

An application of spreadsheets, not specific to any particular spreadsheet, is provided. It provides an exploration involving numbers in the form of 3x3 magic squares and 3x3 magic cubes. Strategies for their use are noted. (MNS)

The method of finite differences is discussed with some applications. The method is described in detail, with illustrative sequences, and several problems are presented. (MNS)

Why the term precalculus was introduced is first noted. Then five reasons why it should be eliminated are given, focusing on the points that it is vague, misleading, and misused. (MNS)

Discontinuing use of the term "negative" in reading -x is suggested; rather, "the opposite of x" is suggested. A definition is given, plus two worksheets to help students understand the meaning. (MNS)