Presented with appropriate formulas and illustrations are five lessons suitable for college mathematics undergraduate students, including Pi and the limit of (sin alpha)/alpha, the structure of orthogonal transformations, a simple proof of Zorn's Lemma, the converse of Liouville's Theorem, and visualizing the p-adic integers. (JJK)

Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)

Analysis of students' work on tasks relating to reflections, translations and rotations is discussed. Findings from research with regard to students' understanding of a subject would help teachers prepare for the class.

In the nineteenth century many people tried to seek a value for the most famous irrational number, [pi], by means of an experiment known as Buffon's needle, consisting of throwing randomly a needle onto a surface ruled with straight parallel lines. Here we propose to extend this experiment in order to evaluate other irrational numbers, such as…

Paper folding activities can illustrate transformations that are circular and finite under one set of conditions and become rectangular and infinite when conditions change. (SD)

Four prominent oblique transformation techniques--biquartimin, direct oblimin, promax, and the Harris-Kaiser procedure--are described and compared as to optimality of solution. Additionally, two newly-developed procedures--falling into the category designated as Case III by Harris and Kaiser (1964)--are presented and included in the comparisons.…

In this paper a rather general theory of oblique factor rotation is outlined. The main results are formulated as four theorems. Necessary and sufficient conditions are derived for two factor matrices to admit identical factor structures and/or factor patterns with factors having unit variances. These conditions are expressed in terms of…

A new general approach to the problem of oblique factor transformation is identified and presented as an alternative to the common "blind" transformation techniques currently available. In addition, techniques for implementing such an approach are developed. The first section of the paper contains a brief review of the procrustes problem. The next…

This essay discusses the sketching and transformation of parabolas and other curves as areas where learners can exercise and develop control of their mental imagery. (MN)

The article is based upon the author's experiences in England and America. (JM)

The results of a study of UICSM materials for seventh and eighth grade low achievers show that students studying Stretchers and Shrinkers learned just as much arithmetic as students in traditional programs and that students studying Motion Geometry did significantly better in arithmetic application and total score on the Stanford Achievement Test…