Discusses a program in New Zealand to assist high school students who have an aptitude for mathematics. Uses the philosophy of extension and enrichment rather than acceleration and has a teaching emphasis of problem solving and the methodology of the research mathematician. (MKR)

Presents a lesson plan for building and investigating three- dimensional cubes and a representation of a four-dimensional cube, sometimes called a hypercube. Includes reproducible student worksheets. (MKR)

Presented is a series of examples that illustrate a method of solving equations developed by Leonhard Euler based on an unsubstantiated assumption. The method integrates aspects of recursion relations and sequences of converging ratios and can be extended to polynomial equation with infinite exponents. (MDH)

Presents a proof of Euler's Theorem on polyhedra by relating the theorem to the field of modern topology, specifically to the topology of relief maps. An analogous theorem involving the features of mountain summits, basins, and passes on a terrain is proved and related to the faces, vertices, and edges on a convex polyhedron. (MDH)

Discussed is a method of approximating the roots of a quadratic that allows the discovery of relationships between parabolas and circles and between the use of geometry and algebra. Included are the procedure and justification of the method. (KR)

The purpose of this study was to determine how well high school chemistry students can do the basic mathematical operations needed in chemistry and to compare these student abilities to teacher expectations. (CW)

An open-ended data-analysis activity, prompted by a Royal Mail advertisement, explores the claim that the real cost of first class postage has fallen below the inflation rate. The activity provides realistic exercises in both arithmetic and statistical indices, and in logical interpretation of, and deduction from, the data. (JJK)

Presents illustrated examples that promote problem solving through the student's consideration of a visible predicament from a three-dimensional viewpoint rather than the typical planar perspective. Includes six student exercises involving rays, circles, quadrilaterals, and hexagons, with hints and solutions provided. (JJK)

A study analyzed data from the International Association for the Evaluation of Educational Achievement survey of 13 year olds from 20 countries to examine gender differences in mathematics achievement. Multivariate analysis indicated differences varied from country to country and a significant difference in favor of boys in geometry achievement.…

Describes an exploratory geometry course in which students were challenged to develop their own axiomatic system instead of using a textbook. They developed a Euclidean system and learned to write proofs as a natural consequence of building the system. (13 references) (MKR)

Described are classroom strategies chosen to elicit greater involvement by students in the learning process and to furnish opportunities for practice in critical thinking. The advantages and disadvantages of this teaching approach are discussed. (CW)

Compared are the van Hiele levels of geometric thinking and the geometry curriculum recommended by the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Activities which illustrate the various levels are provided by grade level with procedures. (CW)

Included are a list of research summaries and annotations of articles and dissertations listed by author within each category. Grade or age levels are indicated for each level. Articles and dissertations are indexed by mathematics education topics, and a list of the journals covered is included. Over 400 references are reported. (MDH)

An experimental design study compared the effect of periodic use of the "Geometric Supposers" software to nonuse on geometry achievement of two tenth grade classes (n=58). Results suggest that "Geometric Supposers" promotes higher achievement, particularly on Higher Level and Application Problems. No difference on Lower Level…

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)