From a very young age, shoes for boys tend to be wider than shoes for girls. Is this because boys have wider feet, or because it is assumed that girls are willing to sacrifice comfort for fashion, even in elementary school? To assess the former, a statistician measures kids' feet. (Contains 2 tables and 3 figures.)

Forty-two studies comparing students with access to graphing calculators during instruction to students who did not have access to graphing calculators during instruction are the subject of this meta-analysis. The results on the achievement and attitude levels of students are presented. The studies evaluated cover middle and high school…

Mathematics is usually seen as a field in which there is value-free. Such a situation causes only a few studies about values teaching to be done in mathematics education. But, mathematics is a field that has various values in it, and that must be considered seriously from this perspective. Values are taught implicitly rather than explicitly in…

Ithaca College, in New York, has developed and tested a projects-based first-year calculus course over the last 3 years which uses the graphs of functions and physical phenomena to illustrate and motivate the major concepts of calculus and to introduce students to mathematical modeling. The course curriculum is designed to: (1) emphasize on the…

This volume contains the papers and comments from the Workshop on Mathematics Education, a special session of the 15th Conference on Stochastic Processes and Their Applications, held in Nagoya, Japan, July 2-5, 1985. Topics covered include: (1) probability; (2) statistics; (3) deviation; (4) Japanese mathematics curriculum; (5) statistical…

This paper is a discussion of algebraic factoring. It is suggested that factoring is frequently presented in textbooks and by teachers without specifying one of the great values of this technique; that is, finding some of the factors of any number that can be generated by a particular polynomial. Concrete examples can help students understand the…

Competence in dealing with mathematical model building requires mathematical knowledge, technological knowledge about how to develop a model, and reflective knowledge relevant for evaluation of the model building process. A general conceptual framework for identification of reflective knowledge is presented by a structural and a developmental…

Describes a college-level course that develops an awareness and understanding of environmental issues through instruction of mathematical concepts and processes, presenting sample mathematical problems which illustrate how environmental issues are used as themes for teaching mathematical skills. Also provides a list of annotated references for…

In this paper, we discuss issues in planning and conducting research into mathematics learning. We emphasize two central themes: (1) the learners' mathematics (especially the issues and ideas, in given problem situations, that learners choose to think about and to present; and (2) the kinds of knowledge that learners may be building (including…

The "call for change" issued by the Board of Governors of the Mathematical Association of America (MAA) in "A Call For Change: Recommendations for the Mathematical Preparation of Teachers of Mathematics, 1991" may appear at first glance to concern only the mathematical preparation of teachers. However, two ingredients combine…

The use of exponentiation as a starting point for an open-ended exploration of real number ideas is presented. (MP)

The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)

That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)

Presented is an example of a question that can be used to investigate probability and random triangles. Included is the question, analysis, and procedure for solving the question. (KR)

Described is a geometric view of Singular Value Theorem. Included are two theorems, one which is a pure matrix version of the above and the other that leads to the orthogonal diagonalization of certain matrices, i.e., the Spectral Theorem. Also included are proofs and remarks. (KR)