Presents a sequence of hands-on activities to help students understand the concept of arithmetic mean and gain experience in using mathematical models. Students create models in the process of solving problems and communicate to the class the meaning attached to the models. (MDH)

Discusses the problem of finding the amount of fence it would require for the outfield fence of a baseball field of given dimensions. Presents different solution methods for each of the levels from grades 9-12. The different methods incorporate geometry, trigonometry, analytic geometry, and calculus. (MDH)

Explains how students can perform a refutation of the ether theory using information from the Global Positioning System (GPS). Discusses the functioning of the GPS, qualitatively describes how position determination would be affected by an ether wind, and illustrates the pertinent ideas with a simple quantitative model. (WRM)

Statistical data can be represented in a number of qualitatively different ways, the choice depending on the following three conditions: the concepts to be investigated; the nature of the data; and the purpose for which they were collected. This paper begins by setting out frameworks that describe the nature of statistical thinking in schools, and…

Whenever teachers of young children get together there will be differences of opinion about how far children should be taught to count. Some will argue that the focus should be on small numbers to 9, building up the notion of what, say, the name 5 means, what it looks like, and how it can be represented. Others argue that with ice blocks retailing…

Presents a device to illustrate the concepts of entropy of mixing and the contribution of one term in the Gibb's equation. Notes the device is relatively easy to construct and provides a visual demonstration on diffusion. (MVL)

Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

Senior secondary mathematics students could justifiably question the relevance of subject matter they are being required to understand. One response to this is to place the learning experience within a context that clearly demonstrates a non-trivial application of the material, and which thereby provides a definite purpose for the mathematical…

How do teachers conceptualize and deal with context of mathematics word problems in their teaching? This question is discussed based on a study of 14 experienced teachers at the elementary, junior high and senior high school levels. Bruner's notions of paradigmatic and narrative modes of knowing formed the basis of analysis of data from sources…

To solve problems of causality and measurement in educational research, this paper combines seven variables into a proposed model of educational productivity on achievement tests. The authors first review psychological models of educational production that relate learning to aptitude and environment, and note that these models do not allow for…

Discussed is the place and teaching of trigonometry in a NCTM Standards-based mathematics curriculum. Presented is how these standards can be implemented in a technology-rich environment that encourages reasoning, communication, problem solving, and confidence building. Examples focus on functions, graphical sense, modeling, and identities. (KR)

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Two mathematical models of paired-associate learning were used to develop optimal strategies for presenting spelling words to 42 elementary school children. The study was conducted within a computer-based drill-and-practice project. For the study two computer programs were developed. One program presented and corrected the lists of words. The…

A rationale for the use of gaming and simulation for instructional purposes is developed in the introduction to this paper. The major portion of the text is comprised of several models of computer programs for economics instruction. (SHM)

Described is a game that is used to introduce the concept of multiplying integers. Serving as a physical model for the concept, "Froggie Frolic" races frogs along a number line by moves that indicate direction, magnitude, and number of jumps, thus modeling integer multiplication. A teacher's guide and worksheets are provided. (MDH)