The "positive-negative charge" model is described and demonstrated with all four operations on integers. Its major advantages are that it is both concrete and complete. (MNS)

A model for directed numbers, using a sentry moving along the number line, is described. (MNS)

A model is offered which can be used for teaching addition, subtraction, multiplication, and division with directed numbers. Illustrations for all operations are given. (MNS)

Shows how to model Newton's method for approximating roots on a spreadsheet. (MKR)

Mastering the basic number combinations involves discovering, labeling, and internalizing relationships, not merely drill-based memorization. Counting procedures and thinking strategies are components, and it may be that using stored procedures, rules, or principles to quickly construct combinations is cognitively more economical than relying…

A way to use tongue depressors in a model of multiplication is presented. The original intent was to use the sticks to teach about fractions, but "mistakes" in student responses led to new ideas. It is felt that teachers should use the model in teaching multiplication. (MP)

Uses chaos theory to investigate the nonlinear phenomenon of population growth fluctuation. Illustrates the use of computers and computer programs to make calculations in a nonlinear difference equation system. (MDH)

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

Models to assess the impact of a college on the local economy are examined. A primary objective was to derive equations for which data could be obtained from normal records kept by colleges, local governments, and businesses. The models, which are designed to be used by college presidents and their staffs, are linear cash-flow formulas, including…

Emphasizes a real-world-problem situation using sine law and cosine law. Angles of elevation from two tracking stations located in the plane of the equator determine height of a satellite. Calculators or computers can be used. (LDR)

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

This document describes the contributions of African peoples to the science of mathematics. The development of a number system is seen as related to need. Names of numbers, time reckoning, gesture counting, and counting materials are examined. Mystical beliefs about numbers and special meanings in pattern are presented. Reproductions of patterns,…