Identifies difficulties of using microcomputer-based systems as surrogate teachers and some benefits from their appropriate use in partnership with the teacher. Uses considered include application program, simulation program, drill and practice, tutorial program, computer modeling, and administration program. (JEG)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

Presents examples of the use of mathematical modeling in mathematics courses in order to not lose sight of the essence of the mathematical attitude; encourage students' concern with problems that surround them; appreciate human resources; and associate mathematics with other sciences. (MKR)

This document consists of seven chapters. The first chapter analyzes the modeling process and gives reasons for introducing a modeling approach in classrooms, arguing that students will develop more confident and positive attitudes toward mathematics. The next five chapters contain case studies, which focus, respectively on: whether it is more…

It is noted that helping children learn how to solve problems has become a major goal for school mathematics. However, many children are not very successful at deciding what operation is appropriate for solving a given problem, and teachers often have difficulty describing or explaining how to identify the key features of a particular problem that…

The utilization of computer programed mathematical models for educational planning has a brief but rapidly accelerating history. This paper describes and, to some extent, evaluates several of these models. It also discusses some of the theoretical problems associated with their formulation and implementation. Models surveyed are of: (1) the…

The paper contains a model of a technique for increasing the quality of educational and instructional opportunity for all students. This model is developed around the flexible or modularly scheduled secondary school. Also included is a procedure containing a computer program, with which the administrator can develop the master schedule of the…

Some concrete examples of the use of historical materials in developing certain topics from precalculus and calculus are presented. Ideas which can be introduced with a reformulated curriculum are discussed in five areas: algorithms, combinatorics, logarithms, trigonometry, and mathematical models. (MNS)

How children can be guided to see and feel the power of thinking with and about mathematical symbols is discussed. A strategy to help them bridge the gap between manipulative models and symbols is detailed. (MNS)

Using manipulative materials and pictures is considered valuable, but the need to use models appropriate for individual children is stressed. Suggestions for using well-structured physical space are given. (MNS)

Helping children to bridge the gap between physical materials and symbolic representations is the focus of this article. Examples are drawn from numerical topics, with several hierarchies illustrated. (MNS)

The use of saltine crackers to illustrate whole numbers, decimal fractions, common fractions, percents, money, and other mathematical concepts is reviewed. (MP)

Focuses on the concept of compound functions and an application of this concept using the tax rate schedules from 1999. Presents an activity designed to help students learn how much income goes to pay federal income tax. (KHR)

Argues the usefulness of algebraic and topological mathematical models and general principle formulation for educational research. Applies an algebraic model to relate learning to the pace of instruction. Formulates two broad principles: the Quantitative and Qualitative Teaching Principles (more teaching produces more learning; and learning is…