Methods of instructing students in problem solving are suggested that get pupils to view mathematics as a tool. The author states students should look beyond the numerical answer to the other components and highlights areas of the mathematics curriculum that afford an opportunity to explore these many facets. (MP)

Four teaching ideas are discussed: a "giant" math problem designed to motivate students to use library sources, calculators, computers, and textbooks; a different way of finding fractional equivalents; a task-card project designed to encourage mathematics students to use libraries; and journal writing in a mathematics class. (MP)

A model of competition probabilities using past performances of competitors against common opponents is constructed. Application to predicting victories in athletic competitions is also reviewed. (MP)

The use of silent instruction as a tool to present mathematics to young elementary school students is reviewed. (MP)

The issue of how much emphasis balancing chemical equations should have in an introductory chemistry course is discussed. The current heavy emphasis on finishing such equations is viewed as misplaced. (MP)

Samples of materials available to students from grades 4 through 12 at a Mathematics Center are reviewed. The examples are part of a collection of more than 200 mathematical tasks using solid materials in a new approach to problem solving. (MP)

Data from some geometric exercises administered during the 1977-78 mathematics assessment of the National Assessment of Educational Progress (NAEP) are analyzed, and suggestions for correcting student deficiencies are presented. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Discusses the implications of a research study of more than 2000 students aged 11 to 15 that explored why the students interpret algebra in certain ways. Recommends strategies that can help teachers deal with prior knowledge that students may bring to their study of algebra. (DDR)

Presents an extension of the hog game that satisfies the mathematical process activities of observing patterns; forming, testing and proving hypotheses; and applying and extending proved results. Discusses use of technology in the investigation of problems and in the process of devising and validating general rules. (ASK)

Contains 10 miscellaneous mathematics questions and their answers that teachers can use in their lessons. Topics include estimation, prime numbers, line equations, and investment strategies. (ASK)

Describes an activity whose objectives are to encode and decode messages using linear functions and their inverses; to use modular arithmetic, including use of the reciprocal for simple equation solving; to analyze patterns and make and test conjectures; to communicate procedures and algorithms; and to use problem-solving strategies. (ASK)

Presents materials and methods that maintain student interest and encourage them to think creatively, develop mathematical reasoning, and look at problems from different perspectives, all within an open-ended approach to problem solving. Includes questions for discussion. (KHR)

Addresses the early stages of children's introduction to the use of variables in formal algebraic notation. Describes a teaching approach that aims to situate the use of formal notation in meaningful contexts. Presents a study of a teaching sequence based on children working with this approach using graphical feedback in problem solutions. (AIM)

Two aspects of instructional practice in mathematics are discussed: the process of developing instructional activities and the importance of engaging students in mathematical discussion. The National Council of Teachers of Mathematics (NCTM) Standards are evaluated based on this discussion. (CW)

This special section on cognition and mathematics contains an introduction and 13 articles on advances in the psychology of mathematics learning. The articles focus on how students learn to solve mathematics problems, including arithmetic computation problems, arithmetic word problems, and computer programing problems. (SLD)