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…

While functions and relations are important concepts in the teaching of mathematics, research suggests that many students lack an understanding and appreciation of these concepts. The present paper discusses an approach for teaching functions and relations that draws on the use of illustrations from database management. This approach has the…

Mathematical skills and reasoning and their applications are considered as forming one of the basic and essential areas of knowledge and experience that should be available to all Australian children. This collection of essays explaining problem solving in mathematics as an organizing theme for current and future curriculum development is a means…

Algebraic equations and geometric forms are useful in teaching and learning composition. Algebraic equations can illustrate the modular nature of paragraph structures and can be refined by students to describe types of paragraphs. Discussion of the "slippery" nature of words and their power of transformation can be a lecture topic as the class…

This report is concerned with the observation that many teenagers and adults are unable to apply arithmetic even when they know how to perform the operations. It is speculated that this is probably due to not having been taught when to use the fundamental operations. Examples of types of "real" problems which require the various…

Several models for problem solving are discussed, and the idea of a heuristic frame is developed. This concept provides a description of the evolution of problem-solving skills in terms of the growth of the number of algorithms available and increased sophistication in their use. The heuristic frame model is applied to two sets of physical…

The author outlines the development, structure, and teaching and assessment problems of one introductory discipline-independent mathematical modelling course. (MN)

Strategy games are used to expose teachers and their students to the techniques and strategies involved in true problem solving. (JT)

Analysis of errors children make is modeled both with and without computers. Patterns of thinking are traced for a fifth grader, with the discussion focused on getting clues for remedial instruction by analyzing the dialog. (MNS)

A variety of tips about problem solving are included, with the focus on helping students recall an image. Manipulative materials and models using grids are included in most of the activities. (MNS)

Traditional word problems have not fulfilled the goal of mathematical sense-making for many students. Some studies have shown that authentic contexts, such as model-eliciting tasks, have the potential to engage students in making sense of realistic situations. However, there has been little research on the kinds of knowledge needed by teachers to…

Student weaknesses on problem-solving portions of the NAEP mathematics assessment are discussed using Polya's heuristics as a framework. Recommendations for classroom instruction are discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).