The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" (the "Standards"), provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. When completed, it is expected…

The purpose of this guide is to provide a resource for teacher use in computer mathematics instruction. Although it is not intended to be used as a textbook or a complete course syllabus, the guide does include a set of student objectives which are designed to define the content of a 1-year course in computer mathematics. The major focus of the…

This document contains a list of recommended essential mathematical skills and outcomes developed for Arizona students from primary through secondary grades. These skills have been developed by using a spiral structure of individual clusters of objectives that are taught at an initial level and then retaught at higher levels as students progress…

This document is the sixth of seven units developed by the Math Network Curriculum Project. Each unit, designed to be a 2-week module, is a teacher's guide which includes detailed directions along with the courseware and software needed. Teacher intervention in the non-computer activities that begin each unit is required, and the consistent use of…

This paper reports the results from one of a series of related, collaborative studies carried out in Sandy Bay, Tasmania, Australia, in 1979 and 1980, examining how young children acquire the skills to represent and solve addition and subtraction problems. The purpose of this study was to relate children's cognitive processing capabilities and…

When one encounters a problem that one has no adequate way of representing, a new mental model for the problem may have to be found. When a possible model is found, an important next step is to evaluate the validity of the model. In this document, examples of subjects finding and evaluating mental models used as problem representations are…

This book is a collection of 21 articles by mathematics teacher Ernest Ranucci (1912-1976) grouped into five categories: (1) "Patterns" (for developing inductive reasoning skills); (2) "Mathematics in the World Around Us"; (3) "Spatial Visualization"; (4) "Inventiveness in Geometry"; and (5) "Games to Learn By", which demonstrates that mathematics…

This document contains 53 plenary and contributed papers presented at the eighth Psychology of Mathematics Education (PME) meeting. Two plenary addresses focused on mathematics research in Australia and Japan, and problem solving and symbolism. Contributed papers were classified under 13 headings including: teaching and learning theory; cognition;…

This collection of documents promotes simulation as an attractive topic in mathematics instruction that provides game-like activities likely to interest pupils, by illustrating the important ideas of probability and showing how mathematical models can be used in practical problems clearly relevant to everyday life. While computer programs written…

Presented is a detailed review of eight computer software packages. Strengths, weaknesses, and recommendations for each game are listed. Mathematical and thinking skills, problem solving, drill and practice, procedural activities, decision making, understanding money, and basic skills are emphasized. (KR)

Many teachers use cooperative learning methods during instruction but face the problem of aligning evaluation techniques with that instruction. Described are methods to include cooperative problem solving in evaluation, including strategies to identify possible grading schemes, to make appropriate problem choices, and to evaluate individual versus…

Suggests instructional modifications that utilize liberal arts students interests and strengths to stimulate their interest in mathematics. Suggestions recommend that teachers (1) relate mathematics to current critical issues; (2) make use of projects and open-ended problems; (3) utilize collaborative learning; and (4) provide opportunities for…

Describes seven problems designed to enhance the development of four types of student communication in mathematics: (1) describing observations; (2) justifying solutions and solution processes; (3) documenting thinking; and (4) completing or creating mathematical problems. (MDH)

Describes Thinking Mathematics, a research-based approach to teaching mathematics. Value is placed on thinking and communicating mathematically and using what is known to find the unknown. The program requires teachers to rethink their beliefs and assumptions about teaching and learning mathematics. Examples of program implementation are given.…

The use of strategies is an important part of mathematical thinking. Presented are several games that help develop the reasoning strategies of hypothesis making and testing, proving and disproving, looking for patterns, and simplifying a difficult task. (MDH)