This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in January 1985, it contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved calculators may be used. Scoring is done by the…

This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in June 1985, it contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved calculators may be used. Scoring is done by the…

Research findings on problem solving and ideas for improving problem-solving instruction are presented. What a problem is and the fact that few problems appear in textbooks are noted. What successful problem solvers do is discussed, with the stages of problem solving described, including the point that checking their work may be the most important…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

A study was conducted to: (1) observe through a case study approach the exploratory behavior exhibited by 8-year-old boys and girls when calculators were made available in problem-solving situations; (2) investigate changes that occur in the kinds of arithmetical problems children construct following the introduction of calculators; and (3)…

The problem of finding the area of a regular polygon is presented as a good example of a mathematical discovery that leads to a significant generalization. The problem of finding the number of sides which will maximize the area under certain conditions leads to several interesting results. (LS)

A case is given against teaching division of fractional numbers. Types of problems usually solved by division are solved by methods involving only multiplication. (JP)

This document describes seven steps that were followed to develop and validate a pool of mathematical problem-solving situations and a set of questions for each situation which were designed to provide information about students' qualitatively different levels of reasoning ability. For each stage a description is presented of the work that was…

Nineteen Calculus II students were randomly sampled and divided into calculator (n=9) and noncalculator (n=10) groups. These students were asked to "think aloud" while solving 24 Advanced Placement calculus problems. Each student interview was videotaped, coded and analyzed for reasoning process as well as outcome. The results indicated…

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

Some general suggestions for the teaching of mathematics study skills are provided in this paper. The suggestions offered are as follows: (1) teach the specialized mathematical vocabulary directly, (2) show students how the mathematical symbol system works, (3) give practice in understanding graphics, (4) give practice in spotting unstated…

Upper elementary students are the focus of this paper, intended to present a few studies that have been done in the past five years that are related to two aspects of problem solving: strategies used by the problem solver and tasks used in studying problem solving. The review is not intended to be exhaustive, but is designed to present examples of…