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…

This teacher's guide contains instructional material for use in a module designed to help students learn to use a list as one way to organize information. Detailed teaching procedures are given for each of eight lessons as well as objectives, student pages and transparencies. An answer key is provided. The lessons address the following goals: (1)…

Verbal protocols were collected from math-anxious and math-comfortable college students while they solved algebra problems. These protocols were then examined for differences in problem-solving processes. Differences occurred in the use of two basic strategies: generating values and symbolic transformations. Math-anxious students generated more…

This study was undertaken to explore the problem solving processes of secondary-school students. Geometry students were given an experimenter-constructed test of convergent and divergent thinking and classified as high on both, high convergent, high divergent, or low on both. Of these 105 students, 49 were selected for individual observation as…

In recent studies, several structural variables have accounted for a good portion of the score variances on verbal problem solving tests. This study investigated changes in the variance accounted by structural variables on problem solving tests when subjects were given instruction to overcome the structural variable influence. Effects on subjects'…