This book shows how to increase one's power to analyze and comprehend problems. First, it outlines and illustrates the methods that good problem solvers use in attacking complex ideas. Then it gives some practice in applying these methods to a variety of questions in comprehension and reasoning. Chapters include: (1) "Test Your Mind--See How…

These materials are intended to provide meaningful mathematical experiences for pre-algebra students. These experiences emphasize the development of computational skills, mathematical concepts, and problem-solving techniques. This bulletin may be used as the basis for the first term of a one-year course. The complete course is divided into 12…

This study investigated the relationships between the mathematical problem-solving performance of fourth-grade children, their attitudes toward problem solving, their teachers' attitudes, and related sex and program-type differences. Three instruments were used to gather data. Data were gathered for the first part of the study from 30 classes in…

Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed…

Presented is a discussion of the nature of individual differences in the learning of mathematics, which leads to a review of field-dependent and field-independent cognitive styles. Field-dependence-independence is noted as an important variable in school learning and a study is cited that investigated the relationship between pupil success at…

Sixty-four fifth and sixth-grade pupils were taught number series extrapolation by either an algorithm, fully prescribed problem-solving method or a heuristic, less prescribed method. The trained problems were within categories of two degrees of complexity. There were 16 subjects in each cell of the 2 by 2 design used. Aptitude Treatment…

Applied mathematics is seen often to involve the solution of single equations or systems of equations. A particular technique for solving equations in the context of functions on the real line is examined. This technique includes an iterative process, which is viewed as an algorithm that can be implemented readily on inexpensive and widely…

This study explored the variance in mathematical problem-solving achievement accounted for by sex and ethnicity. Each of 316 adolescents in a rural school district in southeast Texas was administered the California Achievement Test and a set of five affective scales. Reading scores accounted for 49.5% of the variance; computation, 14.6%; affective…

This study addressed: (1) what difference, if any, would calculators make on a typical mathematics assessment instrument; (2) what might occur if students were allowed to use, but were not furnished with, calculators for testing; and (3) what implications do answers to these questions have for future statewide assessment. Eighth-grade students…

This collection of material is designed to illustrate the nature and variety of the idea of proof in mathematics. It is intended to be a "background book" for the use of teachers, particularly those in initial training courses. Individual chapter titles are: (1) The Role of Proof in Mathematics; (2) Logical Reasoning: The Idea of Implication; (3)…

Presented are 13 articles which contain abstracts and analyses of research reports related to mathematics education. The first article considers six working papers, on a variety of topics, from E. G. Begle and the Stanford Mathematics Education Study Group. Of the remaining reports, two deal with problem solving, five with some aspect of learning…

This study attempted to identify the things that help elementary school students solve verbal problems. Among the types of things included for examination were: the attributes of problems, the tools used, and the problem transformations that were possible. The summary of findings is comprised of 29 diverse types of statements grouped under four…

This paper describes in detail the paper-and-pencil POE (Pelham Odd 'R Even) game, in which units of space are the allocated resources. The game is designed to provide an introduction to the rule structure common to the games of EQUATIONS, WFF 'N PROOF, and ON-SENTS & NON-SENTS. Techniques of playing POE, including goals, solutions, moves, scoring…

In this study the researcher investigated the feasibility of constructing a valid paper-and-pencil measure of problem solving ability. (Rationale and design of the study are discussed in Part 1.) The principal feasibility criterion, correlation of at least .71 with scores on taped and coded individual "thinking aloud" problem-solving…

A number of space science resource materials and activities are developed into a useful format for classroom presentation. The application of mathematical properties in making scientific discoveries is the major emphasis. Each section has a discussion centered on the men and history behind the discovery of physical laws and phenomena relevant to…