This study was designed to investigate the effectiveness of a heuristic approach to problem-solving instruction. The 330 subjects were randomly assigned to either a Problem Solving, Calculator Problem Solving, or Control group. The two experimental groups studied problem-solving heuristics applied to nonroutine problems for 18 weeks, after which…

This document is designed to aid students who wish to comprehend the algebraic problem-solving process for mixture problems. The instruction set was designed to be low stress, patiently delivered, and easy to follow. It was set up to be accompanied by a 25-minute audio cassette tape. The content of this document and the tape is directed to the…

This report discusses some of the activities of the Iowa Problem-Solving Project (IPSP). The document has three main sections: (1) Materials Development, where IPSP teaching materials and test development are discussed; (2) Summative Evaluation of Materials, presenting the procedures, results, and findings of the 1978-79 evaluations; and (3)…

The development of a theory of algebraic problem solving is discussed. The domain of the investigation is restricted to single sentence word problems. There were three experiments, the first involving 42 college students from the University of California, Santa Barbara. These subjects were divided into two groups, half in an equation group and…

The investigation reported is primarily a description of how college students solve or fail to solve algebra equations. Protocols were collected from two groups of college students; one group was expected to be good solvers, the other group contained many poor solvers. The investigators sought to identify and classify the difficulties students…

The twenty-two essays on problem solving included in this publication give ideas and examples for use in the classroom at all levels of instruction. Topics discussed in the essays include but are not limited to: problem posing, clues from research, story problems, calculators, textbook problems, and measuring problem solving. Polya's heuristics as…

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…

The process of change and development of the mathematics curriculum in the United States is reviewed. Fundamental changes of implemented curricula from 1960-1980 are discussed in the light of the considerable efforts at reform during the 1950's and 1960's. Elements of the educational system are mapped out, and reasons for the lack of effective…

This paper is divided into three parts. Part I connects the reality of the classroom with the idealism which arises from some of the problem solving literature. It is argued that a broader concept of problem solving is needed to provide a perspective for bridging the gap between the conceptions of problem solving in the literature and typical…

This study was presented at the 1979 meeting of the American Education Research Association (AERA), San Francisco. It investigated the relationship between the structure of simple addition and subtraction problems and the types of processes children use to solve them prior to receiving formal arithmetic instruction. Specific strategies which young…

Differences between problems in mathematics and problems in other subject matter areas are explored. Problems that explore the potential for application are unique to mathematics and therefore are also discussed. (JT)

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

The authors trace the growing concern over mathematics and its relationship to other disciplines in the curriculum of the secondary schools from the early 1960's. The case is then argued for a mathematics curriculum in which students become heavily involved in solving problems which are interdisciplinary and are real and of interest to them. (MN)

A lawn-mowing problem is discussed in terms of clarifying the problem; making initial conjectures; experimenting; developing a solution; and supporting formulas, theorems, and corollaries. (MNS)

Discusses use of mathematics problem cards written in foreign languages. Indicates that contextual cues from mathematics problems provide helps to translation. Gives example problems in French, Norwegian, and Japanese. (JM)