Prior research on problem solving is discussed, followed by a review of research on mental processes, intellectual development, information processing, mental images, and conceptual imagery. Then four intact fourth grade classes of 23 pupils each were assigned to a 2 x 2 factorial design. One factor was the type of instruction (Method A and Method…

Five steps common to different problem solving models are listed. Next, seven specific abilities related to solving problems are discussed and examples given. Sample activities, appropriate to help in developing these specific abilities, are suggested. (LS)

Nine problem situations involving the use of random numbers are given. Topics include cooking, hunting, bacteria contamination, waiting lines, ransom walks, and branching. In addition to the problem situation, questions are suggested which can be used to extend the investigations. (LS)

The focus of this study was on the processes students used in making mathematical conjectures for five divergent problem situations. The relationship of the processes to creativity factors across the problems was also examined. The results of various cluster analyses and correlational measures indicated that students use different sequences of…

This study investigated the effect of initial instruction on the processes children use to solve basic addition and subtraction verbal problems. Prior to instruction and following a 2-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different models of addition…

A set of 58 problems that may be solved by using lists is presented. This set is part of the Mathematical Problem Solving Project. The problems are coded for three levels of difficulty and are designed for students in the intermediate grades. Answers are provided. (MP)

This teacher's guide contains instructions for the use of a booklet designed to teach problem solving through guessing. For each lesson the purpose, an overview, and detailed teaching procedures are presented. The five lessons are: (1) using guesses and computation to solve problems; (2) using guesses to solve two-step problems; (3) using guesses…

This appendix to the technical report "Module Development and Formative Evaluation" contains two forms of the quiz covering the module "Using Tables to Solve Problems" as well as teachers' comments on the module. (MP)

Four instruments were selected or developed for the summative evaluation of the Mathematical Problem Solving Project and pilot tested. The instruments were: (1) Student Attitude Questionnaire (SAQ), developed and validated by the MPSP evaluation staff; (2) problems selected from the National Longitudinal Study of Mathematics Achievement (NLSMA);…

This is unit eleven of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include coordinate geometry and problem analysis. (MP)

THIS LEARNING ACTIVITY PACKAGE (LAP) IS DESIGNED TO GUIDE STUDENTS IN LEARNING HOW TO USE AXIOMS, IN WRITING PROBLEMS INTO EQUATION FORM, AND IN SOLVING EQUATIONS. IN ORDER TO ATTAIN THESE GOALS, THE STUDENT AT SOME POINT IN HIS PROGRAM MUST BE ABLE TO (1) WRITE A DEFINITION OF "AXIOM", (2) USE THE AXIOMS OF A FIELD IN SOLVING EQUATIONS, (3)…

Analyzed was the increase in problem-solving ability when students were exposed to, and participated in, various aspects of a problem-solving process. Also analyzed was the nature of the relationship between problem-solving ability, as measured by the author's instrument, and the intelligence quotient, creativity index, and sex of seventh grade…

This study investigated differences in problem-solving performance following instruction varying in the type of heuristic advice given. The subjects, 176 college students with two years of high school mathematics experience, were provided programed instruction over a three-week period in three topic areas: finite geometry, Boolean algebra, and…

Reported are the results of an investigation of the effects of syntax and vocabulary difficulty on the problem solving ability of children. Four tests of verbal arithmetic problems are prepared with either easy or difficult syntax and either easy or difficult vocabulary. Easy syntax was defined as being as nearly a kernel sentence as possible,…