These materials were developed in response to the Utah State Board of Education's new high school graduation requirements, particularly as they relate to the identification, teaching, and assessment of certain basic functional competencies. The document has been compiled as a guide and aid to mathematics teachers. Thirty competencies have been…

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

Computer programing and problem-solving steps in mathematics are viewed to have related concepts. Some heuristics are compared with some suggestions for structured programing. The one fundamental difference between problem solving in general and when using the computer is seen as the computer solution must be finite. The computer is viewed as a…

The philosophy and activities of the Mathematical Problem Solving Project (MPSP) are described. The main focus is on the research and development efforts, especially the attempt to develop a conceptual framework for problem solving through the creation of an appropriate model. An extensive discussion of models of problem solving is included. Four…

Appendices A - H to the technical report "Developmental Activities Related to Summative Evaluation" are presented. These are: (1) Evaluation of Standardized Tests; (2) Student Attitude Questionnaire (First Draft); (3) Mean Scores for Dichotomous and Continuous Forms for Each Item in Part I of the Student Attitude Questionnaire (First…

As part of the Mathematical Problem Solving Project, MPSP, the goals and purposes of miniprojects are explored. Various conjectures are presented which are based partially upon observation of children working on projects and partially upon the opinions of mathematicians who have observed how problem-solving processes are used in real-world…

The purpose of this study was to determine if children's performance in solving verbally stated arithmetic problems varied when word clues were included or omitted. The sample consisted of 382 fifth-grade children enrolled in four schools of one school system. Twelve sets of problems were so constructed that each set contained two similar problem…

This study investigated the question of whether young children can form response chains in problem solving. After reviewing the literature relating to chaining as a component of problem solving, the author argues that a test of chaining should be free of requirements to recall previously learned material, remember general information, or apply…

This study is one of several conducted by the authors in their investigation of the use of "higher order rules" in the solution of problems. The focus of the current experiment was determination of the compatibility of identified rules with the knowledge of average teenagers, and of the extent to which instruction in higher order rules…

The problem was to determine the relationship between performance on Piagetian class inclusion tasks and on missing-addend computation and verbal problem tasks for first-Grade students, and to describe the methods used by the children in solving both the missing-addend and the verbal problem tasks. From 168 first-grade students who received a…

This paper presents the results of three experiments studying routine problem-solving tasks in simple addition and subtraction. Indications are that children tend to solve such problems by internalized counting procedures which may be learned independently as a consequence of practice in problem solving. Brief descriptions of exploratory studies…

The purpose was to investigate the effects of computer programming on performance in mathematics. The LOGO programming language was taught to 18 fifth graders. A pretest-posttest design was employed to determine whether the mathematical concept of variable could be learned through computer programming; a non-computer group of 20 fifth graders was…

This study identified and defined 30 structural variables related to problem solving. Four dependent variables (only one, percent correct, is analyzed in this report) were derived from data retained by the computer from 172 arithmetic word problems presented to and solved by junior college students on IBM 2741 computer terminals. The structural…

The purpose of the study was to investigate problem-solving performance with regard to non-routine problem experiences in which the computer and flow charts were used as aids. Performance data were collected using an investigator-constructed posttest. Sixty-eight eighth grade students were partitioned into four treatment groups: G1 used neither…

The overall results of the fourth U.S.A. Mathematical Olympiad are discussed. The names of the eight finalists are listed, as are the problems in the test. (SD)