This study investigated children's representation of addition and subtraction problems with canonical and noncanonical number sentences, to see whether children would directly represent the structure of a problem if both types of sentences were available. Subjects were 22 first graders and 41 second graders randomly assigned either to a Canonical…

This course is designed to review the arithmetic skills used by many Marines in the daily pursuance of their duties. It consists of six study units: (1) number systems and operations; (2) fractions and percents; (3) introduction to algebra; (4) units of measurement (considering both the metric and United States systems); (5) geometric forms; and…

Research findings related to the development of language, abstract reasoning, and problem solving-skills by children from three to eight years old are integrated by consideration of classroom implications. Individual differences, the teacher-child relationship, and other topics are also discussed in this context. (SD)

The focus is on the problem-solving behaviors of primary age children on one-step verbal or story problems involving addition and subtraction. When children are given a simple word problem for which they have not learned the necessary algorithms, they are often able to derive a solution on their own. This report focuses on the child-invented…

A group is viewed to be one of the simplest and most interesting algebraic structures. The theory of groups has been applied to many branches of mathematics as well as to crystallography, coding theory, quantum mechanics, and the physics of elementary particles. This material is designed to help the user: 1) understand what groups are and why they…

One hundred twenty-eight undergraduates were randomly assigned to one of four treatment conditions formed by crossing two levels of task difficulty (computationally easy or difficult problems) with two modes of calculation (solving by hand or calculator). When solving problems by hand, there was a large increase in state anxiety between easy and…

Problem solving approaches often find a path from the givens to the unknown or from the unknown to the givens. This study explores those approaches using written protocols of Navy subjects while solving for the numerical value of an unknown from several knowns and a system of equations. For a subset of the items, solutions require subjects to…

Presented are four interpretive reports and a list of current publications of the Mathematics Work Group at the Wisconsin R&D Center. The first interpretive report gives a brief overview of their work. Reports two through four are concerned with individual interviews, carried out during a longitudinal study, in which primary children are asked to…

Thirteen research reports related to mathematics education are abstracted and critiqued in this publication. The topics of the research include counting, addition, subtraction, ratio, proportion, geometry, problem solving, and teaching strategies. Also included is an editorial comment by T. Kieren on mathematics education research. Research…

To ascertain if children's use of manipulatives and/or the teacher's presentation of the problem in parts (chunking) affect children's ability to model and/or solve addition and/or subtraction problems, 146 first-grade subjects were administered the Houston Addition and Subtraction Problem-Solving Test which provided accuracy and modeling scores…

This brief report describes an exploratory pilot project in which sixth-grade students used hand-held calculators throughout the school year. The report includes guidelines on the purchase and use of calculators as well as advice on gaining community support for such a project. Issues related to classroom management are discussed; in particular,…

The activities described in this report are focused on a preliminary investigation of the effects of presenting problems to children without any prior formal problem-solving instruction, on the children's ability to solve the problems, and on their subsequent problem-solving performances. The work was an outgrowth of activities related to the…

Instructional materials used in two pilot studies are presented. Appendix A contains components of the problem-solving bulletin board. Eighteen problems are stated along with suggestions for solving each problem. Problems 1-10 contain questions extending the original problem. Teacher answer sheets are given for problems 4-18. Appendix B contains…

These instruments were used in the evaluation of the problem-solving modules used in the Mathematical Problem Solving Project "Module Development and Formative Evaluation." Forms presented are: (1) teacher's instruction sheet-evaluation; (2) time record-instructional booklet; (3) time record-problem deck; (4) lesson rating form; (5)…