In April 1989, the National Council of Teachers of Mathematics issued a major report which presented 13 standards for elementary school mathematics. Among the most important and wide reaching of the Standards are those stating that the study of mathematics should emphasize problem solving, mathematical reasoning, and number sense. The project…

This booklet is a collection of puzzles, investigations, and games. They are designed to be used with large objects such as tins or stones and diagrams marked on the ground. The children are to be encouraged to use an experimental, trial-and-error approach at first, and then develop methods of solution. (MNS)

This booklet is a collection of puzzles, games, and investigations. All that children need are some stones or shells, on some of which they must write numerals. For playing with the whole class, the game or puzzles may be marked out on the floor or in sand; in that case, larger objects such as small rocks and empty tins may be used. Children are…

The effect on algebra achievement of college students of using a specific study method, algebra notecards, was examined. Whether achievement differed for adult learners and traditional college students, and the interaction between the study method and the status of the learner were also investigated. The research was conducted at the University of…

This document contains the appendices to a study of problem-solving instruction. In Appendix A are sample instruments for the teacher problem-solving interview and instructional planning interview, the teacher post-study interview, coversheet for narrative notes and narrative notepad page, rating form for the lesson rating instrument, lesson…

This report describes the content of the 115 programs comprising "Square One TV" after two seasons of production, relating that content to the three goals of the series. Appended is a listing of the shows, with complete specification of each segment's content, description, format, length, and other information. The goals and the extent…

This document reports on the initial phase of a project investigating how to relate formal mathematical representational and problem solving skills to informal strategies that children naturally invent to solve simple addition and subtraction problems. A program was developed that allows pupils to solve word problems on a microcomputer. A pilot…

This brief report highlights findings from the two assessments in mathematics and three assessments in science conducted by the National Assessment of Educational Progress between 1969 and 1978. In mathematics, average scores declined during the mid-1970s, especially on problem solving. In science, students generally declined in knowledge, skills,…

The study was designed to investigate: (1) the relative effectiveness of three techniques for teaching verbal problem solving to general education mathematics students in a junior college; and (2) the relationships between various student variables and problem-solving ability after treatment. Three classes (N=72) at Florida College were randomly…

This document focuses on a series of studies that viewed aspects of conditional reasoning. The investigations were concerned with the processes children use to acquire patterns of deductive inference and logical relationships pertaining to propositional reasoning. The first experiment, involving 96 children each in grades 2 and 5, investigated the…

The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the…

Vector analysis is viewed to play a key role in many branches of engineering and the physical sciences. This unit is geared towards deriving identities and establishing "machinery" to make derivations a routine task. It is noted that the module is not an applications unit, but has as its primary objective the goal of providing science,…

This material considers the questions of: 1) What is basic in mathematics? 2) What mathematics do all children need for their lives in a society that depends on technology? and 3) What do pupils need in order to go on and learn the mathematics they will need for access to jobs in business, industry, and careers in the professions? What mathematics…

Presented are abstracts of 14 research reports. Topics covered include: (1) the effects of games on mathematics skills and concepts; (2) the use of problem-solving heuristics in the playing of games involving mathematics; (3) sex differences in electing mathematics; (4) the origins of sex differences in high school mathematics achievement and…

The purpose of this document is to survey at least some of the important research literature on solving linear equations in order to identify information that might suggest ways to improve teaching effectiveness. The studies that are examined employ a wide range of research techniques, are based often on quite different perspectives, and span over…