This paper studies the difficulties children have solving word problems that correspond to one of the situations modeled by multiplication; that of a ratio (e.g. "candies per box"), multiplied by an extensive quantity (e.g. "boxes") (I x E). Sixty children were individually observed solving and repeating I x E problems. Various…

This document presents six chapters on four-dimensional geometry, whose titles are: (1) A Brief History; (2) What Is Four-Dimensional Geometry?; (3) Selected Drawings and Models; (4) How to Study the Configurations; (5) Selected Topics; and (6) Applications. The text, suitable for students in advanced levels of secondary school mathematics,…

This collection of activities shows how teachers can help pupils develop problem-solving techniques or strategies using a basic four-function calculator. The techniques "look for a pattern,""make a chart or organized list," and "guess and check" are used repeatedly in activities that range from discovery to application to strategy games. The…

This student textbook is designed to incorporate programable calculators in grade 11 mathematics. The eight chapters contained in this document are: (1) Using Calculators in Mathematics; (2) Exponents and Logarithms; (3) Trigonometry of the Right Triangle; (4) Trigonometry Beyong the Right Triangle; (5) Graphs of the Trigonometric Functions and…

Fourteen research reports related to mathematics education are abstracted and analyzed. Two of the reports deal with teacher education, two with problem solving, three with basic operations, and one each with learning disabled students, rational numbers, proportional reasoning, counting, teacher effectiveness, group cooperation on mathematical…

Fourteen research reports related to mathematics education are abstracted and analyzed in this publication. Five of the reports deal with sex differences in mathematics learning and instruction, and three reports deal with assessment or prediction of mathematics achievement. Remaining reports involve the topics of calculators, logical implication,…

This supplementary mathematics textbook is designed to teach pupils in the intermediate grades about the vocabulary and use of the metric system of measurement. The book limits exploration to the units of measurement for length, capacity, mass, temperature, area, and volume, with only the following prefixes considered: kilo, hecto, deka, deci,…

A three unit mathematics course entitled Introduction to Computing evaluated the effectiveness of programing as an aid to learning math concepts and to developing student self-reliance. Sixteen students enrolled in the course at the College of Notre Dame in Belmont, California; one terminal was available, connected to the Stanford Computation…

The purpose of this study was to determine if selected mental, mathematical, reading, and personality assessments of sixth-grade pupils could predict high achievers in mathematical verbal problem solving. The subjects were 112 sixth graders, 56 classified as high achievers in mathematical verbal problem solving and 56 classified as low achievers…

This study was designed to determine if there were certain aspects of cognitive/personality style that affected prospective teachers' choice of problem-solving paradigm and presentation of inquiry. Fifty-six undergraduate elementary education majors were given the Paragraph Completion Test, which measures conceptual level, and the Group Embedded…

It is argued that microcomputer technology has evolved to the stage that it should be routinely used by mathematics students at all levels. It is shown how the use of microcomputers can change the way problems are solved. Computer-generated graphics are highlighted. (PK)

Describes an ongoing project involving 23 second grade teachers who are teaching all mathematics, including computation, through small-group problem solving and whole class discussion. The authors suggest that teachers are generally successful in creating a "problem-solving atmosphere" and consequently the children persist in attempting…

Describes an exploratory investigation of how children reacted to problems with missing, surplus or contradictory data. It was found that the majority of children gave unsatisfactory answers to such problems. (PK)

Presents five puzzles or problems that may be used for mathematics enrichment. Ideas include magic squares, tests for divisibility, geometry, palindromic numbers, and a jigsaw puzzle. Solutions are included. (PK)

Seven research conclusions concerning computers in elementary schools are presented. A summary conclusion suggests that researchers have been unable to detect improvement in mathematical skills, although some evidence suggests that students using computers acquire attributes related to success in mathematics. (PK)