A hierarchy for learning to solve different types of addition with fractions problems was hypothesized on the basis of both content analysis and psychological considerations. Problem types were defined according to the relationship of the two denominators to each other (e.g., equal, prime, etc.) Students in grades 4 through 8 were each given 45…

This manual is designed for use in inservice work with teachers preparing to use the Comprehensive School Mathematics Program (CSMP) in grades K-2, and as a resource guide for later use. In it, the nonstandard topics used in the CSMP primary program are developed through discussion and a variety of exercises. These topics include the minicomputer…

The contemporary mathematics program set forth in this publication developed as a result of experimentation and evaluation in classroom situations. This is Part 2 of "Mathematics: 8th Year." Part 1, a separate bulletin, was published during the school year 1967-68. The materials in this bulletin are intended to serve as guidelines for…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for…

The purpose of this study was to collect data to determine the mathematical concepts used in everyday industrial work by technicians in the area of electronics, particularly the graduates of New Mexico Highlands University. The instrument used to gather information was constructed from information contained in related studies, textbooks, and a…

A survey test in mathematics (see TM 000 965) was administered to all pupils in Grade 7 of the Vancouver School System. Test content included arithmetic fundamentals, modern mathematical concepts and mathematical applications in problem solving. A summary of test results is presented in three tables. (CK)

This test was designed to cover the new seventh grade mathematics course (see TM 000 964) in the Vancouver schools. The 45-item multiple choice test designed to be completed within a 70 minute period stresses arithmetic fundamentals, modern mathematical concepts, and mathematical applications in problem solving. (CK)

Test development efforts for constructing 12 items to measure achievement of each of 30 selected mathematics concepts are described. The topics covered are sets, division and expressing relationships. Item and total score statistics for data collected on 196 girls who had just completed the fifth grade during early summer of 1970 and 195 boys who…

TWO METHODS OF RESPONSE DESCRIBED BY PIAGET AND INHELDER FOR DRAWING APPROPRIATE BOUNDARIES AND SELECTING APPROPRIATE PREDRAWN BOUNDARIES FOR HYPOTHETICALLY CUT, SOLID GEOMETRIC FIGURES WERE INVESTIGATED TO SEE WHETHER SECONDARY SCHOOL STUDENTS COULD RESPOND IN APPROPRIATELY TO THE MATHEMATICAL TASKS. THE RESPONSES OF 8TH-, 10TH-, AND 12TH-GRADE…

Language arts games are described that combine mathematical experiences and language development.

Discussed are "moves" in teaching mathematics that can serve as a basis for defining understanding. How to characterize and use moves is discussed, with specific examples and research evidence. (MP)

Some suggestions are given of how various decimal concepts can be introduced using Multibase Arithmetic Blocks, base ten. (MN)

Using a pegboard and different colored pegs, students were able to visualize mathematical concepts, generate and solve problems, and test hypotheses. Illustrations included. (MA)

Reasoning patterns and learning difficulties of six students are illustrated in support of the contention that language and notation often disguise thought. (MN)

Thirty-nine elementary education majors used manipulative aids to work laboratory exercises while thirty-nine control subjects completed the same exercises without the use of manipulative materials. No significant differences were found between groups in demonstrating numerical and structural properties of the four basic arithmetic operations…