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 relationship between 18 preparatory teachers' verbal behavior and their students' attainment of number concepts in investigated. The study is based on research of teacher observational systems used to identify "low inference" teacher-variables; this literature is reviewed in this report. The six variables measured by analyzing ten…

This is a volume of teacher-developed units to supplement the textbook in a first-year algebra course. The units consist mainly of statements of objectives and student worksheets with some examples and references to the textbook given as aids. Major topics covered are basic operations with signed rational numbers and with polynomials,…

The purpose of this study was to develop and evaluate procedures for validating a learning hierarchy from test data. An initial hierarchy for the computational skills of adding rational numbers with like denominators was constructed using Gagne's task analysis. A test designed to assess mastery at each of the 11 levels in this hierarchy was…

The purpose of this project was to determine if the method of subtraction of integers taught to seventh grade students affected their mathematics achievement or retention. Computation, concept, and problem-solving sections of the California Achievement Test were given as pretests and posttests. An investigator-constructed test of the addition and…

Twenty-four nursery school children ranging from 3.11 years to 5.11 years were tested in counting objects that varied in similarity and contiguity. Objects were presented in three arrangements: arrangements composed of subgroups of contiguous identical objects; arrangements without subgroups; and arrangements composed of subgroups of discontiguous…

An outline is presented for the scope and sequence of the following topics to be covered in grades K-8: sets, operations, number theory, measurement, geometry, and number sentences. Details of a coding scheme for mathematics units, exemplary units for each level, and a description of the procedures used to correlate science and mathematics courses…

As the 12th in a series of interim reports prepared for the United States Congress on the metric system, this study was authorized by law to reduce uncertainties concerning the issue of converting to metrication and to provide a better basis upon which the Congress may evaluate and resolve it. The testimony of over 230 nationally representative…

The relationships among the perception, representation, and construction of series are examined within a model of the acquisition of seriation abilities. The model is then related to two experiments with three-, four- and five-year-olds. The key feature of the model is the delineation of parallels among developmental changes in three arenas:…

Eighteen research reports related to mathematics education are abstracted and critically analyzed. Seven of the reports deal with general instructional concerns (feedback on homework, error patterns, teacher-student interaction, reading strategies, teacher effectiveness, school attendance, and learning environment), four with topics in mathematics…

For STET students who still have difficulty with the basic operations on whole numbers, the author has developed a "periodic table" of whole numbers, which can be used to add, subtract, multiply, and divide. (MP)

Five activities involving an array of numbers called an even triangle are given. Properties of the triangle are listed and some generalizations are proven. (MP)

Forty-three preschoolers learned the concept of one-to-one correspondence by matched discovery, expository, or observational learning. The groups did not differ on short-term recall and near transfer, but the discovery group excelled on far transfer and delayed recall. The effect of guided discovery on broader learning outcomes was also discussed.…

Capturing junior high school students' interest in computation is the aim. Three activities are described in which computation acts as a needed tool within a problem-solving context. (MN)

A 3-year study was conducted to compare the effectiveness of laboratory and lecture strategies in a course for prospective elementary teachers on the structure of the number system. Results showed that neither strategy was superior to the other as judged by students' examination achievement, attitudes towards mathematics, student teaching…