This military-developed text contains the first section of a four-part course to train environmental support specialists. Covered in the individual course blocks are basic mathematics necessary to the study of waste processing and water analysis as well as waste and waste processing and water and water analysis (basic chemistry, air forced water…

The relationship between expert teachers' classroom behavior and their subject matter knowledge is an area of research that has not been examined extensively. To begin that study, one topic, fraction knowledge, was explored in depth as it occurred in natural teaching settings. Fractions are one of the more difficult topics in elementary…

Some students can perform operations on fractions when using physical materials, but are unable to transfer this ability to operations with symbolic expressions. They seem to view the manipulative and paper-and-pencil problems as different and are not surprised to get different answers. (SD)

This book is for boys and girls who know the numbers from one to thirty thoroughly, who can count to one thousand, who know something of the multiplication tables of two, three, four, five, six, ten, and twelve, and who understand the simplest facts about fractions. This book is both to be read and to be studied. It calls for oral recitation and…

This report describes the test performances of 26 students who displayed a variety of erroneous rules in completing a 48-item test of fraction addition problems, constructed to diagnose at least 88 projected erroneous rules. Cases were selected for their potential usefulness in designing and implementing an error-diagnostic testing system and in…

The purpose of this study was to investigate the effects of the use of hand-held calculators on the teaching of decimal arithmetic in seventh and eighth grade pre-science units. In particular, the effects of calculators on pencil and paper computational skills and on conceptual understanding were studied. The study consisted of a pre-unit…

This booklet consists of three units selected from the SMSG text materials for grade 4, "Mathematics for the Elementary School." These three units were selected as being necessary for students about to undertake the grade 5 SMSG text materials. Chapter topics include concept of sets, sets of points, and concept of fractional numbers. (MP)

This monograph focuses upon the teaching of fractional concepts. The introduction to fractional concepts is treated through sets, number lines, and area. Included are three diagnostic pretests, one of which can be administered to a nonreader. The major core of the monograph consists of 23 worksheets which can be removed for duplication. The…

This study was concerned with the verification of a learning hierarchy for the mathematical task of adding fractions, when group learning procedures involving teacher-student interaction were used. Through a task analysis procedure a hierarchy of 13 subordinate skills was hypothesized, behavioral objectives were specified, and a curriculum…

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…

This guidebook, which sets minimum course content, is designed for the student who has acquired basic computational skills with non-negative rational numbers. The booklet covers computation skills with decimals. General goals and performance objectives, a course outline, teaching strategies, and sample test items are included. The quin is based on…

The purpose of the study was to examine the effect of instruction using Dienes' perceptual variability principles on primitive generalization and mathematical generalization. The following was studied: the effect of achievement-to-criterion on one, two, or three non-symbolic embodiments of an objective using a selected class of variables on the…

The purpose of the study was to examine the effect of instruction using Dienes' perceptual variability principle on the development of ability to operate with symbols in a meaningful way. The following was studied: whether an increase in the number of enactive and/or iconic embodiments of a concept utilized in an instructional episode will produce…

A program in BASIC which decomposes fractions is provided. Activities related to student use of the program are listed. (SD)