This publication presents teaching strategies to develop understanding of fractions as sensible numbers. Written for the mathematics teacher in grades K-5, it gives suggestions for teacher-led discussions and structured exploratory activities. The activities are conducted with manipulative materials that emphasize the important characteristics and…

This is a teacher's guide to an easy-to-read, slower-paced mathematics text designed for students who have learning, reading, and language problems. What fractions are, how to find equivalent fractions, how to simplify fractions, and computation with fractions are included. Each lesson in the eight units focuses on only one major concept, and…

This workbook is designed as an easy-to-read, slower-paced mathematics text for students who have learning, reading, and language problems. Helping students fulfill mathematics requirements for graduation is a goal; the book can be used as the core or supplement to the mathematics curriculum in mainstreamed or special education classrooms, in…

An understanding of fraction addition can be thought to involve two quantitative ideas: (1) the understanding that adding to an original quantity increases its size, and (2) a sense of how much increase occurs. Both of these ideas should underlie or inform a child's approach to problems involving fraction addition and thereby constrain the class…

The purposes of the present study were to ascertain whether or not two particular formatting characteristics influenced seventh grade student performance on math tests. One research question focused on the effects of decimal positioning in multiple choice options for computational items. In a second question, labeling format was compared with…

This document was initiated with the collection of 150 questions in telephone interviews of a national sampling of junior high school and high school teachers. A Mathematics Consultant Panel reviewed the questions, and selected topics were developed, for which there were research bases for answers. The material covers: (1) Effective Mathematics…

A new system of order analysis, developed by Takeya and called Item Relations Structure Analysis (IRSA), was described and used for examining the structural relations among a set of 24 items on the addition and subtraction of fractions. A diagraph showing 16 chains of items that had discernibly common features was generated by this method, and…

The purpose of the two studies reported was to develop and validate clinical assessment instruments designed to identify both the progress of learners through a hierarchy of mathematics content and the mode of presentation through which learners can best handle the content. In Study 1, 73 second graders were given one of two forms of a 15-item…

This curriculum bulletin is designed to help teachers meet the diverse needs in mathematics of the children in fifth grade classes. In addition to the emphasis that is placed on arithmetic computational skills, the bulletin shows how to include other areas considered important, such as concepts, skills, and ideas from algebra and geometry. The 80…

The problems in the workbook are designed to help the vocational high school student understand and become adept at working with decimals and percents. Emphasized are the use of decimals in money and the application of percents to problems in daily living. Topics covered include: addition, subtraction, multiplication and division of decimals; the…

This is the first of two guidebooks for Grade 7 recommended to build fundamental concepts necessary for success in algebra. Topics covered include numeration systems, operations in non-decimal bases, whole numbers, factors and primes, and fractions. Goals for the course are stated, then, for each topic, performance objectives, a course outline,…

This volume presents a partial description of the lessons in the preliminary version of the PLATO fractions curriculum. Each lesson has three parts: review, new material, and a student-selected option. Students receive immediate feedback from the computer as they progress through each lesson. Five groups of lessons are described: meaning of…

This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. The instruction primarily concerned representing fractions and ordering fractions on number lines. (Author/PK)

Presents a rationale and activities for using teacher-made laminated strips to teach fraction division concepts. (PK)

Two experiments investigate how attributes of peer models influenced achievement behaviors among children who had experienced difficulties learning mathematical skills in school. Children in the single-coping-model, multiple-coping-model, and multiple-mastery-model conditions demonstrated higher self-efficacy, skill, and training performance,…