Results of cognitive diagnoses were validated using the rule-space model, and the usefulness of cognitive diagnosis for instruction was demonstrated. Through preliminary studies, 33 stages of knowledge were defined as cognitive diagnoses to be applied to results from a test of knowledge about fractions of seventh and eighth graders (initial test…

This book provides a comprehensive collection of 66 teaching strategies and ideas to help overcome problems with number, each linked to a specific kind of error described in the related manual. Most of these strategies are classroom-ready and easily implemented. Some are notes for the teacher to read and then plan activities accordingly, and many…

Given the current and widespread practical interest in mathematical understanding, particularly with respect to higher order thinking skills, curriculum reform advocates in many countries cite the need for teaching mathematics with understanding. However, the characterization of understanding in ways that highlight its growth, as well as the…

This paper looks at the issue of mathematics learning from a developmental perspective. It begins by focusing on the importance for teachers of understanding how mathematical thinking develops. The New Zealand Number Framework is used as an example of a developmental progression that is of particular relevance to the teaching of mathematics. The…

The "General Mathematics" series is intended to introduce students to basic mathematic principles and concepts and to provide the opportunity to apply those principles and concepts. This module, one of six in the series, will allow students to build or increase their level of understanding of decimals and percents, and will help students…

This module is the first in a series of 12 learning modules designed to teach occupational mathematics. Designed for improving machine shop technology skills, this module begins with an introduction to the topic. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are…

This module is the ninth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include measurement conversions, the English system of…

This module is the 11th in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include multiplication, powers, calculator use, and roots.…

This is the teacher's guide to an easy-to-read, slower paced mathematics text designed for students who have learning, reading, and language problems. Basic concepts and skills about decimals and percents, including computation with decimals and using proportions to solve percent problems, are presented. All 10 units begin with a brief discussion…

This document is part 2 of the workbook for grade 1 pupils in the Comprehensive Instructional Management System, a unified mathematics curriculum for kindergarten through grade 7. Each objective is developed by a variety of strategies, with mastery of objectives diagnosed through a testing component. The activities in the student workbook are…

This book contains revised versions of the major papers presented at the Research Agenda Project Conference on Number Concepts in the Middle Grades. It is organized into three major sections, along with an introductory chapter and two brief summaries. Part I includes chapters that deal primarily with analyses of subject matter. The four chapters…

This issue of the journal contains abstracts and critiques of 11 research reports. They concern: a case study of one child's strategies for mental addition; children's understanding of fractions; computation routines prescribed by schools; models in verbal problem solving; predicting eighth-grade algebra achievement; the effectiveness of…

This study examined various misconceptions committed by junior high school students in fraction addition and subtraction problems. Almost 600 subjects were administered two tests, addition and subtraction, and their performances were analyzed by several computer programs, including two programs (FBUG and SPBUG) which are so flexible to any items…

This report illustrates a network of procedures which can be used to solve problems involving the addition and subtraction of fractions. This network, which is based on a skills hierarchy, is used to classify seven levels of student competency. The determination of student competency depends upon the careful construction of error-diagnostic tests.…

This module, concerned with fractional parts, contains 15 activity sheets, 12 of these involve students in making fractional parts and discovering the relationships of less than, equal to, and greater than, between different fractional parts. The last three sheets are for extending and enriching experiences with fractional parts. Teaching…