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…

Describes software tools designed to help students investigate relationships among representations of rational numbers that emphasize the part-whole model of a rational number. (KHR)

Discusses ways teachers can encourage students to construct useful meanings for the fractional unit. Provides three examples of representations of common fractions and illustrates misconceptions in fraction problems. Includes a brief summary of constructivist mathematics education and an example in which a teacher misunderstands a fractional unit.…

This paper describes how a target group of seven students in a combined fourth and fifth grade mathematics class used structured representations to solve fraction problems situated within various realistic contexts. Emphasis is given to the ways in which students' thinking about rational number concepts influences and is influenced by the…

The Education Technology Center (ETC) Fractions Group works to investigate well-documented difficulties that children have in understanding fractions. A central assumption underlying this group's inquiry is that students' difficulties in manipulating fractions arise from their lack of understanding about the nature of fractions. In order to learn…

This book contains a collection of fraction lessons that support curriculum and instruction. The goals of the lessons are to give all students the chance to: (1) extend their understanding of the place value system to include decimals; (2) learn how decimals relate to fractions; (3) represent, read, and interpret decimal numerals; (4) compare…

Described are the conceptions held by United States and Israeli students about multiplication and division that may impede their work with decimals. Included are the introduction, method, division and multiplication task results, and the implications for education and textbook development. (KR)

This paper describes a 4-month-long experiment in computer-based learning called Instructional Software Design and presents aspects of the software evaluation. Results included greater mastery of LOGO and fractions by the experimental class than for either control class and greater acquisition of metacognitive skills. (Author/CW)

This guide contains a collection of alternative techniques for teaching arithmetic that have proved useful in teaching both children and adults with various learning problems. Discussed first are several underlying principles of instructing individuals with learning disabilities, problems, and differences and special accommodations for…

This instructor's guide contains materials for a course designed to prepare employees for statistical process control (SPC) training given at their workplace by refreshing math skills and building the concepts and vocabulary necessary to understand SPC in manufacturing environments. SPC-Prep 1 addresses the math skills necessary to perform SPC…

This teacher's guide is the ninth in a set of 20 activity booklets for teaching mathematics to children in grades 1-8. The 20-level curriculum embodies carefully delineated areas of learning arranged in progressive stages, eliminating grade restrictions and permitting continuous growth according to the individual's ability and rate of learning.…

In this practicum students' (n=27) learning styles were used to develop teaching lessons and strategies that would improve mathematics learning in a second grade classroom. Each child's learning style was determined through the Swassing-Barbe Modality Index (SBMI). Pretests for mathematics concepts were given. Each concept was then taught…

This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…

This document, which was developed to meet the needs of trainers and workers in Australia's automotive industry for learning activities designed to boost auto workers' numeracy skills, contains a total of 33 learning activities organized into 8 sections. The topics covered in the individual sections are as follows: calculators (key words and…

This module is the third 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 calculator addition, adding measurements of…