This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…

In this important book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose a child's level of mathematical understanding and provide guidance for teaching. By focusing on the inherent delight and curiosity behind young children's mathematical reasoning,…

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

Teachers and teacher educators interested in synthesizing their current practice with new mathematics standards will welcome this highly useful volume. The QUASAR Project at the University of Pittsburgh presents prevalent cases of mathematics instruction drawn from their research of nearly 500 classroom lessons. The Mathematical Tasks…

This paper suggests that many adult learners lack the skill of reading and writing larger numbers. Two Ovid computer searches of the ERIC (Educational Resources and Information Center) database are used to provide the background research. Issues in and teaching methods of reading and writing larger numbers, particularly a language-symbol approach,…

A strategy is presented for teaching arithmetic to students with mental retardation, based on subitizing, skill of recognizing number of objects in a set without actually counting, and pattern recognition. The strategy helps children understand concept of addition by representing number configurations on 5-frames and 10-frames, and reduces need…

"Chisanbop" is a Korean word which means finger calculation method. It is based on the Korean abacus, and its emphasis is on fives. By using Chisanbop techniques, one can add, subtract, multiply, and divide large numbers. Chisanbop can be taught most effectively to large groups in the second grade. (JN)

This article offers teaching strategies for developing number sense for children who are blind and braille users. Suggestions focus on developing number meanings, exploring number relationships with manipulatives, understanding the relative magnitude of numbers, developing intuitions about the relative effect of operating on numbers, and…

This article offers specific strategies to diagnose and remediate difficulties students may have in learning multiplication facts. Analyzes strategies students use to go from a known fact to an unknown fact. The point is made that, for many students, the order of interpretation of a number fact may affect accuracy. (DB)

Describes the use of a variety of strategies to teach estimation and other mathematics concepts in an inclusive urban fifth-grade classroom. The collaborative program (involving the teacher, the mathematics consultant, and the special-education consultant) utilized cooperative learning, estimation techniques, calculators, graphic organizers, links…

This article argues that the reason the mathematics performance of students with mild disabilities is so limited is the mathematics. Using illustrations from subtraction, the article proposes number sense be a primary goal and that within the realm of number sense, big ideas be included among the dependent variables. (Contains references.)…

Arithmetic programming for students with mild mental disabilities requires a comprehensive perspective that includes attention to curriculum, instruction, and appraisal. Arithmetic computation should not dominate educational programming, but should be included in ways that are functionally relevant and meaningfully presented within a framework of…

This book is intended to provide practical guidance to elementary grade teachers in inclusive classrooms with students having difficulties in learning mathematics. Following an introductory chapter, chapter 1 provides an overview through the use of case studies of three students that note research on learning difficulties in mathematics, and on…

This book is based on the underlying philosophy that mathematics learning at the elementary level should be active. Children should learn through meaningful hands-on activities with manipulative materials, pictures and technology. More than 400 pupil activities and suggestions for designing more activities are described. Because mathematics is to…

Insights from both cognitive psychology and learning disabilities intervention research are presented to improve understanding of the processes by which number fact fluency develops. Discussion includes assessment guidelines and learning strategies such as counting all, counting on, and alternative groupings. (Author/JDD)