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)…

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…

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,…

This second edition of the bestselling book "The Young Child and Mathematics" reflects recent developments in math education in a wealth of vignettes from classrooms, activity ideas, and strategies for teaching young children about math processes and concepts. Using standards and guidelines from the National Council of Teachers of Mathematics…

This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…

"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)

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)

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,…

An approach to teaching mildly retarded children math skills using finger calculation is discussed. Drills progress from using one to two hands and doing multiplication and division. The appropriateness of finger calculation with children in the sensory motor and preoperational stages of development is noted, and the approach's ability to enhance…

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…

The STAR (Stop, Think, Ask, Recite) strategy was developed to help a kindergarten student write numerals. The child was encouraged to recite a "saying" while he formed each numeral. For example, to make a "5," the child would say "the man went down the street, around the corner, and his hat blew off." (JDD)

This book, with accompanying CD-ROMs, was written to help readers understand children's intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding. Based on more than twenty years of research, this book portrays the development of children's understanding of basic number concepts. Detailed…

Suggests that the history of mathematics is a fluid field within which lively debate occurs. Shares a math problem that requires a community of scholars to simulate the process by which the history of mathematics is actually developed. (KHR)

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…

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…