How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

This bulletin concerns the role of memorization in mathematics instruction. Sections of the bulletin are devoted to discussions of: old math vs. new math; the importance of memorization ability on mathematics learning; misconceptions about memory; how to enhance the memory, including short-term vs. long-term memory systems, attention, interest,…

Two transcripts of children exploring and solving problems presented by computer programs are given. The transcripts show the insight that occured. (MNS)

Providing students with realistic problems will facilitate a better understanding of and reason for computation. Specific suggestions for introducing and for increasing problem-solving skills are described. (CJ)

The terms generalization and abstraction are used with various shades of meaning by mathematicians and mathematics educators. Introduced is the idea of "generic abstraction" that gives the student an operative sense of a mathematical concept and provides a passage point in the process toward formal abstraction. (MDH)

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…

This discussion is primarily designed to increase teachers' awareness of Piaget's theory of cognitive development and implications for mathematics in the middle school. It is hoped such awareness will compel instructors to adopt strategies that help pupils gain more from mathematical experiences, by providing impetus for innovation and…

Provides examples of the mathematics explored in a project that involved teachers in seminars in which they solved problems that focused on algebraic thinking across the grades. Presents the project as a model for staff development for teachers across grade levels. (DDR)

Recent research in mathematics instruction underscores the importance of problem solving and higher-level thinking. This article presents four themes in instruction for students with learning disabilities: (1) provide a broad, balanced mathematics curriculum; (2) engage students in meaningful problem tasks; (3) accommodate diverse learning styles;…

This document is intended as a resource for persons using, designing, or evaluating instructional materials in whole number subtraction. Its purpose is to provide conceptual machinery: (1) for describing/specifying subtraction tests and exercises and (2) for formulating related questions and conjectures. It is mainly a logical analysis subject to…

Space and shape, estimating and measuring, and number are viewed as the three strands of mathematics that come together as a child develops mathematically. Five cognitive/mathematical levels of development, labeled discrimination, order, application, operation, and estimation, are identified and discussed. (MP)

The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the…

Gifted/talented secondary-school students used the Students Questioning Students method in their mathematics classes. The method stimulated higher-order thinking, made students more attentive listeners, and improved their public speaking self-confidence. The paper offers suggestions for implementing the method and includes three pages of letters…

This article discusses ways to improve mathematics performance of students with learning disabilities through cognitive strategies instruction. Principles of a strategic classroom environment are explained, such as involving students in goalsetting and providing advance organizers. Three specific strategies for math instruction are described:…

Research shows that introducing basic forms of algebraic reasoning in elementary school enhances children's learning of arithmetic. In this guide, a research and a professional development project are described that have taken a practical approach to introducing algebraic reasoning to elementary students in Massachusetts. (Author/SOE)