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 introductory book of a two-part publication, designed as an in-service tool for teachers of grades K-9, is based on the postulate that a teacher should become a better problem solver in order to teach problem solving more effectively to students. This booklet provides an overview of problem solving as a process used daily by all individuals…

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)

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,…

This book is dedicated to George Polya, who focused on problem solving as the means for teaching and learning mathematics. The first chapter is a reprint of his article "On Learning, Teaching, and Learning Teaching." Then, G. L. Alexanderson paints a portrait of "George Polya, Teacher," including some anecdotes that exemplify…

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…

General characteristics of gifted students are listed. Seven attributes that characterize the gifted pupil in mathematics are reviewed in detail. (MP)

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)

Based on the idea that children learn language and mathematics in much the same way, and that they can learn both simultaneously, the five sections of this journal present teaching ideas addressing various aspects of this process. The first section discusses the "language of math" with reference to both the child and the teacher. The…

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…

Describes the method of having children observe videotapes of other children's mathematics activities to gain insights into the observing children's thought processes and the observed children's activities. Discusses the applications of this method as a research tool and as a probe for classroom teachers in evaluating students. (MDH)