We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…

"The Simpsons" is an ideal source of fun ways to introduce important mathematical concepts, motivate students, and reduce math anxiety. We discuss examples from "The Simpsons" related to calculus, geometry, and number theory that we have incorporated into the classroom. We explore student reactions and educational benefits and difficulties…

Math is about the relationship between numbers. Right answers are not the only thing to look for when examining students' work in mathematics. Looking at how children solve computation problems can give teachers insight into their thinking and help determine what math skills they already know and what they still need to learn. The author contends…

The chapters in this book reflect the work of science and mathematics educators who have worked for many years at the international level. As members of the International Consortium for Research in Science and Mathematics Education, their work provides readers with issues, models, practices, and research results that have applicability and…

This study compared the involvement of American and Chinese mothers in their 5- and 7-year-old children's number learning in their everyday experience and during mother-child interaction on mathematics tasks pertaining to proportional reasoning. Results indicated that Chinese mothers of both the 5- and 7-year-old children were more likely to teach…

This numeracy package, which is intended for use by facilitators in group or tutoring situations, consists of materials designed to help adult literacy students understand number systems, appreciate the different roles that numbers play in daily life, and gain the confidence needed to work with numbers in everyday situations. Part 1, which…

This paper posits that, as educators' attention turns to elementary mathematics as preparation for algebra, it is important to begin by examining the kind of elementary mathematics content teaching that is aligned with reform. The paper calls for a close examination of students' development of operation sense. The role of children's engagement…

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…

In this paper four programs are described in which children learn multidigit number concepts and operations with understanding: (1) the Supporting Ten-Structured Thinking projects, (2) the Conceptually Based Instruction project, (3) Cognitively Guided Instruction projects, and (4) the Problem Centered Mathematics Project. The diversity in these…

This study addressed the problem of promoting generalization of knowledge in people with mental handicaps, by presenting an approach based on the idea that certain cognitive representations of strategies and related concepts are common to solving a wide variety of problems. The surface context of these problems may vary considerably, but all will…

The goal of books in this series is to present work that is on the growing tip of research in cognitive development. The theme of this volume is children's logical and mathematical cognition, a field in which Piaget's influence has been extensive. In the first of the six chapters, Acredolo presents a new theory of the cognitive bases for…

The effects of two training sequences on the development of young children's logical operations and number concepts, including rational counting strategies, were investigated. Forty-five preschool children, aged 3.11 to 4.10, were randomly assigned to two treatment groups and one control group. Subjects in the treatment groups received training…

One of the main purposes of a mathematics club is to provide the opportunity for students to study exciting topics in mathematics not ordinarily discussed in the classroom. Each of the 10 chapters in this booklet is a collection of related subtopics. Each idea is presented and discussed; bibliographies then suggest in-depth reading. The chapters…

This set of 13 activities, adapted from "Mathmatters: Developing Computational Skills with Developmental Activity Sequences (by Randall Souviney, Tamara Keyser, and Alan Sarver) was designed to help teachers using the Indigenous Mathematics Project materials (in Papua New Guinea) understand the basic processes involved in computation with…

In a two-year study, frequencies and descriptions of systematic errors in four algorithms in arithmetic were studied in regular and special education classrooms. (Author/SD)