In this issue's "Classroom Notes" section, the following papers are discussed: (1) "Constructing a line segment whose length is equal to the measure of a given angle" (W. Jacob and T. J. Osler); (2) "Generating functions for the powers of Fibonacci sequences" (D. Terrana and H. Chen); (3) "Evaluation of mean and variance integrals without…

The development of conceptual understanding in arithmetic is a gradual process and children may make use of a concept in some situations before others. Previous research has demonstrated that when children are given arithmetic problems with an inverse relationship they can infer that the initial and final quantities are the same. However, we do…

Mathematics lecturers have long expressed concern about their students poor mathematical background and the effect this has on performance in first mathematics courses at university level. This article explores a similar concern about students' numeracy in a statistics course for psychologists.

Leaders in professional development have called for more learner-centered professional development opportunities for teachers. These approaches allow teachers to have some choice about the content and pedagogies on which they focus during professional development courses. This paper shares case studies of three participants from InterMath, a …

Games are among the many types of activities that can be used to help promote number sense. Chosen and used wisely, games encourage learning and motivate many students to grasp concepts more quickly and fully. This article describes a popular and easy-to-implement number sense game--called Digits and Dice--most commonly used in conjunction with…

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)