In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…

Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…

Several formulae for the inradius of various types of triangles are derived. Properties of the inradius and trigonometric functions of the angles of Pythagorean and Heronian triangles are also presented. The entire presentation is elementary and suitable for classes in geometry, precalculus mathematics and number theory.

Previous research has demonstrated that both hearing adults and hearing children with no training in arithmetic successfully performed approximate arithmetic on large sets of elements. Here, the possibility is explored that the same phenomenon can be confirmed in deaf adults who have acquired a signed language as their first language. Results…

Developmental research suggests that some of the mechanisms that underlie numerical cognition are present and functional in human infancy. To investigate these mechanisms and their developmental course, psychologists have turned to behavioral and electrophysiological methods using briefly presented displays. These methods, however, depend on the…

The author cites research from students' misconceptions of decimal notation that indicates that many students treat decimals as another whole number to the right of the decimal point. This "whole number thinking" leads some students to believe, in the context of comparing decimals, that "longer is larger" (for example, 0.45 is…

This article describes an example of a fourth-grade lesson from Taiwan in which number sense is developed through real classroom interactions.

Human cognition is founded, in part, on four systems for representing objects, actions, number, and space. It may be based, as well, on a fifth system for representing social partners. Each system has deep roots in human phylogeny and ontogeny, and it guides and shapes the mental lives of adults. Converging research on human infants, non-human…

This study examines a wide range of numerical representations (i.e., quantity, knowledge of multiplication facts, and use of parity information) in adult deaf signers. We introduce a modified version of the number bisection task, with sequential stimulus presentation, which allows for a systematic examination of mathematical skills in deaf…

This paper discusses the use of Numicon number teaching materials with children with Down syndrome. The theory underlying the design of the materials is discussed, the teaching approach and methodology are described and evidence supporting effectiveness is outlined. (Contains 4 figures.)

This article describes an instructional sequence intended to help students think about why integer operations work the way they do. It introduces the idea of an integer as a composite unit and embeds the well-known debit/credit model in an "allowance" context. (Contains 3 figures.)

This report focuses on prospective secondary mathematics teachers' understanding of irrational numbers. Various dimensions of participants' knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the…

In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…

This publication is designed to help teachers increase awareness of multicultural issues for all students while making science and mathematics more relevant and approachable to children of color. The activities presented in this book are both multicultural and hands-on; they are discoveries to be made by the reader. They will allow teachers and…

This document is a collection of over 200 classroom-ready activities which cover the five strands--Number, Space, Measurement, Chance and Data, and Problem Solving--outlined in Mathematics: A Curriculum Profile for Australian Schools. Each activity is a separate photocopy master, the front for the students to use and the back an assessment page…