Discusses figurate number learning activities using patterns and manipulative models. Provides examples of square numbers, triangular numbers, pentagonal numbers, hexagonal numbers, and oblong numbers. (YP)

Data from (n=4) students in grades three through six showed a consistent parallel between the types of units constructed in a geometric setting with those in a numeric context. Students who constructed abstract composite units in tiling the plane also did so in adding and subtracting whole numbers. (Author/MKR)

Adapted Keil's predictability method to examine adults' and preschoolers' conceptions of numbers, focusing on the ontological distinction between numbers and sets of objects. Found that children, like adults, attribute spatial-arrangement properties to collections much more than to numbers, although both are considered to have quantitative…

Many researchers agree that children's difficulty with fraction and rational numbers is associated with their whole number knowledge, but they disagree on the origin of the whole number bias. This article reviews three explanations of the nature of the bias. These accounts diverge on the questions of whether or not early quantitative…

In this article we describe the mathematics curriculum and teaching practices in a purposive sample of high-poverty elementary schools working with 3 of the most widely disseminated comprehensive school reform programs in the United States. Data from 19,999 instructional logs completed by 509 first-, third-, and fourth-grade teachers in 53 schools…

Patients with corticobasal degeneration (CBD) appear to have impaired number knowledge. We examined the nature of their number deficit while we tested the hypothesis that comprehension of larger numbers depends in part on verbal mediation. We evaluated magnitude judgments and performance on number conservation measures rooted in Piagetian theory…

This paper is written on a level accessible to college/university students of mathematics who are taking second-year, algebra based, mathematics courses beyond calculus I. This article combines material from geometry, trigonometry, and number theory. This integration of various techniques is an excellent experience for the serious student. The…

Not all children are made the same. Learning disabilities like dyslexia, dysgraphia or dyscalculia are either not understood or ignored in schools. As a result, the schoolchildren suffer for no fault of theirs and they lag behind in their course of learning. They may find it difficult to achieve the basic skills of learning such as reading,…

Despite widespread agreement that the activity of "reasoning-and-proving" should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that…

A current issue in developmental science is that greater continuity in cognition between children and adults may exist than is usually appreciated in Piaget-like (stages or "staircase") models. This phenomenon has been demonstrated at the behavioural level, but never at the brain level. Here we show with functional magnetic resonance imaging…

Two intervention studies are described. Both were designed to study the effects of teaching children about the inverse relation between addition and subtraction. The interventions were successful with 8-year-old children in Study 1 and to a limited extent with 5-year-old children in Study 2. In Study 1 teaching children about inversion increased…

The meaning of International Standard Book Numbers (ISBN) and the mathematics involved in the use of a check digit to catch errors in number transcription are discussed. (JM)

Bases such as 5 and 12 provide the same structural place value benefits as base 10. However, when numbers less than one are concerned, base 10 provides friendly decimals for the most common fractions of half, quarter, three-quarters. Base 5 is not user friendly at all in this regard. Base 12 would provide nice dozenimals(?) for the same…

This guide is designed to aid the teacher in planning and teaching an eighth-grade mathematics course which should strengthen the student's understanding of the basic structure of mathematics through experience with and appreciation of abstract concepts. Thirteen units outlined are entitled: Numeration Systems; Natural Numbers and Zero; Integers;…