Reflects on four years of teaching a course called Principle of Major Teachers for pre-service elementary school teachers. Identifies and describes the discord between their formal mathematical knowledge and their informal language used in the context of elementary number theory. Presents encouraging results from a code-switching experiment.…

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…

Creates graphs to see how the relative frequency of an event tends to approach the probability of that event as the number of trials increases. Uses a simulation of a poker machine to provide context for this subject. (ASK)

Discusses numeracy strategy. Focuses on gaining insight into student understanding of number. Discusses the benefits of this long-overdue numeracy strategy. (ASK)

Presents a mathematician's reflections on his experiences as a young mathematician in elementary school and at home, including some mathematical moments that sparked his interest in dimensions and mathematical thinking. Also describes his experiences working with K-6 teachers and students. (Contains 17 references.) (ASK)

Studies two children working in the context of specially developed computer microworlds with a teacher/researcher for approximately 45 minutes a week for 50 weeks over a two-year period. Indicates that the operations and unit types associated with the children's whole-number sequences did not interfere with the reorganization of their fractional…

Presents an activity in which students must arrange five fractions represented by dominoes in ascending order and justify their reasons for the ordering. Representing common fractions with dominoes helps identify students' misconceptions about fractions. (ASK)

Describes a game to generate discussion and confront misconceptions about decimals. (ASK)

Describes a classroom-based model for professional development that allows teachers to gain further insight into matching learning experiences with a child's potential. (ASK)

Presents two problems with multiple approaches concerning the one hundredth of something. Describes student attempts at solving these nonroutine problems using a variety of strategies. (ASK)

Describes a kindergarten teacher's experiences in using the song "The Twelve Days of Christmas" to increase students' awareness of basic number sense and understanding of patterns. (ASK)

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…

This study examines young children's number sense in subjects from Finland (n =254), Hong Kong (n =246), and Singapore (n =130). Chinese, English and Finnish versions of the Early Numeracy Test (ENT; Van Luit et al., 1994) were used. Two highly correlated aspects of number sense were measured, one reflecting children's abilities to organize and…

In this study, six elementary grade children with developmental dyscalculia were trained individually and in small group settings with a one-semester program stressing basic numerical knowledge and conceptual knowledge. All the children showed considerable and partly significant performance increases on all calculation components. Results suggest…