Presents a case study with an at-risk second grade student on counting and numbers. Discusses counting stages that the student went through. (ASK)

Presents an activity in which students build their flexibility in using numbers and explore the connections between numbers and their representations with base-10 materials using the TI-15 calculator. (ASK)

Describes how the card game Numero helps students improve their knowledge of basic number facts while having fun. Suggests ways in which Numero can best be used in the classroom. (ASK)

This study compared 6- to 7-year-olds' knowledge of numerical fractions prior to school instruction in Croatia, Korea, and United States. Results suggested that the Korean vocabulary of fractions may influence the meaning children ascribe to numerical fractions and that this results in children being able to associated numerical fractions with…

Describes the "Count Me In Too" project in New South Wales and provides some insight into the way children were assessed. Introduces the "Learning Framework in Number," a research-based framework for assessing and teaching early number concepts. (Contains 12 references.) (ASK)

Describes a lesson in which second grade students learn about data management, number sense, and patterns as they analyze, classify, and describe their fathers' shoes. (ASK)

Novices and experts used the same metaphors to understand and solve problems with negative numbers. Results suggest that the metaphors used by both the children and the adults are central to understanding arithmetic. (Author/MM)

This study investigated the developmental paths of Japanese Grade 1 students' understanding of quantities through the examination of their addition solution methods over the school year period. The individual students exhibited a wide range of experiences with and knowledge of addition from the beginning to the end of the school year. Students…

Numbers can be represented in a variety of ways--through pictures, diagrams, symbols. Each representation highlights different features of the number and the number system. This study aims to explore pupil understanding of number both within and across representations. A computer environment (suite of programmes) was created within which…

Two alternative hypotheses can be used to explain how young children acquire the cardinal meaning of small-number words. The first stresses the role of counting and predicts better performance when the items are presented in succession. The second considers the role of subitizing and predicts better performance when the items are presented…

We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

The authors provide activities for overcoming some fraction misconceptions using calculators specially designed for learners in primary years. The writers advocate use of the calculator as a way to engage children in thinking about mathematics. By engaging with a calculator as part of mathematics learning, children are learning about and using the…

This paper focuses on the kinds of notations young children make for fractional numbers. The extant literature in the area of fractional numbers acknowledges children's difficulties in conceptualizing fractional numbers. Some of the research suggests possibly delaying an introduction to conventional notations for algorithms and fractions until…

This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…

A solid understanding of equivalent fractions is considered a steppingstone towards a better understanding of operations with fractions. In this article, 55 rural Australian students' conceptions of equivalent fractions are presented. Data collected included students' responses to a short written test and follow-up interviews with three students…