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…

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…

Wishing to explore the complexity of the conceptual, didactic and institutional aspects of learning a scientifically defined object of knowledge, we chose to study the link between the personal relation to numeration developed by six-year-old pupils in first grade ("cours preparatoire" the first level of primary school in France), and…

The What Works Clearinghouse (WWC) looked at elementary school math curricula designed to promote math knowledge and skills among elementary school students (average ages 5 to 10 years). Curricula included in this review are replicable, materials-based instructional programs that cover one or more of the following content areas: numbers,…

The "Connected Mathematics Project" ("CMP)" is a problem-centered mathematics curriculum designed for all students in grades 6-8. Each grade level of the curriculum is a full-year program and covers numbers, algebra, geometry/measurement, probability, and statistics. The program seeks to make connections within mathematics,…

This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…

This document, the first of three volumes, reports on the 15th annual conference of the International Group for the Psychology of Mathematics Education (PME) held in Italy 1991. Plenary addresses and speakers are: "Social Interaction and Mathematical Knowledge" (B. M. Bartolini); "Meaning: Image Schemata and Protocols" (W.…

"How much popcorn will our classroom hold?" This intriguing question sparked a terrific integrated science and math exploration that the author conducted with fifth-and sixth-grade students. In the process of finding the classroom's volume, students developed science-process skills (e.g., developing a plan, measurement, collecting and interpreting…

The purpose of this research is to compare the rural education practices of China, Taiwan, Canada and the United States. International comparisons of mathematics achievement find that students in Asian countries outperform those from the USA. Excluded from these studies, however, are students from rural areas in China. This study compares the math…

Two samples of kindergarten children's representation and understanding of written number symbols were examined in two time points in one academic year. About 85% of Chinese five year olds (mean = 5 years 10 months) were able to use conventional number symbols to represent the quantity of 30 or larger. At the end of the kindergarten year, 94% of…

This work examines the association between symbols and their representation in adult developmental dyscalculia and dyslexia. Experiment 1 used comparative judgment of numerals, and it was found that in physical comparisons (e.g., 3-5 vs. 3-5) the dyscalculia group showed a significantly smaller congruity effect than did the dyslexia and the…

This paper presents a description of the different types of arguments that emerged as two students, working in a computerized environment, engaged in an investigation of several number theory concepts. The emerging arguments are seen as a result of the influence of the computerized environment together with collaborative learning. Using…

This article presents several activities (some involving graphing calculators) designed to guide students to discover several interesting properties of Fibonacci numbers. Then, we explore interesting connections between Fibonacci numbers and matrices; using this connection and induction we prove divisibility properties of Fibonacci numbers.

A conceptually sound, research-based method is presented to make sense of students' thinking about length. It is suggested that the levels of framework is an important tool for improving instruction and formative assessment as well as effectively diagnosing and remediating students' difficulties in learning about length. Some of the measurement…

The authors present an analysis of portfolio entries submitted by candidates seeking certification by the National Board for Professional Teaching Standards in the area of Early Adolescence/Mathematics. Analyses of mathematical features revealed that the tasks used in instruction included a range of mathematics topics but were not consistently…