We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by first-grade teachers in the United States and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered,…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

This is an account of events in a real classroom when the notion that there is a distinction between calculation by counting, and calculation by structuring is a focus for learning. Pupils have "hands-on" experiences that support their understanding of "number". The teaching "aid" might be unfashionable in…

The purpose of this study was to determine variables that predict performance when virtual manipulatives are used for mathematics instruction. This study used a quasi-experimental design. This design was used to determine variables that predict student performance on tests of fraction knowledge for third- and fourth-grade students in two treatment…

Engaging students while providing them with the necessary linguistic and critical skills as a foundation for further exploration are the principle challenges for those of us who teach disciplinary introductory courses. My own response to this challenge has been to develop and implement what I refer to as the "pedagogy of play." Informed…

In this article, the author discusses the creativity of origami and discusses a model she designed in May 2008 in Freiburg at the 20th International Origami Convention of Origami Deutschland. The model resulted from her investigation of a geometric model that exposes the centre part of a square paper sheet. The base model of the series called…

Object use is a ubiquitous characteristic of the human species, and learning how objects function is a fundamental part of development. In this article the authors examine the role that intentionality plays in children's understanding of causal relationships during observational learning of object use. Children observed demonstrations in which…

This article explores the material culture of kindergarten in the United States in relation to the production and consumption of materials and kindergarten theory and pedagogy. The focus is on Friedrich Froebel's building gifts as they were manufactured and sold by the Milton Bradley Company from 1869 to 1939. A review of trade catalogues over the…

Much has been written about the value of concrete manipulatives for supporting students' mathematics learning. This is particularly true for the domain of fractions and decimals. Understanding of decimal place-value is seen as critical for students' mathematics learning. To understand decimals, students need first to have a solid understanding of…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

During an informal, after-school, math program, a group of middle school students worked collaboratively on open-ended problems. The students co-constructed arguments, provided justifications for their solutions, and engaged in mathematical reasoning. This paper describes the specific teacher moves that promoted this phenomenon. The findings of…

The study reported here examined virtual manipulatives as an instructional treatment in 17 third- and fourth-grade classrooms. Students were randomly assigned to two treatment groups: texts and physical manipulatives, and virtual manipulatives. Results revealed no significant differences in achievement between the treatments. Additional results…

Introduction: This article, based on a study of 196 teachers of students with visual impairments, reports on the experiences with and opinions related to their decisions about instructing their students who are blind or have low vision in the abacus. Methods: The participants completed an online survey on how they decide which students should be…

Computer science proficiency continues to grow in importance, while the number of students entering computer science-related fields declines. Many rich programming environments have been created to motivate student interest and expertise in computer science. In the current study, we investigated whether a recently created environment, Robot…