In this article, we draw on assemblage theory to investigate how children aged 5 engage with different material surfaces to explore ordinal and relational aspects of number. The children participate in an activity in which they first interact with a strip on the floor, then with a multi-touch iPad application, to work with numbers in expressive…

The purpose of this study was to examine patterns of mathematical practices evident during children's interactions with touchscreen mathematics virtual manipulatives. Researchers analyzed 33 Kindergarten children's interactions during activities involving apps featuring mathematical content of early number sense or quantity in base ten, recorded…

In this article we present an activity theory based framework that can capture the complex situations that arise when modern technology like multi-touch devices are introduced in classroom situations. As these devices are able to cover more activities than traditional technologies, even computerbased, media, we have to accept that they now take a…

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…

Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

This study investigated the effects of two generative learning activities on students' academic achievement of the part-whole meaning of rational numbers while using virtual manipulatives. Third-grade students were divided randomly in two groups to evaluate the effects of two generative learning activities: answering-questions and…

A concrete approach to prime numbers is presented using rectangles and triangles to construct a building for each number so that each story represents a pair of factors and the triangular-shaped roof represents the number. (MP)

A series of activities designed to help primary school children understand the meaning of the term "fraction," the symbolization, and equivalence of fractions are presented. Identification of units and pictorial representation are stressed, as is the uses of concrete materials. (SD)

Presented are several methods of introducing nondecimal numeration systems to elementary grade students. Various activities for grouping and/or visual displays are used. Games which incorporate nondecimal grouping ideas are also presented. (JP)

This set of 13 activities, adapted from "Mathmatters: Developing Computational Skills with Developmental Activity Sequences (by Randall Souviney, Tamara Keyser, and Alan Sarver) was designed to help teachers using the Indigenous Mathematics Project materials (in Papua New Guinea) understand the basic processes involved in computation with…

The development of number concepts from conservation through order and place value notation is discussed in the context of applications to classroom instruction. Activities designed to motivate, build, and reinforce these concepts are described, and a list of objectives is presented in the form of a suggested progress record. (SD)

A series of nine activities that illustrate prime factorization and other elementary number theory ideas in concrete, representative, and symbolic form are described. (MNS)

Brief articles are included on dropping perpendiculars, working with rational exponents, and finding the square root with base 10 blocks. (MNS)

Activities for teaching mathematics in kindergarten through grade 8 are included in this guide. Both original ideas and ideas gleaned from various sources, including teachers in the district, are presented. The introduction briefly discusses the importance of developing understanding of concepts, processes, and relationships, the need for…