"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

This report examines the importance and efficacy of oral language, literacy, mathematics, and science preschool curricula and how these curricula can be improved through alignment with research on early childhood development and learning. Detailed, research-driven recommendations are presented for what preschool-aged children should be learning in…

This paper discusses the use of Stern teaching materials with children with Down syndrome. The theory underlying the design of the materials is discussed, the teaching approach and methodology are described and evidence supporting effectiveness is outlined. (Contains 2 figures.)

This paper discusses the use of Numicon number teaching materials with children with Down syndrome. The theory underlying the design of the materials is discussed, the teaching approach and methodology are described and evidence supporting effectiveness is outlined. (Contains 4 figures.)

Some questions about the relevance of the philosophy of mathematics to mathematics teaching and to early mathematics learning are discussed. Books by Lakatos, Davis and Hersh, and Kitcher are referred to extensively, with comments on a variety of instructional practices. (MNS)

Guidelines for teachers to better use manipulatives in the teaching of mathematics to learning disabled learners are offered including a rationale for manipulatives, selection crteria, principles underlying productive use of manipulatives, and making the transition from the concrete to the symbolic. Suggested materials and distributors are listed.…

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

An activity for generating approximations of pi is described. (MK)

Reasons for using manipulative materials in mathematics instruction are discussed: motivation, stimulation to think mathematically, and introduction of big ideas in mathematics. (MNS)

The author comments on varying factors she noted as she observed 125 primary schools in 32 countries. Of particular interest to her were approaches in Australia and New Zealand using manipulative materials. Several conclusions pertinent to U.S. schools are drawn. (MNS)

Presents two hands-on mathematics activities for teaching K -3 students to experience fractions on a tactile level. The first uses chocolates to demonstrate that fractions can be part of a whole, can be part of a set, and are equal parts. The second has students design a classroom fraction museum with fraction exhibits designed and presented by…

Attribute blocks are described, with suggestions for developing sets of attribute materials. Various activities and games are described and illustrated. (MNS)

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)

The importance of using concrete materials to teach fractions is emphasized. Suggestions for preparing inexpensive sets of such materials are given, with nine activities for their use. (MNS)

Renaming fractions with the dot method is described with illustrations. It can be used to introduce renaming at the manipulative level in a meaningful way prior to moving to a more abstract level where prime factorization will be involved. (MNS)