The use of a variety of models to develop number concepts is advocated. Four models are discussed, with illustrations: the cardinal number of a set, Cuisenaire rods, the number line, and the Papy Minicomputer. (MNS)

Using manipulative materials and pictures is considered valuable, but the need to use models appropriate for individual children is stressed. Suggestions for using well-structured physical space are given. (MNS)

Investigated what effects two instructional strategies (related to student use of manipulative materials) would have on second-grade students' (N=96) development of logical structures. Also examined the effects of sex on logical development. Results indicate that supplying manipulative materials alone is not adequate in promoting development of…

The relationship in the Pythagorean Theorem is introduced to low-ability seventh graders using Cuisenaire rods. The sequence of instruction is described. (MNS)

Discusses how teachers can help students make the transition from using manipulative materials to abstract mathematical symbols. Includes: (1) a definition of the transition state; (2) ways to bridge the gap (by asking questions and by using activities); and (3) a specific example (teaching place value). (JN)

The preparation of prospective teachers to use manipulatives in the classroom involved three dimensions. Each of these dimensions is discussed within the context of the elementary and early childhood teacher education program at Pennsylvania State University. (JN)

Findings from a study with first-grade children on addition and subtraction help make a case for a conceptual rather than a mechanized approach to the operations. How base ten blocks were used in the program is illustrated. (MNS)

The game of Fractional Dominoes is illustrated. (DT)

Designs on a circular geoboard lead to an investigation of factors, primes, relative primes, and modular arithmetics. (DT)

This paper describes a theoretical model for examining teaching and learning in primary mathematics classrooms. The model in intended to be both analytical--to provide insights into classroom incidents--and heuristic--to inform planning and practice. This paper reports on the elements of the model, which are based on Vygotskian theory and…

A study examined the effect of manipulative instruction on the acquisition and maintenance of perimeter and area problem-solving skills by students with learning disabilities in math. Three rural students with learning disabilities in mathematics in grades 7-10 participated in the study. All training was conducted daily for 15-20 minutes on a…

By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without…

These classic pattern blocks were introduced in the early 1960s as part of the Elementary Science Study materials developed by the Educational Development Center (EDC). The six classic shapes share one common characteristic: all of the angle measurements are multiplies of 30 degrees. Shapes include the regular triangle, square, and hexagon; the…

Multibase arithmetic blocks are used to investigate the minimum number of blocks of each size to make a square of a given size in a given base. Generalizations are made to any size and any base through pattern recognition. The problem is extended to rectangles, cubes, and rectangular solids. (LS)