Discusses children's concept of number and number operations and describes activities which help to develop number concepts and skills. (JP)

A presentation of learning experiences involving materials is recommended which reflects the sequence of the developmental stages. This sequence is concrete, concrete-abstract, pictorial-abstract, and abstract. Instructional examples at each level are presented. (JP)

The study attempted to show that the first grade child's learning in a new area must involve overt concrete experiences from which new ideas will be derived. Forty-nine students, assigned to six groups, were instructed on three scientific concepts. The verbal instruction technique was similar to that suggested in SCIS. The application segment…

Described are two methods of calculating developed by the Dutch WISKOBAS Project: addition and subtraction with a loop abacus and multiplication using a grid model. (MP)

An exploratory investigation designed to gain insights into children's mathematical formulation of observed actions upon objects is presented. Eight episodes in which first and second graders were asked to interpret, in terms of number sentences, a sequence of actions with unifix cubes are also presented. Results of analysis of the videotaped…

Some possible uses of math lab materials and activities that are natural and appropriate to the development of process skills are explored through a discussion of a geoboard activity. (MP)

In the experiment discussed, three modes of presenting materials to second grade students were compared. Data analysis showed that the abstract mode was less successful than the others, but there was no clear difference between the manipulative and pictorial modes. (SD)

Achievement of 20 Trainable Mentally Retarded and 67 Educable Mentally Retarded Students under manipulative and non-manipulative modes of mathematics instruction are compared. (MM)

After a discussion on planning instruction, a series of activities designed to develop pre-number and number concepts are presented. Activities are arranged by difficulty within sections devoted to classifying, comparing, ordering, measuring, organizing data, distinguishing shape and size, recognizing patterns, number awareness, and counting. (SD)

This paper examines some of the manipulative aids used in elementary mathematics instruction from the point of view of the cognitive structures needed to understand them. The number line, measurement activities, models for place value, and models for fractions are discussed. (SD)

Through a mathematical analysis, Piaget's grouping concept can be formally interpreted as being a hybrid between the mathematical concepts of a group and a lattice. Some relevant pedagogical models are presented. Activities with Cuisenaire Rods, Dienes Blocks, and Papy's Minicomputer are shown to take place in groupings. (LS)

This paper discusses six aspects of current practice in mathematics instruction of elementary school children: (1) use of symbolization, (2) use of models, (3) consideration of child development, (4) "logical" vs. "natural" approaches, (5) individualization, and (6) diagnosis and prescription. The author argues that symbols are frequently…