The purpose of the study was to examine the effect of instruction using Dienes' perceptual variability principles on primitive generalization and mathematical generalization. The following was studied: the effect of achievement-to-criterion on one, two, or three non-symbolic embodiments of an objective using a selected class of variables on the…

The purpose of the study was to examine the effect of instruction using Dienes' perceptual variability principle on the development of ability to operate with symbols in a meaningful way. The following was studied: whether an increase in the number of enactive and/or iconic embodiments of a concept utilized in an instructional episode will produce…

Derived from tests presently used by state and federal agencies involved with pollution detection, this Environmental Test Kit contains materials and instructions for ten experiments. Each experiment is designed to test a different aspect of air and water, to find out whether or not the air and water in the tester's immediate area has been…

This essay considers recent research on classification as related to the study of mathematics in the early grades. The first section deals with the bases and types of classification used by children in free sorting activities. The next section specifically relates to elementary school mathematics. Experiments and theory on class inclusion,…

This paper outlines the rationale of the Fundamentals Underlying Number (F. U. N.) program, and describes Unit I, which is primarily intended for nursery and kindergarten children. This unit develops concepts for sets, numbers, and relations. Each major concept is broken into finely sequenced levels, and at each level instruction is through two…

Descriptions and pictures of apparatus for use in teaching measurement are accompanied by descriptions of typical uses of the materials. A list of names and addresses of suppliers is included. (SD)

Addition and subtraction of integers can be approached through the use of chips of two colors. (SD)

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)

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)

Construction of a series of 13 nested, regular tetrahedrons from 12 square sheets of paper without using geometric instruments, scissors, or glue is described. (MN)

This article examines the role of nonverbal activity in mathematics instruction. Use of manipulative materials and visual aids is discussed, and the effects of teacher gestures and facial expressions are analyzed. (SD)

Congenitally-blind (N=16) and sighted (N=16) young adults listened to descriptions of routes and then finger traced routes through a raised line matrix. Route tracing speed and accuracy revealed that spatial sentence verification interfered with route memory more than abstract/verbal sentence verification for all subjects. (Author/CB)

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)

Specific instruction in different contexts provide needed background for solving addition and subtraction problems. The categories of problems and relative difficulties are presented, followed by an explanation of a successful instructional sequence. (MNS)