With recent advances in computer technology, it is no surprise that the manipulation of objects in mathematics classrooms now includes the manipulation of objects on the computer screen. These objects, referred to as "virtual manipulatives," are essentially replicas of physical manipulatives placed on the World Wide Web in the form of computer…

Meaningful educational activities and cognitive tools might improve students' active involvements in the teaching-learning process and encourage their reflections on the concepts and relations to be investigated. It is claimed that usage of manipulatives not only increase students' conceptual understanding and problem solving skills but also…

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…

Following a summary of research pertaining to the Montessori and Whole Language philosophies, this paper examines similarities between the two philosophies. Both philosophies are based on holistic learning, use cross-cultural materials, and stress the teacher's role as a facilitator within the classroom environment. The relationships of the…

Three short articles about tactile illustrating are presented for braille transcribers and teachers of the visually handicapped. Some transcribers have been making tactile maps with water areas textured and land masses smooth; the first article reports on the confusion these "reversed maps" cause braille readers and gives additional tips…

This study was undertaken to gain insights into children's understanding of rational numbers as quantities; that is, the extent to which they associate a size with a fraction like 2/3. Eight children in an experimental group in DeKalb, Illinois, chosen to reflect the range from low to high ability, were observed during 30 weeks of experimental…

The practicum paper describes the development of a mathematics program for primary-level educationally handicapped students, to be implemented by resource room teachers. Developmental areas covered include: numbers (0-10), addition and subtraction (sums to 10), place value, and time and money. The 10-month intervention period was preceded and…

Learning is a complex operation that involves a several factors. In studying the learning process, both the characteristics of the learner and the conditions of instruction must be considered. This study examined some of the factors that may influence the learning of mathematics. In particular, it sought to identify relationships among mathematics…

This ERIC digest examines recent research about the use of manipulatives to teach mathematics. "Manipulatives" refers to objects that can be touched and moved by students to introduce or reinforce a mathematical concept. The digest also speculates on some of the challenges affecting future use of manipulatives. Since the 19th century,…

This booklet is a collection of puzzles, investigations, and games. They are designed to be used with large objects such as tins or stones and diagrams marked on the ground. The children are to be encouraged to use an experimental, trial-and-error approach at first, and then develop methods of solution. (MNS)

This booklet is a collection of puzzles, games, and investigations. All that children need are some stones or shells, on some of which they must write numerals. For playing with the whole class, the game or puzzles may be marked out on the floor or in sand; in that case, larger objects such as small rocks and empty tins may be used. Children are…

This document contains detailed directions for constructing a device that mechanically produces the three-dimensional shape resulting from the rotation of any algebraic line or curve around either axis on the coordinate plant. The device was developed in response to student difficulty in visualizing, and thus grasping the mathematical principles…

Students enjoy learning by doing and by manipulating objects. This paper describes classroom activities using rods with various lengths and different colors. The activities included are: (1) preparation of rods; (2) elementary addition and subtraction; (3) fractions; (4) concept of greater than, less than, and equals; (5) simple division and…

To investigate similarity judgements in different cultural contexts, the performance of two groups of children on seven similarity tasks and on two tests of metaphor was compared. The 45 Canadian and 45 Canadian-Greek children (ages 5, 8, and 11) had different cultural and linguistic backgrounds but common schooling experiences. The seven tasks…