Advocates the use of classification activities in the elementary school curriculum as a means of developing thinking skills in children. Critical preclassification skills, classification activities (including simple and multiple classification), and classification tasks and materials are discussed. (Author/RH)

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)

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)

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)

Provides the instructions to build a homemade calculator that can be used as a reinforcement device to assist primary students in memorizing their addition facts. (MDH)

Strategies used by 150 children as they solved addition and subtraction verbal problems were studied over a period of one-and-a-half years. Number size and presence of manipulative materials were variables manipulated in individual interviews given at three separate intervals. Two addition and four subtraction tasks were used. Processes changed…

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…

Activities for the development of the association of number value and symbols using wooden numerals and pages are described. (MN)

Presents activities that have been used successfully in leading students from concrete experiences through pictorial and symbolic representations of important numeration concepts and patterns, including place value, multiples, and rounding. Each activity includes concept or skill fostered, list of materials needed, recommended grade level, and…

Examined is the notion of "representation" as it is used in mathematics education. The first section explains what appears to the current "received view" of representation within mathematics education. The second section describes the constructivist view of representation, especially as this view is related to Piaget's theory. The third section…

Presents the use of manipulatives in the three stages of concept learning called concrete, bridging, and symbolic. Examines the three stages in developing the concept of rounding two-digit numbers. (MDH)

The development of the place value system and its universal use demonstrate the elegance and efficiency of mathematics. This paper examines the concept of place value by: (1) presenting the historical development of the concept of place value in the Hindu-Arabic system; (2) considering the evolution of the number zero and its role in place value;…

This study was designed to examine effects that access to manipulatives in science instruction have with respect to the development of spatial conceptual abilities and whether the effects were different for males and females. A secondary purpose of this investigation was to examine what relationship sex and access to manipulatives in conjunction…

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)