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…

Students need to enter the interconnected global community with an understanding of how different cultures perceive the world, how the cultures and societies of today evolved from those of the past, and how all peoples impact the development of future societies. Unfortunately, time constraints or lack of resources in schools cause many social…

This study examined teachers' uses of virtual manipulatives across grades K-8 after participating in a professional development institute in which manipulatives and technology were the major resources used throughout all of the activities. Researchers analyzed 95 lesson summaries in which classroom teachers described their uses of virtual…

We focus on the concept of matter and explore how young children in urban schools bridge their spontaneous concepts and everyday experiences with scientific concepts introduced to them by children's literature information books and their teacher. The study shows how material artifacts used in a sorting activity became ideational tools--semiotic…

Manipulatives are the way to our future and the way to new knowledge. No matter where we turn or what we do, we as a society are using some form of manipulative in our lives. Mathematics is changing all of the time from basic arithmetic to basic calculus. Therefore, children in today's classroom deserve to have that extra tool to help them grasp…

This paper describes a 2-year collaborative action research project in which the focus was to investigate the effects of the use of "Hands-On Equations" mathematics manipulatives in an algebra class on students' confidence, interest in, and ability to solve and retain understanding of algebraic equations. The first phase centered on documenting…

The paper shows that the study of mathematics can be organized as a complex learning enterprise integrating manipulative-exploratory play into a newer software tool environment--a dynamic geometry, a spreadsheet, and a relation grapher. The discussion reflects work done in a lab setting with preservice and inservice teachers enrolled in…

This perfect bound teacher's guide presents techniques and activities to teach mathematics using origami paper folding. Part 1 includes a history of origami, mathematics and origami, and careers using mathematics. Parts 2 and 3 introduce paper-folding concepts and teaching techniques and include suggestions for low-budget paper resources. Part 4…

Primary students can use a geoboard to develop perceptual motor skills, pattern observation, and thinking ability by reproducing designs and developing strategies for games. (SD)

This paper discusses the results of questionnaires sent to principals and teachers on the subject of manipulatives, computer, and calculator availability and use in the classroom. The study was done in order to develop a better understanding of teachers' inservice needs. Results of the study include: (1) most teachers have at least some…

This publication presents teaching strategies to develop understanding of fractions as sensible numbers. Written for the mathematics teacher in grades K-5, it gives suggestions for teacher-led discussions and structured exploratory activities. The activities are conducted with manipulative materials that emphasize the important characteristics and…

This volume is a collection of nine papers focusing on different aspects of play. The first section, "Play, Growth, Development, and Learning," contains discussions dealing with make-believe play and learning; an all-in-fun approach to thinking, playing, and language learning for young children; and ways children learn through play. The…

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…

This set of papers was selected from presentations made at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics because of their pertinence to classroom teachers. The papers concern: (1) "Research and Development Related to Learning about Numerals for Whole Numbers: Implications for…

This document suggests ways of using children's intuitive ideas about mathematics as a starting point for an elementary curriculum. Ways are discussed to capitalize on what children already know: to cultivate rather than discourage students' intuitive mathematical sense, and to help students make connections between what they know and what they…