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“If You Can Turn a Rectangle into a Square, You Can Turn a Square into a Rectangle ...” Young Students Experience the Dragging Tool

“If You Can Turn a Rectangle into a Square, You Can Turn a Square into a Rectangle ...” Young... This paper describes a study of the cognitive complexity of young students, in the pre-formal stage, experiencing the dragging tool. Our goal was to study how various conditions of geometric knowledge and various mental models of dragging interact and influence the learning of central concepts of quadrilaterals. We present three situations that reflect this interaction. Each situation is characterized by a specific interaction between the students’ knowledge of quadrilaterals and their understanding of the dragging tool. The analyses of these cases offer a prism for viewing the challenge involved in changing concept images of quadrilaterals while lacking understanding of the geometrical logic that underlies dragging. Understanding dragging as a manipulation that preserves the critical attributes of the shape is necessary for constructing the concept images of the shapes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Technology, Knowledge and Learning" Springer Journals

“If You Can Turn a Rectangle into a Square, You Can Turn a Square into a Rectangle ...” Young Students Experience the Dragging Tool

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Publisher
Springer Journals
Copyright
Copyright © 2007 by Springer Science+Business Media, Inc.
Subject
Education; Learning and Instruction; Mathematics Education; Educational Technology; Science Education; Creativity and Arts Education
ISSN
2211-1662
eISSN
1573-1766
DOI
10.1007/s10758-006-9106-7
Publisher site
See Article on Publisher Site

Abstract

This paper describes a study of the cognitive complexity of young students, in the pre-formal stage, experiencing the dragging tool. Our goal was to study how various conditions of geometric knowledge and various mental models of dragging interact and influence the learning of central concepts of quadrilaterals. We present three situations that reflect this interaction. Each situation is characterized by a specific interaction between the students’ knowledge of quadrilaterals and their understanding of the dragging tool. The analyses of these cases offer a prism for viewing the challenge involved in changing concept images of quadrilaterals while lacking understanding of the geometrical logic that underlies dragging. Understanding dragging as a manipulation that preserves the critical attributes of the shape is necessary for constructing the concept images of the shapes.

Journal

"Technology, Knowledge and Learning"Springer Journals

Published: Jan 12, 2007

References