http://dx.doi.org/10.1007/s10649-013-9492-4">
 

Document Type

Journal Article

Department/Unit

Department of Education Studies

Title

Discernment of invariants in dynamic geometry environments

Language

English

Abstract

In this paper, we discuss discernment of invariants in dynamic geometry environments (DGE) based on a combined perspective that puts together the lens of variation and the maintaining dragging strategy developed previously by the authors. We interpret and describe a model of discerning invariants in DGE through types of variation awareness and simultaneity, and sensorimotor perception leading to awareness of dragging control. In this model, level-1 invariants and level-2 invariants are distinguished. We discuss the connection between these two levels of invariants through the concept of path that can play an important role during explorations in DGE, leading from discernment of level-1 invariants to discernment of level-2 invariants. The emergence of a path and the usefulness of the model will be illustrated by analysing two students' DGE exploration episodes. We end the paper by discussing a possible pathway between the phenomenal world of DGE and the axiomatic world of Euclidean geometry by introducing a dragging exploration principle. © 2013 Springer Science+Business Media Dordrecht.

Keywords

Discernment, Dragging control, Dynamic geometry, Perception, Variation

Publication Date

2013

Source Publication Title

Educational Studies in Mathematics

Volume

84

Issue

3

Start Page

439

End Page

460

Publisher

Springer Verlag

ISSN (print)

00131954

ISSN (electronic)

15730816

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