Educational Studies in Mathematics

, Volume 84, Issue 3, pp 439–460 | Cite as

Discernment of invariants in dynamic geometry environments

  • Allen LeungEmail author
  • Anna Baccaglini-Frank
  • Maria Alessandra Mariotti


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.


Dynamic geometry Discernment Variation Perception Dragging control 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Allen Leung
    • 1
    Email author
  • Anna Baccaglini-Frank
    • 2
  • Maria Alessandra Mariotti
    • 3
  1. 1.Hong Kong Baptist UniversityKowloonHong Kong
  2. 2.Università di Modena e Reggio EmiliaModenaItaly
  3. 3.Università degli Studi di SienaSienaItaly

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