Discernment of invariants in dynamic geometry environments

Allen Y L LEUNG*, Anna Baccaglini-Frank, Maria Alessandra Mariotti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)439-460
Number of pages22
JournalEducational Studies in Mathematics
Issue number3
Publication statusPublished - Nov 2013

Scopus Subject Areas

  • Mathematics(all)
  • Education

User-Defined Keywords

  • Discernment
  • Dragging control
  • Dynamic geometry
  • Perception
  • Variation


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