Making sense of qualitative geometry: The case of Amanda

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This article presents a case study of a seven-year-old girl named Amanda who participated in an eighteen-week teaching experiment I conducted in order to model the development of her intuitive and informal topological ideas. I designed a new dynamic geometry environment that I used in each of the episodes of the teaching experiment to elicit these conceptions and further support their development. As the study progressed, I found that Amanda developed significant and authentic forms of geometric reasoning. It is these newly identified forms of reasoning, which I refer to as "qualitative geometry," that have implications for the teaching and learning of geometry and for research into students' mathematical reasoning.

Original languageEnglish
Pages (from-to)73-94
Number of pages22
JournalJournal of Mathematical Behavior
StatePublished - Dec 1 2014


All Science Journal Classification (ASJC) codes

  • Education
  • Applied Mathematics
  • Applied Psychology


  • Geometric reasoning
  • Student thinking
  • Teaching experiment
  • Topological reasoning

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