Discourse Perspective of Geometric Thoughts

  • Sasha Wang

Part of the Perspektiven der Mathematikdidaktik book series (PERMA)

Table of contents

  1. Front Matter
    Pages I-XXIII
  2. Sasha Wang
    Pages 1-4
  3. Sasha Wang
    Pages 5-39
  4. Sasha Wang
    Pages 41-50
  5. Sasha Wang
    Pages 51-181
  6. Sasha Wang
    Pages 183-206
  7. Back Matter
    Pages 207-232

About this book


Sasha Wang revisits the van Hiele model of geometric thinking with Sfard’s discursive framework to investigate geometric thinking from a discourse perspective. The author focuses on describing and analyzing pre-service teachers’ geometric discourse across different van Hiele levels. The explanatory power of Sfard’s framework provides a rich description of how pre-service teachers think in the context of quadrilaterals. It also contributes to our understanding of human thinking that is illustrated through the analysis of geometric discourse accompanied by vignettes.


  • Theoretical Basis: The van Hiele Model
  • Theoretical Framework: Learning as Communicating, Sfard’s Discursive Framework, and the Levels of Geometric Discourse
  • Methodology: Participants, the van Hiele Geometry Test, Interview Tasks
  • Data Collection and Analysis
  • Results from the van Hiele Geometry Test and One-on-One Interviews
  • Changes in van Hiele Levels and Changes in Geometric Discourse

Target Groups

  • Researchers, academics, and scholars of mathematics and didactics
  • Teachers

The Author

Dr. Sasha Wang is an assistant professor of mathematics education at the Boise State University, Idaho, United States.


Mathematics educatio Geometric discourse Pre-service primary teachers Quadrilaterals Van Hiele model Geometry

Authors and affiliations

  • Sasha Wang
    • 1
  1. 1.Department MathematicsBoise State UniversityIdahoUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Fachmedien Wiesbaden 2016
  • Publisher Name Springer Spektrum, Wiesbaden
  • eBook Packages Education Education (R0)
  • Print ISBN 978-3-658-12804-3
  • Online ISBN 978-3-658-12805-0
  • Buy this book on publisher's site