© 2016

Discourse Perspective of Geometric Thoughts


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

  1. 1.Department MathematicsBoise State UniversityIdahoUSA

About the authors

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

Bibliographic information

  • Book Title Discourse Perspective of Geometric Thoughts
  • Authors Sasha Wang
  • Series Title Perspektiven der Mathematikdidaktik
  • Series Abbreviated Title Mathematikdidaktik
  • DOI
  • Copyright Information Springer Fachmedien Wiesbaden 2016
  • Publisher Name Springer Spektrum, Wiesbaden
  • eBook Packages Education Education (R0)
  • Softcover ISBN 978-3-658-12804-3
  • eBook ISBN 978-3-658-12805-0
  • Edition Number 1
  • Number of Pages XXIII, 232
  • Number of Illustrations 61 b/w illustrations, 0 illustrations in colour
  • Topics Mathematics Education
  • Buy this book on publisher's site