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.

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. Contents 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.