Geometric Discourse at Van Hiele Level 3: The Role of Definition and Informal Deductive Reasoning

• In Event: Poster Session 20
  In Poster Session: Mathematical Reasoning and Proof Across Grades

Abstract

To examine students’ thinking about geometry, this study connects Sfard’s (2008) Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing, a systematic approach to analyzing the discursive features of mathematical thinking, including word use, visual mediators, routines, and endorsed narratives, to the van Hiele theory (van Hiele, 1959). The van Hiele theory describes students’ five levels of geometric thinking. This study reveals discursive similarities and differences in students’ geometric discourses at van Hiele level 3, a level is crucial to students’ development of abstract thinking in geometry. The study also investigates the usefulness of a discursive framework in providing details of students’ thinking processes.

Authors

• Sasha Wang, Boise State University

• Margaret T. Kinzel, Boise State University