PME-NA

The Role of Diagrams in Geometric Thinking and Learning: The Case of Mariah

• In Event: Shape and Space

Description

Frameworks of mathematical thinking influence researchers’ interpretations. These influences can lead to increased attunement to certain nuances and blind spots to others. In the case of geometric thinking, popular cognitive frameworks orient researchers to think in terms of Van Hiele Levels and figural concepts. In the literature on hierarchical geometric relationships, little attention has been paid to learners’ interpretation/use of diagrams to represent relationships. We report on a teaching experiment involving a preservice teacher whom we call Mariah. In the analysis process, it became necessary to analyze Mariah’s interpretation and use of diagrams in order to make sense of her thinking and learning about hierarchical geometric relationships. We show how we applied the construct of figural concepts to Mariah’s thinking about diagrams (not only shapes) and how the interpretation of diagrams was intertwined with her learning process.

Authors

• Ian Whitacre, Florida State University

• Azar Kamaldar, Florida State University

• Domonique Caro-Rora, Florida State University