Abstract

Although it has been many years, I still remember the story of Ricky as if it were only yesterday. I was a teacher consultant in a district where one of my roles was to support teachers in their classroom practice. A colleague had invited me to join one of her eighth-grade mathematics classes. The students were studying quadrilaterals, and our objective for the lesson was to discover what the students knew about quadrilateral properties. The lesson was informed by the van Hiele model of geometric thinking (Fuys, Geddes, and Tischler 1988). The van Hieles hypothesized that students' thinking begins at a visual level. At this level, the learner recognizes shapes by an overall gestalt based on visual clues rather than defining properties. From this level, the model suggests, learners move to a level of analysis that uses defining properties to categorize shapes and classes of shapes.

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