# Cultivating inquiry about space in a middle school mathematics classroom

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## Abstract

During 46 lessons in Euclidean geometry, sixth-grade students (ages 11, 12) were initiated in the mathematical practice of inquiry. Teachers supported inquiry by soliciting student questions and orienting students to related mathematical habits-of-mind such as generalizing, developing relations, and seeking invariants in light of change, to sustain investigations of their questions. When earlier and later phases of instruction were compared, student questions reflected an increasing disposition to seek generalization and to explore mathematical relations, forms of thinking valued by the discipline. Less prevalent were questions directed toward search for invariants in light of change. But when they were posed, questions about change tended to be oriented toward generalizing and establishing relations among mathematical objects and properties. As instruction proceeded, students developed an aesthetic that emphasized the value of questions oriented toward the collective pursuit of knowledge. Post-instructional interviews revealed that students experienced the forms of inquiry and investigation cultivated in the classroom as self-expressive.

## Keywords

Mathematical inquiry Interest and disposition Mathematical habits-of-mind Spatial mathematics Mathematical practices## Notes

### Acknowledgments

We thank the editor, three anonymous reviewers, and Leona Schauble for their constructive and productive critique. Parts of this research were supported by the National Science Foundation, DRL-1252875. Any recommendations or conclusions stated here are those of the authors and do not necessarily reflect official positions of the NSF.

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