Teacher appropriation and student learning of geometry through design

In 4 Grade 2 classrooms, children learned about transformational geometry and symmetry by designing quilts. All 4 teachers participated in professional development focused on understanding children's thinking in arithmetic. Therefore, the teachers elicited student talk as a window for understanding student thinking and adjusting instruction in mathematics to promote the development of understanding and used the same tasks and materials. Two of the 4 teachers participated in additional workshops on students' thinking about space and geometry, and they elicited more sustained and elaborate patterns of classroom conversations about transformational geometry. These differences were mirrored by students' achievement differences that were sustained over time. We attribute these differences in classroom discourse and student achievement to differences in teachers' knowledge about typical milestones and trajectories of children's reasoning about space and geometry.