Teacher appropriation and student learning of geometry through design

In 4 Grade 2 classrooms, children learned about transformational geometry a nd symmetry by designing quilts. All 4 teachers participated in professiona l development focused on understanding children's thinking in arithmetic. T herefore, the teachers elicited student talk as a window for understanding student thinking and adjusting instruction in mathematics to promote the de velopment of understanding and used the same tasks and materials. Two of th e 4 teachers participated in additional workshops on students' thinking abo ut space and geometry, and they elicited more sustained and elaborate patte rns of classroom conversations about transformational geometry. These diffe rences were mirrored by students' achievement differences that were sustain ed over time. We attribute these differences in classroom discourse and stu dent achievement to differences in teachers' knowledge about typical milest ones and trajectories of children's reasoning about space and geometry.