Abstract:

In a National Science Foundation funded research project, we implemented a dynamic geometry (DG) intervention, which was effective in providing well-designed professional development (PD) to help teachers develop their DG skills, their mathematical reasoning abilities, and their technological pedagogical content knowledge. This presentation will use examples to show the main features of the PD component of the project and their impact on geometry teaching and leaning in our classrooms.

In the PD sessions, we focused on emphasizing teachers’ active involvement and their conceptual understanding of mathematics. We never introduced DG skills, geometry content, and pedagogy separately. Important geometric concepts, processes, and relationships were presented or revisited through investigating-conjecturing-proving tasks, usually challenging problem situations. These tasks/situations were explored with DG software as a tool. Teachers learned DG skills in the process of using them to tackle the tasks/problems. The sessions also placed emphasis on using DG software to help teachers develop proof insights. In each of the sessions, at least one proving activity (either small group exploration or large group discussion) or one proof presentation was conducted.

We also emphasized the pedagogy needed for the teachers to use the software well in their classrooms. The participant-centered, inquiry-based training method itself modeled the instructional ideas and strategies we expected teachers to use. We were explicit about this modeling and encouraged participants to use similar behaviors with their classes. To further help teachers to consider changes in their instructional strategies, mathematical explorations were always followed by discussions on questions such as “How can we teach this content effectively using DG software?” and “How should we engage students in conjecturing and proving using DG software?” We felt these discussions would facilitate student learning and enhance the relationship between teachers and students. We also stressed the importance of developing learning communities in which teachers learn from each other and share ideas. Therefore, teachers were encouraged to work collaboratively, share their successes and their challenges, and help each other think of new ways to deal with the challenges.

All of these features, as a whole, positively impacted participating teachers’ growth. The PD sessions helped the teachers refresh and deepen their geometric content knowledge and gain new teaching strategies to engage their students in active learning within a technology intensive environment using DG software.