Professional development through lesson study: teaching the derivative using GeoGebra

This study focuses on mathematics teachers' professional development through elements of Japanese lesson study. The teachers designed a research lesson with regard to sense-making of the derivative using the integration of GeoGebra. In the second year of the four-year lesson study project, seven secondary school teachers - from different Dutch schools - worked cooperatively, building on the first-year experiences with the introduction of the derivative. The teachers designed a lesson that focused on encapsulation of the conceptual understanding of the derivative before solving problems with operational symbolism later in the course. They tried to make sense of the calculus using GeoGebra as a tool to realize surprise in which conceptual embodiment and operational symbolism blend together. The teachers integrated GeoGebra to consolidate the derivative using the visual idea of zooming in on the graph to see its local behavior (where a differentiable function looks 'locally straight'). The teachers reported that they have learned to use visualizations and experienced the importance of student interaction. The teachers realized that this approach of the derivative - integrating GeoGebra - encouraged them to reflect on how the students made sense of learning activities in general.