ABSTRACT
This chapter discusses the ideas of curriculum, learning, and teaching into a consideration of instructional improvement in geometry, particularly providing a way to address how instruction can be organized to facilitate students' study of the means of predicting and controlling their interactions with figures, where figures can be navigations of space, captures of large objects, descriptions of artifacts or diagrams, or constructions of artifacts or diagrams. The theory of didactical situations (TDS) provides a means for thinking about instruction that seeks the development of targeted conceptions. A communication task might involve students in providing a set of directions orally or through a diagram, or in comparing trajectories by processing information provided in diagrams and instructions; in doing so the communication task might bring forth other existing conceptions of figure to model the macrospace and the navigation activity.
