Learning about polyhedra through visual and tactile perception and discussion

This thesis is concerned with understanding in three-dimensional geometry. The study focuses on how visual perception and imagery of polyhedra are related to van Hiele levels and to Del Grande's spatial perception abilities. A written test is developed which is designed to assess van Hiele levels in three-dimensional geometry, as well as Del Grande's spatial perception abilities. Two empirical studies address how perception and imagery of polyhedra are related to geometric thought. The first of the empirical studies looks at the role of group discussion in enhancing visual perception and image formation of polyhedra. The second examines the role of purely tactile information about polyhedra and its role in forming stable models of polyhedra. The findings of the study reveal a distinction between visual perception and image formation of polyhedra. This distinction is marked, and is not normally drawn in the mathematics education literature. Visual perception is strongly connected to van Hiele levels but image formation is not. The findings of the study also reveal a strong influence through verbal discussion on increasing student's visual perception.