Abstract
The purpose of this paper is to prepare good examples for promoting spatial cognition in the geometric education. Two concrete teaching materials for geometry are offered and analyzed from both points of view, mathematics education and mathematics itself. One material treats a problem which asks the number of domains given by subdividing the Euclidean space by hyperplanes. The solution includes various aspects involving topology and combinatorics, and the answer enlightens us on a beautiful combination of geometry and arithmetic. Another material is concerned with transformations in the space, and it is illustrated that the affine method works well for understanding of compositions of isometric transformations. The problems given in the contents are related with thought on the group theory, and also promote spatial cognition on movement of objects.
