ABSTRACT
This chapter identifies the forces that have shaped the geometry curriculum, instruction, and learning from a historical and an international point of view. The discourse of teaching and learning geometry over the centuries provides rich, at times unexpected, source of examples and indicators of why and how geometry can be taught and learned. The study of geometry in its practical applications to agriculture, construction, and astronomy is indeed virtually as old as civilization itself. Applications in craftsmanship and astronomy were the source of pragmatic, hands-on geometric rules since the beginning of highly developed civilizations in ancient Egypt, Arabia, and India. Throughout Europe, there were numerous attempts, beginning in the late sixteenth century, to craft new textbooks, more suitable for school use but still organized essentially around Euclid's content. A century after Euclid, Apollonius of Perga wrote the Conics, and Archimedes of Syracuse developed the method of exhaustion as a means to prove geometric theorems about the area of a circle.
