ABSTRACT
This chapter introduces the roots of geometry, showing that Euclid's Elements is founded on the efforts of generations of mathematicians who brought geometry to the paradise of abstraction. It shows that the geometric intuition is a locus classicus of European philosophy stretching from Plato to Helmholtz. The chapter discusses the classic model of the emergence of geometric skills introduced by van Hiele and van Hiele-Geldof. It presents the cognitive revolution that allowed for the development of a broader research perspective on geometric cognition. The model consists of three main component-parts: a description of theoretical assumptions, levels of geometric thinking, and, finally, phases of instruction. Although there are numerous ways of understanding what “embodiment of the mind” really is, most researchers agree that it refers to claims that cognitive processes are causally grounded in sensorimotor activity and that the body shapes the mental activity.
