The Role of Intuition in Geometry Education: Learning from the Teaching Practice in the Early 20 Century

Intuition is often regarded as essential in the learning of geometry, but questions remain about how we might effectively develop students’ such skills. This paper provides some results from analyses of innovative geometry teaching in the early part of the 20 century, a time when significant efforts were being made to improve the teaching and learning of geometry. As examples, we examine the tasks for students that can be found in Treutlein’s “Geometrical Intuitive Instruction” (Germany) and Godfrey’s geometry textbook (England). The analyses suggest that educators at that time attempted to develop students’ intuitive skills through various practical tasks such as drawing, measurement, and imagining and manipulating figures, which could be useful for current geometry teaching. We also identify different approaches taken to the development mathematics teaching in Germany and England.