| Summary: | The dual nature of geometry, in that it is a theoretical domain and an area of practical experience, presents mathematics teachers with opportunities and dilemmas. Opportunities exist to link theory with the everyday knowledge of pupils but the dilemmas are that learners very often find the dual nature of geometry a chasm that is very difficult to bridge. With research continuing to focus on understanding the nature of this problem, with a view to developing better pedagogical techniques, this paper examines the place of experimental tasks in the process of learning geometry. In particular, the paper provides some results from an analysis of innovative geometry textbooks designed in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis suggests that experimental tasks have a vital role to play and that a potent tool for informing the design of such tasks, so that they build effectively on pupils' geometrical intuition, is the notion of the geometrical eye, a term coined by Charles Godfrey in 1910 as "the power of seeing geometrical properties detach themselves from a figure".
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