Geometrical Intuition and the Learning and Teaching of Geometry

Intuition is often regarded as essential in the learning of geometry, but how such skills might be effectively developed in students remains an open question. This paper reviews the role and importance of geometrical intuition and suggests it involves the skills to create and manipulate geometrical figures in the mind, to see geometrical properties, to relate images to concepts and theorems in geometry, and decide where and how to start when solving problems in geometry. Based on these theoretical considerations, we illustrate a range of student tasks that we argue should contribute to developing students’ geometrical intuition. INTRODUCTION Across the world there is considerable variation in the design of the geometry curriculum. Some countries favour an approach using congruence as a central element, while other use similarity and transformations (Hoyles, Foxman and Küchemann, 2002; Jones, 2000a; 2002). Yet, as Hoyles et al found, “there is evidence of a state of flux in the geometry curriculum, with most countries looking to change” (op cit p121). This means that there remain considerable opportunities to improve the specification of the curriculum for geometry. In this paper we argue that ‘geometrical intuition’ should have a crucial role. While we admit that it is not straightforward to define ‘intuition’ clearly, we can illustrate that geometrical intuition is a kind of skill to imagine, create and manipulate geometrical figures in the mind when solving problems in geometry.