A case example of insect gymnastics: how is non-Euclidean geometry learned?

The focus of the article is on the complex cognitive process involved in learning the concept of 'straightness' in Non-Euclidean geometry. Learning new material is viewed through a conflict resolution framework, as a student questions familiar assumptions understood in Euclidean geometry. A case study reveals how mathematization of the straight line concept in Euclidean and Non-Euclidean geometry emerges through the use of analogy, imagination and motion, moving the student from an extrinsic view to an intrinsic view, thus providing a psychological account of how students learn a new geometry. Practical implications for mathematics education are provided.