A Case Example of Insect Gymnastics: How Is Non-Euclidean Geometry Learned?
IJMEST Volume 39, Number 8, ISSN 0020-739X
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. (Contains 7 figures.)
Junius, P. (2008). A Case Example of Insect Gymnastics: How Is Non-Euclidean Geometry Learned?. International Journal of Mathematical Education in Science and Technology, 39(8), 987-1002.