Transitioning from definitions to proof: Exploring non-Euclidean geometry in a college geometry course

International audienceGeometry is the subject where U.S. students are weakest on international assessments, but college geometry is an area of proof that is understudied. Since geometry is secondary students' only exposure to proof, it is vital our secondary teachers can prove effectively in this content area. However, one obstacle to developing deeper understanding of geometric concepts in college geometry courses is that students tend to try recalling prior geometry instruction instead of engaging in any new material within a Euclidean geometric context. A document analysis of student portfolios revealed that although pre-service teachers in this document study began the semester with limited abilities to work with formal definitions, by the end of the semester all were able to propose and justify conjectures on novel surfaces