Designing Activities to Support Prospective High School Teachers' Proofs of Congruence from a Transformation Perspective

Undergraduate mathematics instructors are called by many cur- rent standards to promote prospective teachers’ learning of geometry from a transformation perspective, marking a change from previous standards. The novelty of this situation means it is unclear what is involved in undergraduate learning and teaching of geometry from a transformation perspective. To approach this problem, we illustrate how specific in-class activities and design principles might help prospective teachers make conceptual links between congruence proofs and a transformation approach to geometry. Additionally, to illustrate these activities for instruc- tors, we provide examples of prospective teachers’ work on some of these problems.