Should proof be minimal? Ms T's evaluation of secondary school students’ proofs

Calls for reform in mathematics education around the world state that proofs should be part of school mathematics at all levels. Turning these calls into a reality falls on teachers’ shoulders. This paper focuses on one secondary school teacher's reactions to students’ suggested proofs and justifications in elementary number theory. To determine whether the justifications are acceptable, the teacher used not only her SMK regarding mathematical aspects, but also her PCK about what a student giving this justification might know or not know. A discussion of the findings is followed by some questions that arise.