The purpose of this study is to reveal how
prospective mathematics teachers evaluate proofs that are proved by others in
the field of analysis. In this regard, skills of prospective teachers to
evaluate the accuracy of arguments are presented in various ways, and
strategies they use during the evaluation process are examined. This study, in
which the qualitative approach is adopted, is a case study. The sample
consisted of eight prospective teachers who were studying primary school
mathematics teaching in their third year at a state university in Turkey. The
data were collected with the help of task-based clinical interviews on subjects
of functions, sequences, limit and derivatives. In the study, it was found that
prospective teachers were successful at choosing valid proofs, whereas they had
difficulties in identifying invalid proofs. It was determined that especially
some prospective teachers were not able to distinguish proving methods, they
were not aware of the power of counterexample, and they considered inductive
arguments and, even if they were not correct, they accepted deductive arguments
as valid proofs. It was found that prospective teachers used three strategies
while evaluating proofs. These were structural examination, argument
examination and authoritarian examination.
Mathematical proof, Proof evaluation, Prospective mathematics teachers, Analysis