Proof construction and evaluation practices of prospective mathematics educators

This study was conducted with 93 freshmen and 82 senior prospective mathematicians and mathematics teachers in order to investigate how they construct and evaluate proofs and whether there are any significant differences in their proof construction (with respect to department and grade) and proof evaluation (with respect to department) performances. Instruments developed for this purpose are Proof Exam (PE) and Proof Evaluation Exam (PEE). While no significant differences were observed among freshmen with respect to department in PE scores; senior students’ mean scores differ significantly both in PE and PEE. It has been observed that freshmen students mostly rely on inductive reasoning when they attempt to prove given mathematical statements. Even though seniors are mostly aware of the necessity of generalizing their results and attempting to use procedures involving deductive reasoning, they still have difficulties in constructing and evaluating proofs. Implications for teaching are discussed.