Examination of secondary mathematics teachers' perceptions of proof in a generic example context

In general, the use of generic examples in activities related to proof makes the proof more explanatory and more meaningful. In this context, in order to support their students' proof skills, teachers should have advanced proof skills and be able to carry out the proof process correctly. The aim of this study is to examine secondary school mathematics teachers' proof processes, their evaluation of different arguments and their understanding of the generic example. The data of the study, which was designed with the case study method, were collected through semi-structured interviews with 10 secondary school teachers. Open coding and content analysis methods were used in the analysis of the data. It was observed that the teachers mostly produced proofs based on examples, and about half of them thought that they made proofs by giving examples. It has been determined that the criteria used by the teachers when evaluating the arguments are logical, general, giving examples, benefiting from previous knowledge, finding correct, using algebraic expressions, being explanatory, persuasive, useful, concretizing, and finding complex. It has been determined that the majority of teachers accept numerically expressed generic examples as valid proof, while the number of those who accept visually expressed generic examples as valid proof is low. It was concluded that the teachers found the generic examples to be convincing and explanatory among the different arguments given, while they saw the algebraically expressed argument as the most convincing and explanatory argument. It has been concluded that the teachers' proof skills are low, but they are aware of the conditions necessary for a valid proof. It was concluded that the teachers distinguished generic examples from example based arguments, stated that they adequately represented the generality and accepted it as a valid proof.