Prospective Mathematics Teachers’ Strategies for Evaluating the Accuracy of Proofs in the Field of Analysis

Abstract

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. 

Keywords

• Mathematical proof,Proof evaluation,Prospective mathematics teachers,Analysis

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