An Ontological Study on Proof: If and only If Propositions

Abstract

This study was carried out in order to determine how the 3rd grade students of the Department of Elementary Mathematics Education structured their "if and only if propositions”. The data were obtained by examining the students' answers given to the midterm exam questions and discussing the solutions with the students in the classroom. The study is a case study. As a result of the application, it was found out that the students had difficulty in determining the parts of the hypothesis that are included in “if and only if” proposition and therefore dividing the proposition into two “if” proposition. Some students think that the part or parts given as hypothesis should also be proved. When defining propositions, in addition to their “if and only if propositions”, it is suggested to define new types of proposition in the form of “hypothesis-containing if and only if propositions”.