An Ontological Study on Proof: If and only If Propositions

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International e-Journal of Educational Studies
Volume:7 Issue:15
An Ontological Study on Proof: If and only If Propositions

An Ontological Study on Proof: If and only If Propositions

Pages : 453-464

View : 136 | Download : 113

Publication Date : 2023-10-21

Article Type : Research Paper

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”.
Keywords : Theorem, if and only if proposition, cognitive structuring, definition, proof

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