Organizing the mathematical proof process with the help of basic components in teaching proof: Abstract algebra example

Abstract

The aim of this study is to identify the basic components of the mathematical proof process in abstract algebra and to organize the proof process into phases with the help of these basic components. A basic component form was prepared by arranging a draft basic component form, which was created as a result of a document analysis in accordance with the opinions of three academicians, who were experts in algebra. The data obtained as a result of both document analysis and expert examination were analyzed by the descriptive analysis method and are explained here in a detailed manner. It is believed that this basic component form will facilitate the step-by-step addressing of such a complex process as proofs in a non-compulsory and non-hierarchical order.