Abstract:

The study aims to depict the mental actions of mathematics pre-service teachers during the process of proof, with the employment of the forward-backward method. Clinical interviews were conducted with three pre-service mathematics teachers, whose academic achievements were good, moderate and low, based on one geometry and one algebra questions. Mental maps for the forward-backward technique were developed based on the analysis of the proof processes adopted by each pre-service teacher, and the role of these maps in the achievement of the proof was discussed. The results demonstrated that three pre-service teachers intensively employed the forward-backward technique in proof, albeit not always consciously, regardless of their academic achievement levels and the field of the question. It was determined that the number of forward-backward steps increased with the increase in academic achievements of the pre-service teachers. Since the technique allows the faculty members to express their ideas verbally, this could provide the opportunity to turn proof into a creative construction process for the pre-service teachers.

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