Preservice Middle School Mathematics Teachers’ Understanding of Triangle Inequality through Collective Argumentation

The purpose of the present study was to examine how preservice middle school mathematics teachers develop the understanding and reasoning of triangle inequality through collective argumentation. Data collection process was based on whole class and peer group discussions and written documents. The data including the transcriptions of the discussion processes with the written documents were analyzed by using Toulmin’s model of argumentation. Through this collective argumentation process, they attained the knowledge and understanding of triangle inequality by suggesting and challenging their geometrical ideas about the concept and they developed and constructed their knowledge and understanding of this concept. It was found that the participants improved their knowledge and understanding of triangle inequality by argumentation through criticizing their mathematical ideas