The development of mathematical argumentation: A case study on two mathematics classrooms

Mathematical reasoning has been a critical concern in Turkey especially since the structure of the student selection examination for high schools changed six years ago. The ability to solve the questions in the new exam requires high level reasoning and argumentation skills. Schools, whether they are public or private, prepare 8th graders for this exam with intense educational programs. They frequently use skill-based questions–similar questions to the ones in the new exam, which require high level mathematical reasoning. This study indicates that students gain better mathematical reasoning skills in learning environments promoting collective discussion and argumentation. Hence, these questions need to be solved in these kinds of environments. In this study, two cases are analyzed to understand the argumentation process in classrooms in depth. Audiotapes of two 8th grade classrooms, one from a public school, another from a private school, are analyzed. The same teaching material–a worksheet including skill-based questions–is used in the classrooms. During analyzing, qualified argumentation pattern–a pattern including students’ claims and justifications/evaluations for those claims- is defined. Analysis of classroom audiotapes revealed that that there are significant differences between two classrooms’ argumentation structure and type of dialogues emerged in the classroom. In one classroom there is a more qualified argumentation process than in the other classroom. In addition, analysis of the type of the dialogues indicates that two classrooms have different types of dialogues. Overall, the study reveals that despite the differences, both classrooms mostly included teacher-individual interactions and they have little collective discussion.