Bir yedinci sınıfta matematiksel uygulamaların gelişimi: Öğrencilerin orantısal akıl yürütmelerinin gelişiminin incelenmesi

The first purpose of this study is to develop, test, and revise a Classroom Hypothetical Learning Trajectory and related instructional sequence for teaching proportional reasoning in seventh-grade. The second purpose is to explain students' communal ways of reasoning with informal tools and how this reasoning evolves over time to reasoning with formal tools in line with a Realistic Mathematics Education perspective. The third purpose is to document students' collective development of mathematical ideas and concepts related to proportional reasoning (i.e., documenting mathematical practices). To those ends, an instructional sequence developed in the United States by Stephan and colleagues was tested and revised in two subsequent design experiments in two years with a design-based research perspective. Data were collected from an experienced middle school mathematics teacher's two seventh-grade classrooms in two years in a public school in Altındağ District of Ankara. The videotapes of the classroom implementation in the second experiment, which lasted six weeks, were analyzed by an adaptation of Toulmin's argumentation model (Classroom Mathematical Practices Analysis). Findings showed that the instructional sequence has extensive potential in supporting a classroom community's proportional reasoning in increasingly sophisticated ways. In particular, it revealed that the classroom community started to make sense of proportional situations by reasoning with pictures and ratio tables (informal tools), and this reasoning evolved to reasoning with the symbolic representations of ratio and proportion (formal tools). Lastly, it presented that five mathematical practices were established in the classroom. Keywords: Classroom Mathematical Practices, Proportional Reasoning, Realistic Mathematics Education, Design Research, Hypothetical Learning Trajectories