Consolidation of Similarity Knowledge via Pythagorean Theorem: A Turkish Case Study

Understanding how students learn is important for both researchers and teachers. In terms of mathematics, constructing a new mathematical structure depends on conceptual understanding and connection with previous construct and they needs to be consolidated. A construct can be consolidated when the construct is recognized and used in the further activities or while new structure is being constructed. In this paper, our aim is to observe consolidation of similarity knowledge by the help of Pythagorean Theorem in terms of characteristics of consolidation; immediacy, self-evidence, confidence, flexibility, awareness. We would like to observe consolidation in different ages. Participants of this study are one master, one undergraduate and one high school students from Turkey. The consolidation of similarity knowledge was observed when students tried to prove Pythagorean Theorem. The data were analyzed by using RBC+C-model's characteristics. As a result, it was seen that characteristics of consolidation were useful to analyze consolidation. However, there is a need for posterior experiments to investigate whether "immediacy' is an essential characteristic of consolidation. It can be said that awareness and flexibility are seen essential and easily observable characteristics of the consolidation process.