Analyzing ninth-grade students' algebraic thinking in geometry: An application in triangles sub-learning domain

The aim of this dissertation is twofold; it aims at promoting the understanding about the relationship between algebra and geometry through foregrounding algebra and algebraic reasoning in the triangles sub-learning domain and, improving the algebraic reasoning of students. The dissertation employed the teaching experiment method, which is one of common qualitative research methods, at a ninth-grade classroom that involved thirty-three participants and lasted for eight weeks. Prior to the research, algebraic thinking and van Hiele geometric thinking tests were employed in the class and, accordingly, three clinical interviews were conducted with six focus group students with low, medium, and high achievement levels. The teaching experiment was designed based on Kaput's algebraic reasoning as well as the theoretical framework of McCrory's and his colleagues' studies about teaching algebra at the secondary education level. To facilitate students' discovering the geometric relationships, discussion environment was created in the classroom as well as Cabri II Geometry dynamic software was used in the teaching episodes. Video and audio recordings of the pre, mid, and final clinical interviews with the focus-group students as well as of the teaching episodes; worksheets of the focus-group students during the clinical interviews, and the researcher's diary were used as the data gathering tools in the research. Because the focus-group students were the micro sample of the class, the clinical interviews provided the researcher with important findings regarding to what extent the students prioritized algebra and algebraic reasoning in the process of solving geometry questions. The dissertation concludes that the structures of both algebraic reasoning and geometric knowledge interact while students work on solving geometry problems and that the lack of either one prevents students from reaching a solution.