Özet:

Abstract Generalization, which has a pioneering function in the development of learning algebra and algebraic thinking, is the baseline for mathematical thinking process. As an essential step in revealing generalization, patterns are highly effective. The aim of this study is to determine prospective primary school teachers' cognitive structures in generalizing patterns and the types of generalizations they employ in this process. Using qualitative research methods, this study administered a teaching experiment to the participant prospective primary school teachers. Pre and post interviews were conducted with a total of 16 prospective primary school teachers chosen as the focus group and the obtained results were discussed under two main headings: prospective teachers' generalization diagrams and algebraic generalization types. This study found that all of the prospective teachers who performed arithmetic generalization and naive induction in the pre interviews reached algebraic generalization in the post interviews and, by performing easier abduction and inductive reasoning in this process, they repeated this cycle over and over in different and complex algebraic generalizations. The post interviews carried out at the end of the teaching experiment revealed that the prospective teachers showed a clear tendency toward the visual approach. The study also found that the generalization strategies used by the prospective teachers under these approaches were diversified, their use of representation improved and they discovered dependent-independent meaning of variables rather than its unknown meaning. To sum up, this study suggests that the prospective teachers' abilities to generalize patterns algebraically were improved as a result of the teaching experiment. Key Words: Mathematics Education, Algebra, Patterns, Generalization

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