In the master's thesis I consider the understanding of linear functions in three different types of secondary schools from the perspective of theory of reification of A. Sfard. Anna Sfard introduced and described three levels of understanding of mathematical concepts: internalization, condensation, and reification. In the thesis I discussed the levels of understanding linear functions according to Sfard's theory, and I also presented the levels of understanding of concepts according to some other authors (Dubinsky, Gray and Tall). I also described how different levels of understanding manifest themselves in the case of the concept of linear function. The empirical part of this thesis considers the way of introducing linear functions in mathematics textbooks for three different types of secondary schools (vocational, technical, gymnasium). I also conducted hospitations at three different types of secondary schools. Finally, using a test and interviews I assessed the level of understanding of linear functions of 9 students: 3 from each type of school.
The research has shown, that there are differences in the understanding of linearnih functions in the tested students. The differences are manifested in mathematcs textbooks, where the textbook for gymnasium is the only one with proofs, the understanding of which indicates the level of reification.
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