Interactions between knowledge of variables and knowledge about teaching variables
The purpose of this study is to find out Turkish prospective teachers' subject matter knowledge of variables and pedagogical content knowledge of variables and also the nature of the interactions between these two types of knowledge. One hundred and eighty four students participated in the study. Questionnaires were distributed to 2nd, 3rd, 4th year mathematics education faculty students of three different universities. The questionnaire included 16 fixed and open-ended questions about (a) the principal uses of variables, (b) the awareness about different roles of variables, (c) the flexibility, versatility and connectedness among the different roles and uses, and (d) ways of presenting the subject matter, (e) curriculum knowledge. As a follow-up study, ten students of different year groups who completed this questionnaire were interviewed. The outcome of this study is that prospective teachers have different perceptions of the notion of the variable which are reflected in their pedagogical content knowledge in a complex way. Results indicate that the majority of prospective teachers are successful in manipulating variables; however they have problems in moving flexibly between different meanings and representations. Concrete objects and numbers are identified as two main forms of analogies that they would use to explain ideas relating to manipulation of symbols. The results indicate that there is a complex interaction between subject matter knowledge of variables and pedagogical content knowledge which may involve the prospective teachers' own learning experiences, general pedagogical knowledge and the robustness of one type of knowledge.