Investigation of the algebraic thinking of sixth grade students with three parameters: The quantitave reasoning, the covariational thinking and the functional thinking

Although the transition period from arithmetic to algebra in secondary school mathematics learning process is quite important, it is often a source of difficulty for students. The literature reveals that the process of algebraic thinking to develop from arithmetic to algebra should be supported by various mathematical thinking skills such as quantitative reasoning, covariational thinking and functional thinking. The aim of this study was to investigation of the algebraic thinking with the quantitative reasoning, the covariational thinking and the functional thinking and, if any, the relationship between these forms of thinking of sixth grade students. According to this purpose; the open-ended data collection tools were administered and then in-depth individual clinical interviews in two sessions to the nine participants in sixth grade level selected by criterion sample method. Data were analyzed by content analysis method. In general; it was concluded that the students' covariational thinking skills were at the lowest level than according to other thinking skills, the linear functional relationships between the independent and dependent variables were understood and generalized, and the thinking skills decreased when they were taken out of the methods used in school and in their daily lives. In addition, the mentioned four thinking skills are associated; it was found that quantitative reasoning was central to the development of other thinking skills.