Investigating prospective middle school mathematics teachers' modeling processes and cognitive competencies for linear relationships

The purpose of this study was to investigate modelling processes and cognitive competencies of prospective middle school mathematics teachers for linear relationships. Case study design was utilized. The study was conducted as part of a fourteen week course that included nine modeling task in a public university in 2014-2015 academic year. Data were collected through observations, interviews and document checking. Content analysis was used. Linear relationships were examined in three groups as exact linear, partial linear and near-linear. The tasks were structurally divided three groups in respect to giving open data, closed and non-closed data or giving data indirectly. Modeling processes included four phases: description, manipulation, prediction and verification. In this qualitative study, the data were analyzed according to modelling competencies which was prepared according to steps of description, manipulation, prediction and verification. The findings indicated that cognitive competencies could be varied based on the type and the structure of the modeling tasks. Findings further showed that one needs to show more competencies for those tasks in which data were not given directly or given as closed-data. Furthermore, data suggest that some sub-competencies play critical role and tolerate other sub-competencies so they are not needed for the modeling process. However, if one doesn't show those critical sub-competencies then the modeling process cannot be completed or a model cannot be developed. The findings also suggest that if an appropriate learning environment and modelling tasks are provided prospective teachers' modeling competencies can be improved. Keywords: Mathematical modelling process, Cognitive competencies, Mathematical modelling competencies, Linear relationships, Prospective teachers.