Examination of Conceptual Knowledge of Freshmen Classroom Teacher Candidates on Function in the Context of Multiple Representations

Abstract

The aim of this study is to question conceptual knowledge of freshmen classroom teacher candidates on function. In this context, after the teaching of the function, students’ skills of defining the concept of function, interpreting the definition and multiple representations for the function were examined. In the study, qualitative research approach was adopted and was an example of a case study. The participants of the study constitute 15 students who were educated in the first class of the classroom teaching department of a state university in Turkey. The data of the study was collected in four consecutive stages. Each stage was arranged according to the information obtained from the previous stage. The students were applied to the understanding form (AF), Multiple representation form (MRF), algebraic and graphical representation form (AGRF) and semi-structured interview form (IF) for the function concept developed by the researcher respectively. As a result of the study, it emerged that more than half of the students have difficulty interpreting the definition, although the function was accurately defined. It was found that students were more successful in the schema and list representations than algebraic and graphical representations of function. Moreover, students had difficulty in transforming between algebraic and graphical representations. In general, sources of these difficulties were; lack of adequate understanding of the function definition, not taking into consideration domains of functions, complex structure of the concept of function and negativity of the students’ mathematical backgrounds.