Investigation of preservice mathematics teachers' algebraic thinking through translations among multiple representations

Abstract

The objective of this explanatory study was to gain insight into thinking pro cess of preservice secondary school mathematics teachers as they approached problems that required for translations from graphical representations to model representation. Previous research has indicated preservice teachers’ weakness on transition of multiple representations as well as their tendency to use symbolic demonstrations and proce dures. Algebraic thinking is a cohesive thread of exploring mathematical relationships, formulating generalizations and reasoning and connecting of multiple representations. In this aspect, this study strongly emphasized preservice teachers’ patterns of behavior that elicits algebraic thinking while translation process are required between graphi cal representation and model representation. For this purpose, explanatory research design (Creswell, 2008) was implemented. Semi-structured and video-recorded inter views with four preservice teachers who recruited according to their relatively different positions in the study constituted the main data sources of this study. The find ings demonstrated preservice teachers’ relatively weak conceptual understanding on the concept of functions and difficulties with coordinating and interpreting dependent and independent variables. Besides, some participating teachers elicited their complex ity between perception of the shape of the graph and attributes of the graph, which pointed their limited knowledge on mathematical model representations. These results may indicate importance of addressing translations among multiple representations in functions during preservice teacher education.