Flexible Conceptions of Perspectives and Representations: An Examination of Pre-Service Mathematics Teachers' Knowledge

The concept of multiple representations of functions and the ability to make translations among representations are important topics in secondary school mathematics curricula (Moschkovich, Schoenfeld, & Arcavi, 1993; NCTM, 2000). Research related to students in this domain is fruitful, while research related to teachers is underdeveloped. This research looks in fine-grained ways at the nature of understanding exhibited by 59 preservice mathematics teachers as they approached four problems that called for translations between representations of functions. Teachers' written and verbal responses were examined according to the extent to which they utilized essential constructs of process and object perspectives. Findings suggest that teachers exhibited three conceptions - flexible, disconnected or constrained. Specifically, teachers demonstrated: (1) constructs of both perspectives and operated within algebraic and graphical representations, (2) constructs of both perspectives, but not transitional enough to link them across problems, or (3) constructs of one perspective and did not operate within algebraic and graphical representations.