Supporting Innovation: The Impact of a Teacher's Conceptions of Functions on His Implementation of a Reform Curriculum

In this study we investigate the content conceptions of an experienced high school mathematics teacher and link those conceptions to their role in the teacher's first implementation of reform-oriented curricular materials during a 6-week unit on functions. The teacher communicated deep and integrated conceptions of functions, dominated by graphical representations and covariation notions. These themes played crucial roles in the teacher's practice when he emphasized the use of multiple representations to understand dependence patterns in data. The teacher's well-articulated ideas about features of a variety of relationships in different representations supported meaningful discussions with students during the implementation of an unfamiliar classroom approach to functions.