One Preservice Secondary Teacher's Understanding of Function: The Impact of a Course Integrating Mathematical Content and Pedagogy

Abstract

This study examines the evolving knowledge and beliefs of a preservice secondary mathematics teacher as she participated in a mathematics education course that emphasized mathematical and pedagogical connections and applications of the function concept. Her conceptions were revealed during a 10-week period through interviews, observations, and written work. The teacher's initial understanding of functions as computational activities (e.g., function machines, point plotting, vertical line test) was consistent with her larger view of mathematics as a collection of “concrete” procedures. Although her understanding of function grew substantially during the study, her anticipated approach to teaching, which was dominated by her narrow view of mathematics, was less significantly affected by course activities.