This case study report provides information that can be useful in implementing rational changes in mathematics teacher education. Considering teachers' thinking about a specific mathematical topic, such as functions, allows one to better understand the broader domain of teachers' mathematical thinking and its influence on teaching and learning. This study used the categories of concept definition and concept image as described by Vinner and Dreyfus to examine 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 over 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. Contains 26 references. (Author/MPN)