This study examined factors that influenced the acquisition of pedagogical content knowledge for two groups of prospective secondary mathematics teachers (undergraduate mathematics majors and post-graduate scientists and engineers seeking mathematics certification) in the content domain of functions and graphs. Both groups, enrolled in a one-semester methods course, were assessed on a wide variety of tasks designed to investigate the acquisition of pedagogical content knowledge. Participants also completed a beliefs scale as the course commenced. The primary objective of the study was to document evidence of their subject-matter knowledge; their beliefs about learners, learning mathematics, and mathematics; and how their knowledge and beliefs influenced their instructional practices. The results suggested that subject-matter knowledge and beliefs among both groups were very similar. Results also indicated that the complex endeavor of acquiring pedagogical content knowledge was significantly influenced by the content knowledge and the belief structures that prospective teachers held when entering the methods class. An appendix contains the tasks that participants completed. (Contains 36 references.) (SM)