An Assessment of Prospective Secondary Teachers' Pedagogical Content Knowledge about Functions and Graphs.

The study discussed in this paper examined the pedagogical content knowledge of prospective secondary mathematics teachers with respect to the content area of functions and graphs. The pedagogical content knowledge was examined through an analysis of the transformation of knowledge and beliefs about the content and the learner into instructional practices. It is proposed that the transformation takes place through developing explanations, planning lessons, simulating teaching, and reflecting on teaching. The study documented the subject matter knowledge, the pedagogical content knowledge, and the beliefs about learners and mathematics as this potential transformation was taking place. An assessment of 11 prospective secondary mathematics teachers based on 5 tasks was designed to present a composite view of their pedagogical content knowledge in the area of functions and graphs. The task discussed in this paper was an audiotaped interview of prospective teachers' responses to vignettes of students solving problems in this content area. This task provided the opportunity for the prospective teachers to construct explanations in response to students' misconceptions. This task is considered important because it serves as the link between those tasks which examine baseline data sources and those tasks which examine the transformation process. Vignettes of teaching functions and graphs are included. (Contains 30 references.) (LL) ************************************************************i-********** Reproductions supplied by EDRS are the best that can be made from the original document. **************************************************************t********