Preservice mathematics teachers' knowledge of functions and its effect on lesson planning at the secondary level

Many preservice mathematics teachers are leaving college unprepared to teach mathematics in a manner consistent with the National Council of Teachers of Mathematics "Principles and Standards for School Mathematics" (NCTM, 2000). The motivation for this study was to help find a solution to the problem of under-prepared preservice teachers. The main goals of this study were (1) to find a vehicle for helping preservice teachers improve their mathematical knowledge, (2) to investigate relationships between subject matter knowledge and pedagogical knowledge, and (3) to determine what benefits preservice teachers gain from participating in a capstone experience as recommended by the Conference Board of Mathematical Sciences (2001).;Participants in this study were six preservice mathematics teachers from a large midwestern university. They completed a questionnaire designed to assess their mathematical background and their attitudes towards teaching mathematics, learning mathematics, and their own preservice education. Participants were also assessed on their knowledge of functions both before and after participating in a treatment designed to increase their subject matter knowledge of functions. The treatment consisted of five mathematics study sessions in which students closely examined the concept of functions. Participants also planed an introductory lesson on the concept of functions for secondary school students both before and after participation in the study.;Data analysis showed that participants started the study with relatively weak subject matter knowledge of functions and through the process of participating in the study sessions significantly improved their subject matter knowledge. Participants' pedagogical content knowledge, as measured via their lesson plans, improved as their subject matter knowledge of functions increased. Many of the improvements in participants' lesson plans could be directly linked to the content they examined during participation in this study. Finally, after participation in the capstone experience, participants seemed to more highly value the taking of additional mathematics courses in college than they had prior to participating in the study activities.