Date of Award
Thesis and Dissertation
Doctor of Philosophy (PhD)
Department of Mathematics: Mathematics Education
McKenzie A. Clements
Although current reform movements have stressed the importance of developing prospective middle school mathematics teachers' subject matter knowledge and understandings, there is a dearth of research studies with regard to prospective middle school teachers' confidence and knowledge with respect to quadratic functions. This study was intended to fill this void. It generated information on prospective teachers' knowledge of quadratic functions as well as of their confidence to answer questions involving quadratic equations and multiple representations of functions.
The study employed a multiple-perspectives design, with data being collected from different vantage points - documents, pre- and post-teaching tests, artifacts, interviews, classroom observations, and questionnaires - over a five-month period during the spring semester of 2008. Fifty-two prospective teachers and two instructors participated in the study. Five of the 52 prospective teachers were purposely selected for interview, the aim being to probe interviewees' conceptions, misconceptions, skills, faulty techniques, and understandings with respect to quadratic equations and multiple representations of functions.
Two theoretical frameworks guided the analysis of data - Clements and Ellerton's (2009) 5-R Model and Skemp's (1976) model contrasting instrumental and relational understanding. Analyses of data indicated that at the pre-teaching stage, the thinking of many of the prospective teachers was guided by misconceptions with respect to basic algebraic concepts that they had first studied in high school algebra. Often, there were mismatches between prospective teachers' confidence and their actual mathematical understandings. After the prospective teachers had participated in AFT22 sessions on quadratic functions, however, their knowledge, skills and understandings were much better developed and their confidence had improved.
Duarte, Jonathan Taniola, "The Effects of an undergraduate algebra course on prospective middle school teachers' understanding of functions, especially quadratic functions" (2013). Theses and Dissertations. 20.