An examination of the knowledge base for teaching among undergraduate mathematics faculty teaching calculus

Date of Completion

January 2004

Keywords

Education, Mathematics|Education, Higher

Degree

Ph.D.

Abstract

Several national organizations (Committee on the Undergraduate Program in Mathematics, 1991; NRC, 1991, 2003; NSF, 1996) have declared a “state of crisis” in undergraduate mathematics education, citing high student failure rates, fewer mathematics majors, and minimal consideration of advancements in technology (Hillel, 2001; Wood, 2001). As a result, more attention has been directed at the teaching and learning of undergraduate mathematics in recent years. ^ Research (Fennema & Franke, 1992) conducted at the K–12 level, has shown that one's knowledge base for teaching [KBT] has the most significant influence on his/her instructional practice. Since the time that Shulman (1986b, 1987) articulated a framework of the KBT, considerable research has been conducted in this area. However, existing models of teacher knowledge base still need to be refined. This study extended this line of research to higher education and examined the KBT among undergraduate mathematics faculty teaching calculus. A dynamic framework of the KBT mathematics was developed and included knowledge and beliefs of: educational contexts, the nature of disciplinary mathematics, personal practical knowledge, general pedagogy, and research about the teaching and learning of mathematics. ^ The participants were seven undergraduate mathematics faculty teaching calculus at colleges and universities in the Northeast. Data were collected through interviews, observations, and video-recorded lessons. Interview data were coded according to the categories outlined in the framework of the KBT and then sorted to identify existing themes and patterns for within- and cross-case analyses. The video-recorded lessons from two purposefully selected participants were analyzed using a coding scheme adapted from the research (Brenderfur & Frykholm, 2000; Lotman, 1988; Nassaji & Wells, 1999; Schoenfeld, 1998, 2000; and Wells, 1994). ^ As a result of this study, the KBT framework was revised and subcategories of knowledge were added and removed from the model as appropriate. Rich knowledge base profiles were developed for each participant and themes across participants' KBT profiles were identified. Two participants were selected for case study to examine whether professed knowledge, beliefs, goals and images were consistent with decision-making and teaching behaviors. In general, the selected participants' KBT and instruction were highly consistent in each case, though some inconsistencies were identified. ^

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