How does prior subject matter knowledge affect the learning of pedagogical content knowledge in a mathematics methods course at the preservice level?

摘要

The National Council of Teachers of Mathematics created standards for teaching mathematics that suggest a constructivist approach. Research indicates prospective elementary teachers have limited understandings in mathematics. This dissertation addresses the question "How does prior subject matter knowledge affect the learning of pedagogical content knowledge in a mathematics methods course at the preservice level?";Skemp's (1978) definitions of instrumental and relational understandings were used to describe both subject matter knowledge and pedagogical content knowledge of fractions for six preservice teachers both before and after a mathematics methods course. The participants' understandings of fractions and pedagogical content knowledge were qualitatively analyzed by case and cross-case using two task interviews, a mathematics education biography, three student teaching classroom observations in mathematics, and the classroom observations of the mathematics methods course.;Four preservice teachers with an initial instrumental understanding of mathematics demonstrated improved instrumental subject matter knowledge during the final task interview and one demonstrated a relational understanding of fractions. One participant with an initial relational understanding of fractions subsequently demonstrated a relational pedagogical content understanding of fractions. Another participant with an initial relational understanding of fractions exhibited instrumental pedagogical content knowledge.;Participants with initial instrumental understandings of fractions improved their understandings of fractions in the methods course. However, they did not improve as much in pedagogical content knowledge because of the need to simultaneously learn both subject matter and pedagogical content knowledge. These findings suggest that mathematics teacher education programs should reconsider the type of subject matter knowledge required by preservice teachers. Conceptual subject matter knowledge should be emphasized so that adequate pedagogical content knowledge can be developed. Courses designed to develop subject matter knowledge and pedagogical content knowledge should consider students existing beliefs about mathematics and teaching mathematics. Care should be taken to create appropriate student teaching placements that reinforce the NCTM standards.