Leth, Steven C.
University of Northern Colorado
Type of Resources
Place of Publication
University of Northern Colorado
Research suggests that preservice elementary teachers may lack the mathematics understanding necessary to teach mathematics for understanding. The literature has consistently linked student success in mathematics with teacher pedagogical content knowledge (PCK), and recent study suggested a link between teachers’ mathematical content knowledge and student achievement. There are gaps in the literature concerning preservice elementary teachers’ understanding of number theory, and little is known about how they develop number theory PCK or the relationship between their content knowledge and their PCK. The goals of this dissertation were to investigate the nature of mathematics concentration preservice elementary teachers’ content knowledge of number theory, the nature of their potential PCK in number theory, and the relationship between the two. To address these goals, I conducted a qualitative, interpretive case study of undergraduate students enrolled in a number theory course designed for preservice elementary teachers, using an emergent constructivist-based theoretical perspective. I gathered observational, interview, and document data and conducted analysis using constant comparative methods. Many of my findings concerning preservice elementary teachers’ understandings of number theory content pertain to their understandings of greatest common factor (GCF) and least common multiple (LCM). In particular, participants were more comfortable creating LCM story problems than creating GCF story problems, but their understandings of GCF story problems were closely related to the two meanings of division. In contrast to their understanding of story problems, participants were more comfortable with procedures for finding the GCF than with procedures for finding the LCM. In response to my other research questions, evidence suggests that preservice elementary teachers do possess potential PCK in number theory, namely potential knowledge of content and students and potential knowledge of content and teaching, and that they are related and influenced by specialized content knowledge, curricular content knowledge, experiences working with students, and epistemological perspectives. My data also suggest that preservice elementary teachers possess a type of PCK that is not explicitly represented by the literature, which I call general mathematical pedagogy. My findings hold many implications for practice. For example, data suggest a process through which preservice elementary teachers might develop a robust understanding of GCF story problems, which builds on their understandings of division. With this observed development process, instructors can scaffold preservice elementary teachers’ understanding of GCF story problems. My results also imply specific ways in which mathematics teacher educators and mathematicians may help preservice elementary teachers develop PCK in number theory. For example, instructors can pose hypothetical student conjectures and ask preservice elementary teachers to reflect on the knowledge necessary to teach the content, determine the validity of the conjecture, identify the concepts the student does and does not understand, suggest how they might respond to the student, and reflect on how they used their content knowledge to do so.
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