Open Access Dissertation
Geometry--Study and teaching (Secondary); Mathematics teachers--Training of--United States; Mathematics teachers--United States--Psychology;
The lack of mathematical understanding of elementary preservice teachers with respect to many mathematical topics has been well documented. Far fewer studies have been conducted on any content area of knowledge of secondary teachers and even less in the mathematics content area. The assumption by the general population is that mathematics majors are adequately prepared to teach the content of secondary mathematics because they major in mathematics. Mathematics educators, however, note the lack of conceptual understandings in many content areas in these mathematics teaching majors. While mathematics educators are aware of this deficiency, there is little research data at the secondary level to support those beliefs.
Euclidean geometry is regularly taught in high schools, a content area with which U.S. students have difficulty. Perhaps the reason students have difficulty learning geometry is that their teachers have not developed a deep knowledge of the subject themselves and are not able to teach their students with enough understanding to enable their students to gain mathematical proficiency in that content area. Therefore the focus for this study was secondary preservice teachers' knowledge of Euclidean geometry.
The research participants were 15 secondary mathematics education majors who were taking a mathematics methods course at a Midwestern state university. Mixed methods were used to ascertain the mathematical proficiency that secondary preservice teachers have in the content area of Euclidean geometry. A paper-and-pencil test revealed a wide span of mathematical knowledge ranging from the top three participants who correctly answered all 15 questions to the bottom three participants who only answered eight of the 15 questions correctly. Follow-up, in-depth interviews were conducted with five participants: two from the high group, two from the low group, and one from the middle group.
The participants in the high group demonstrated conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and a productive disposition—the five strands of mathematical proficiency (NRC, 2001). The participants in the low group, on the other hand, showed deficiencies in each of the five strands. The interviewed participant in the middle group shared more closely the characteristics of the participants in the high group than the participants in the low group. This study showed that successful completion of the required mathematics content courses does not guarantee the presence of a thorough understanding of the mathematics that secondary preservice teachers will be expected to teach.
The possible lack in mathematical proficiency in secondary preservice teachers needs to be brought to the attention of the mathematics community and documented so that improvements in teacher education can be made. Implications from this study may prompt teacher educators to integrate conceptually-based content along with pedagogy into the methods courses.
Year of Submission
Doctor of Education
Department of Curriculum and Instruction
Linda May Fitzgerald, Chair
Elana Joram, Co-Chair
1 PDF file (vii, 125 pages)
©2009 Karen Sabey
Sabey, Karen, "Secondary preservice teachers' understanding of Euclidean geometry" (2009). Theses and Dissertations @ UNI. 691.