Portland State University. Department of Mathematics and Statistics
Date of Award
Doctor of Philosophy (Ph.D.) in Mathematics Education
Mathematics and Statistics
1 online resource (ix, 170 pages)
Abstract algebra -- Study and teaching (Higher), Mathematics -- Study and teaching (Higher), Community college students
This dissertation consists of three related papers. The first paper, Rethinking mathematics bridge courses--An inquiry model for community colleges, introduces the activities of conventionalizing and axiomatizing from a practitioner perspective. In the paper, I offer a curricular model that includes both inquiry and traditional instruction for two-year college students interested in mathematics. In particular, I provide both examples and rationales of tasks from the research-based Teaching Abstract Algebra for Understanding (TAAFU) curriculum, which anchors the inquiry-oriented version of the mathematics bridge course.
The second paper, the role of past experience in creating a shared representation system for a mathematical operation: A case of conventionalizing, adds to the existing literature on mathematizing (Freudenthal, 1973) by "zooming in" on the early stages of the classroom enactment of an inquiry-oriented curriculum for reinventing the concept of group (Larsen, 2013). In three case study episodes, I shed light onto "How might conventionalizing unfold in a mathematics classroom?" and offer an initial framework that relates students' establishment of conventions in light of their past mathematical experiences.
The third paper, Collective axiomatizing as a classroom activity, is a detailed case study (Yin, 2009) that examines how students collectively engage in axiomatizing.
In the paper, I offer a revision to De Villiers's (1986) model of descriptive axiomatizing. The results of this study emphasize the additions of pre-axiomatic activity and axiomatic creation to the model and elaborate the processes of axiomatic formulation and analysis within the classroom community.
Yannotta, Mark Alan, "Conventionalizing and Axiomatizing in a Community College Mathematics Bridge Course" (2016). Dissertations and Theses. Paper 3105.