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Conventionalizing And Axiomatizing In A Community College Mathematics Bridge Course, Mark Alan Yannotta

Dissertations and Theses

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: …

The Intermediate Value Theorem As A Starting Point For Inquiry-Oriented Advanced Calculus, Stephen Raymond Strand Ii

Dissertations and Theses

Making the transition from calculus to advanced calculus/real analysis can be challenging for undergraduate students. Part of this challenge lies in the shift in the focus of student activity, from a focus on algorithms and computational techniques to activities focused around definitions, theorems, and proofs. The goal of Realistic Mathematics Education (RME) is to support students in making this transition by building on and formalizing their informal knowledge. There are a growing number of projects in this vein at the undergraduate level, in the areas of abstract algebra (TAAFU: Larsen, 2013; Larsen & Lockwood, 2013), differential equations (IO-DE: Rasmussen & …