Date of Award

8-11-2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

First Advisor

Draga Vidakovic

Second Advisor

Valerie Miller

Third Advisor

Alexandra Smirnova

Fourth Advisor

Yi Zhao

Abstract

Over the past decade, research about students' proof capabilities has been a prevalent topic in collegiate mathematics education. Also, while not as prevalent, there has been interest in research about the teaching practices of the introduction to proof and other proof--based collegiate mathematics courses. To investigate the link between these two topics, this dissertation examined the assessment and teaching practices of Dr. Wyatt, a research mathematician who participated in mathematics education research alongside mathematics educators from multiple universities, utilized as the instructor of a Transition--to--proof course. An analysis of responses of his former students, observations of his instruction, the examination of a variety of types of assessments used during the course, and an interview at the end of the semester are used to determine the impact his participation in mathematics education research had on his beliefs about teaching and the assessment of students' mathematical understanding/knowledge. This dissertation utilizes an assessment framework developed by Mejia-Ramos et al. (2012) (which focuses on students' proof comprehension) and a framework about teaching practices at the collegiate level developed by Speer et al. (2010). The findings in this dissertation indicate that Dr. Wyatt uses several types of assessment that focus on the foundational aspects of mathematical proof while providing targeted feedback to students' responses. Further, Dr. Wyatt's teaching practices have been enhanced through the use of a new assessment question type modeled on what he learned from the mathematics education research project.

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