First Advisor

Sean Larsen

Term of Graduation

Spring 2020

Date of Publication


Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Mathematics Education


Mathematics and Statistics




Abstract algebra -- Study and teaching, Group theory, Symmetry (Physics), Mathematics -- Study and teaching



Physical Description

1 online resource (xii, 270 pages)


The study of abstract algebra is both required for most mathematics majors and notoriously difficult. Much of the mathematics education literature on investigating student thinking in abstract algebra highlights student struggles with understanding even the most fundamental concepts. The abstract nature of the content of the course has been credited as one of the contributors to student difficulties. While there have been various instructional innovations designed to support students in better understanding abstract algebra, and group theory in particular, they have not specifically focused on the issue of the abstract nature of the content. My dissertation study aimed to develop an instructional theory based on a real-world application of group theory in order to support students in deepening their understanding of abstract algebra. For this study I conducted three teaching experiments with pairs of mathematics students, producing over 35 hours of video data and 235 pages of student inscriptions. The first experiment invited graduate students with ample abstract algebra experience, the second had undergraduates who had recently completed an introductory group theory course, and the third experiment invited undergraduates with no previous exposure to abstract algebra. The study was conducted using the instructional design theory of realistic mathematics education which supplied both an underlying theoretical perspective and accompanying design heuristics. The results from this study are broken into three papers. The first paper reports on the findings of the first teaching experiment and was written for a chemistry education audience. The second paper introduces the local instructional theory (LIT) that was developed over the entirety of the study. The LIT is a generalized sequence of steps for the guided reinvention of a classification system for chemically important symmetry groups. The final paper highlights differences in the students' mathematical activity while engaging in the LIT due to the differences in their mathematical backgrounds and how the LIT was used to support their success.


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