First Advisor

Sean Larsen

Term of Graduation

Fall 2022

Date of Publication


Document Type


Degree Name

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


Mathematics and Statistics





Physical Description

1 online resource (viii, 223 pages)


Given the well documented fact students often struggle with proof and proof-related activity for various reasons, more educators have shifted to incorporating pedagogies involving collaborative learning given their benefits to student learning. However, there is still surprisingly little research focused on the nature of students' collaborative proving activity. Moreover, the recent COVID-19 pandemic, and subsequent shift to remote learning, forced educators and students to adapt and learn how to work within a new learning environment. In this dissertation project, I investigate how students engage in collaborative proving activity in a synchronous online introduction to proofs course. In the first paper, I present a case study of two students working together on a conjecturing activity and study the role that the students' listening activity (i.e., how they listen to one another) played in the co-construction of a shared solution. Findings from this study suggest that by listening to their peers in different ways a student can play a critical role in the co-construction of a shared solution without being the one to appear to be leading the mathematical ideas. In the second paper, I investigate how students operationalize the technological tools available to them in the remote environment to work collectively in small groups. For the results of this study, I identified several uses that the students developed for the tools available to them. I discuss the implication these uses have on students' collective proving activity. Overall, this dissertation provides several insights into the nature of students' collective activity in proof-based courses from both a mathematical and technological perspective.


© Tenchita Alzaga Elizondo

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