#### 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

Michael Stewart

#### Fourth Advisor

Vladimir Bondarenko

#### Abstract

Mathematical proof is of high importance in the advanced proof-based courses which mathematics majors must take in order to graduate. Investigating how a competent student learns the concept of proof may be very beneficial in the pedagogical approaches of proof courses. In this study, the Self-Regulated Learning (SRL) theory and the Action-Process-Object-Schema (APOS) theoretical framework were employed. A competent mathematics major student was observed during two semesters – Bridge to Higher Math and Analysis. The observational data was triangulated through follow up discussions after class observations and a final interview at the end of the semester. The results of data analysis indicated that the participating student was successful in writing valid proofs in the Bridge to Higher Math course but only memorized the proofs in the Analysis course. Results showed that a mismatch in the student’s learning style and the instructor’s teaching style in the Analysis course negatively affected the student’s level of self-regulation and thus attributed to him not moving past the Action conception stage of understanding for the content covered in the course. A lack of conceptual understanding was also a difficulty that arose for the student when learning proof concepts. There was a positive correlation between the student’s level of self-regulation and course grade. The student’s responses to the SRL questionnaire were used to develop a generalized linear regression model to estimate the student’s success based on his/her level of self-regulation. Self-efficacy proved to be the only significant component for the model. From the view of APOS theory, his conception of a proof was at mostly at the Process conception stage of understanding in the Bridge to Higher Math course and was predominately at the Action conception stage of understanding in the Analysis course. Suggestions on how to incorporate self-regulated learning in the classroom and APOS theory in the pedagogical approaches for proof courses were made.

#### Recommended Citation

Grant, Shanah K., "An In-Depth Investigation Of How An Undergraduate Mathematics Major Student Learns The Concept Of Proof." Dissertation, Georgia State University, 2020.

https://scholarworks.gsu.edu/math_diss/72

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