## Graduation Semester and Year

2017

## Language

English

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy in Mathematics

## Department

Mathematics

## First Advisor

James A Álvarez

## Abstract

This study examines the mathematical problem solving (MPS) practices of students enrolled in College Algebra at a large urban university in the southwestern United States. The primary research question explores how to characterize the MPS techniques, strategies or orientations used by College Algebra students. In addition, this study documents MPS approaches that appear to be most prevalent and examines how these approaches relate to student performance. A grounded theory approach is used to formulate a theory for characterizing the MPS of students in College Algebra. Data analysis shows that multiple student-held orientations identified in this theory correlate with improved performance in College Algebra with MPS techniques, strategies, or orientations being influenced by affective factors and problem types. This qualitative study examines 19 MPS student interviews during which students answered questions about their typical approaches in MPS and discussed their solutions to mathematics problems completed both before and during the interview. Open-coding (Corbin & Strauss, 2008) was used to analyze recordings, transcriptions, and student work from the interviews. The MPS techniques, strategies, or orientations naturally arising from the data formed the basis for the theory formulated in this study. Of the eight orientations observed, three common primary orientations emerge from the data with the other five being used much less-commonly across student interviews. For each of the three common primary orientations—formula application, reexamination, and big-picture focus—a particular set of strategies and techniques typically accompany the observed orientation. The formula application and reexamination orientations align with successful grade outcomes in College Algebra. Additional analysis reveals that strategies and techniques vary according to the type of problem presented, and the higher number of strategies used by a student correlates with higher College Algebra course grade outcomes. The characterization of the MPS techniques, strategies or orientations used by College Algebra students and how these relate to course grade outcomes raise important questions regarding the behaviors rewarded with success in College Algebra and the actual MPS capacity needed to succeed in a science, technology, engineering, or mathematics career path.

## Keywords

Mathematical problem solving, Mathematics education, College algebra, Undergraduate mathematics eduation

## Disciplines

Mathematics | Physical Sciences and Mathematics

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

Campbell, R. Cavender, "Characterizing College Algebra Students' Mathematical Problem Solving" (2017). *Mathematics Dissertations*. 238.

https://mavmatrix.uta.edu/math_dissertations/238

## Comments

Degree granted by The University of Texas at Arlington