Relearning: Understanding How Previous Experiences Learning Algebra Influence Students' Perceptions in Developmental Mathematics Programs

Through a series of four papers, this dissertation investigates developmental mathematics students' experiences with relearning, or the experience of learning about content one has already tried to learn in a previous mathematics course. Developmental math courses typically focus on K-12 algebra, and are required for graduation but notorious for their high rates of failure. Current research is notably lacking in descriptions of student learning experiences, so understanding how perceptions of relearning develop over time is an imperative for researchers and practitioners alike. In the first paper, I provide a theoretical overview of the concept of relearning, demonstrating its roots in studies of memory in cognitive psychology and mathematics teacher education. The second paper describes the first empirical study of relearning in developmental mathematics and provides an in-depth look at the perspectives of three students relearning one topic Intermediate Algebra. Interview analysis indicated that students utilized (1) their perceptions of similarity of course content and (2) confidence in the understanding they developed of the topic in a previous algebra course, to inform their expectations and perceptions of the impact of relearning on their understanding of the topic. The third paper describes six longitudinal case studies of Elementary and Intermediate Algebra students that built on prior results by investigating perceptions of relearning individual topics, relearning an entire course, and the role of relearning throughout a developmental mathematics program. Analysis of interviews, surveys, and discussions of course exams revealed how students' developing relationships with relearning motivate larger patterns of behavior and help explain critical shifts in how students decide to experience instruction. In the final study, I present findings from a survey intended to explore how the findings of the previous two studies were reflected in the perspectives of a larger group from the same courses. While the perceived impacts of relearning on students' topic and course-level understanding largely aligned with previous results, perceptions of behaviors and affective responses agreed only moderately, indicating a need for further investigation. Overall, this dissertation highlights the importance of considering students' previous algebraic learning experiences in understanding their trajectory within and through developmental mathematics programs. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]