College Algebra Students' Perceptions of Exam Errors and the Problem-Solving Process

Mary E Pilgrim ¹ Linda C Burks ^2* Megan Ryals ³ Sloan Hill-Lindsay ¹

• ¹ San Diego State University, San Diego, California, United States
• ² Santa Clara University, Santa Clara, United States
• ³ University of Virginia, Charlottesville, Virginia, United States

The first two years of college mathematics play a key role in retaining STEM majors. This becomes considerably difficult when students lack the background knowledge needed to begin in Calculus and instead take College Algebra or Precalculus as a first mathematics course. Given the poor success rates often attributed to these courses, researchers have been looking for ways in which to better support student learning, such as examining the impact of enhancing study habits and skills and metacognitive knowledge. One way that students can enhance their metacognitive knowledge in order to modify their study habits and practices is through reflection on mistakes. For this paper in particular, we focus on mistakes students make on exams. We interviewed students after they took an exam and completed an exam analysis worksheet. As part of a study on the impact of metacognitive instruction for College Algebra students we found that students often attributed their exam errors to "simple mistakes". However, we identified many of these errors as "not simple". To understand students' perceptions of their mistakes within the context of problem-solving, we adapted the Carlson and Bloom (2005) problem-solving framework as an analytical tool. We found that students' and researchers' classifications of errors were not aligned across the problem-solving phases. In this paper we present findings from this work, sharing the adapted problem-solving framework, students' perceptions of their exam mistakes, and the relationship between students' categorizations of their errors and the problem-solving phase in which the errors occurred. Understanding students' perceptions of their mistakes helps us better understand how we might support them as learners and better situate them for success in the future.