The Use of Guided Reflections in Learning Proof Writing

Abstract

We investigated written self-reflections in an undergraduate proof-writing course designed to mitigate the difficulty of a subsequent introductory analysis course. Students wrote weekly self-reflections guided by mechanical, structural, creative, and critical thinking modalities. Our research was guided by three research questions focused on the impact of student self-reflections on student metacognition and performance in the interventional and follow-up class. To address these questions, we categorized the quality of the students’ reflections and calculated their average course grades within each category in the proof-writing, the prerequisite, and the introductory analysis courses. The results demonstrated that writing high-quality self-reflections was a statistically significant predictor of earning higher average course grades in the proof-writing course and the analysis course, but not in the prerequisite course. Convergence over the semester of the students’ self-evaluations toward an experts’ scorings on a modality rubric indicates that students improve in their understanding of the modalities. The repeated writing of guided self-reflections using the framework of the modalities seems to support growth in the students’ awareness of their proof-writing abilities.

Keywords

• self-reflection
• proof writing
• real analysis