Reflective Journaling as a Tool to Support Learning Mathematical Proof
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This study investigates how reflective writing supported students’ learning to prove in an Introduction to Advanced Mathematics course. The students submitted weekly journal entries that were composed of unstructured prompts and structured, proof-related prompts. Students’ reported benefits from the journals were coded according to Borasi and Rose’s (1989) framework for student benefits from journaling in mathematics, and students’ journals about their proof writing process were coded according to Raman’s (2003) ideas about proof writing. In the unstructured journals, students demonstrated primarily therapeutic, problem solving, and content benefits. However, students reported experiencing mostly problem solving and content benefits, as well benefits related to dialoguing with the instructor. A positive and significant correlation was found between the number of journals completed and course grade, which suggests a relationship present between the two. Over half of the students felt the journals influenced their learning to prove by helping them pin down their understandings and write about proof ideas in their own words, which they then connected to the more formal writing in their proofs. There did not seem to be a relationship between the journals and students’ views about mathematics, likely because students rarely wrote about their views related to the nature of mathematics or proving.