Mathematical understanding and ownership in learning: affordances of and student views on templates for proof-writing

• Published in: International journal of mathematical education in science and technology 2024-10, Vol.55 (9), p.2249-2267
• Main Authors: Klanderman, Sarah, Satyam, V. Rani
• Format: Article
• Language: English
• Subjects: Colleges & universities; Creativity; Instructional aids; Instructional Materials; Learning; Mathematics education; Ownership; proof scaffolding; proof writing; Software; Students; templates; Transition-to-proof; undergraduate mathematics education; Universities
• ISSN: 0020-739X; 1464-5211
• DOI: 10.1080/0020739X.2022.2139775

For students taking higher level mathematics courses, the transition from computational to proof-based courses such as analysis and algebra not only introduces a new format of writing and communication, but also a new level of abstraction. This study examines the affordances of one particular tool to aid students in this transition: a proof template. We highlight four cases based on interviews conducted at two universities, both from transition-to-proof classes in which templates were explicitly used and not. Results indicate that when introduced to this tool, students viewed these templates favourably. Two detailed cases provide evidence that templates can contribute to deep understanding and student ownership of learning by deconstructing the template structures for themselves. In settings where explicit templates were not introduced, two cases address possible concerns with templates as well as demonstrate that students may be intuiting this structure. Our work provides evidence for the benefits of templates as a learning aid to struggling and strong students alike that does not reduce creativity in proving, along with students' appreciation of templates for structure and as guidelines to make sense of the increased abstraction required for proof-writing.