Applying Proof Frameworks Is Harder for Students than We Think
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In order to overcome difficulties many students in mathematics and computer science face with rigorous proofs, some higher education institutes present a “Mathematical Reasoning” or “Transition-to-Proof” course. In this paper, we analyzed data from the exams of 310 students in such a course, focusing on the way they approach a proof regarding set inclusion, and whether they use a particular “proof framework” that we taught them when doing so. We found that the students are able to use the proof framework, and that using it is beneficial to them, but that a surprisingly large percentage of them fail to use it consistently.