Abstract / Synopsis

Introduction-to-proof courses are becoming more prevalent in mathematics departments as more recognize the need to support students while they transition from courses focused on computation (such as calculus) to proof-intensive courses (such as real analysis). In such introduction courses, there are some common proving techniques to teach (induction, contradiction, and contraposition to name a few), but the content varies from institution to institution. This note adds to the discussion on content in such courses by analyzing two prior studies, one using a coding scheme designed to illuminate step-by-step justifications in a proof, and the other focused on interviews with course instructors. Our analysis of the literature shows that there may be reason to believe that content-based introduction-to-proof courses inadvertently overemphasize specific mathematical-area reasoning, which may not translate effectively to subsequent proof-based courses in different content areas. Simply put, while some mathematicians may be convinced of this, a real analysis, number theory, or abstract algebra course may not be the most effective introduction-to-proof course for students to transition to other proof-based courses.



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