Engaging students in roles of proof |
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| Affiliation: | 1. Departments of Mathematical Sciences and Teacher Education, University of Texas at El Paso, TX, USA;2. Department of Mathematics, The Universidad Autónoma de Ciudad Juárez, Mexico;3. Department of Methodology of Mathematics, Kazan Federal University, Russia;4. Department of Psychology, Kazan Federal University, Russia;1. University of Oxford, UK;2. University of Oxford, UK;1. Department of Mathematics and Statistics, California State Polytechnic University, Pomona, 3801 W Temple Ave, Pomona, CA, 91768, United States;2. School of Mathematical & Statistical Sciences, Arizona State University, P.O. Box 87804, Tempe, AZ, 85287-1804, United States;1. Shinshu University, 6-ro, Nishinagano, Nagano, 380-8544, Japan;2. University of Southampton, University Road, Southampton, SO17 1BJ, UK;3. Johoku Junior High School, 808, Terusato, Iiyama, Nagano, 389-2413, Japan;4. Tojaku High School, 87-1, Haiwa, Hiratobashicho, Toyota, Aichi, 470-0331, Japan |
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| Abstract: | de Villiers (1990) suggested five roles of proof important in the professional mathematics community that may also serve to meaningfully engage students in learning proof: verification, explanation, systematization, discovery, and communication. We investigate written reflections on an end-of-semester assignment from undergraduates in an inquiry-based transition to proof course, where students reflected on instances during the semester when they engaged in the five roles of proof. We present the types of activities students recalled as influential to their engagement in the roles of proof (presenting, discussing, conjecturing, working on problem sets, and critiquing) and describe how students perceived these activities as influential to their engagement in the roles of proof. We provide student quotations highlighting these activities and offer implications for both research and practice. |
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| Keywords: | Undergraduate Mathematics education Collegiate mathematics education Proving Situated learning |
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