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Monday, March 1 • 2:50pm - 3:05pm
Talk Session 2: Teaching mathematical logic in context

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A fundamental conundrum of teaching and studying logic is that logic refers to content-general understandings while student reasoning is usually highly content-specific. When mathematics courses teach logic in de-contextualized ways, students may often fail to see how it segues with their reasoning about particular topics. In a series of teaching experiments with undergraduate students we have found a productive way to help students reinvent basic principles of logic by comparing mathematical statements across contexts. This process allows us to observe how students create content-general ways of thinking from their content-specific reasoning. The design of the activities draws heavily on the Realistic Mathematics Education tradition of guided reinvention and emergent models. I shall share in the talk some brief insights about how I have learned to revise the formulation of the logic we teach to be more compatible with and responsive to students’ ways of reasoning about mathematical language and categories. In particular, mathematical statements of the form “if then” are essentially always universally quantified (“for all”), though that language is often suppressed in mathematical text. Helping students reason specifically about sets of objects has proven challenging and yet highly productive. I shall also reflect on the importance of helping students construct productive ways of reasoning about negative categories (“not a rectangle” or “not a multiple of 6”).

avatar for Paul Dawkins

Paul Dawkins

Associate Professor of Mathematics, Texas State University
Mathematics educator with focus on proof-based mathematics, specifically the teaching and learning of logic.

Monday March 1, 2021 2:50pm - 3:05pm CST