Exploring Abstraction in Mathematics: Insights from MAA MathFest 2022
Delve into the concept of abstraction with a focus on diverse perspectives, historical influences, pedagogical approaches, and the process of abstraction itself as discussed at MAA MathFest 2022. Engage with enlightening comparisons and references shedding light on this fundamental mathematical principle.
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Presentation Transcript
Defining Abstraction Rahmat Rashid, Rollins College Mark Anderson, Rollins College MAA MathFest 2022 | August 5th 2022
Motivating Ideas From a teacher s perspective From a philosopher s perspective From a mathematician s perspective MAA MathFest 2022 | August 5th 2022
Previous Philosophical Literature Plato vs. Aristotle Descartes vs. Hume More generally: rationalists vs. empiricists MAA MathFest 2022 | August 5th 2022
Previous Pedagogical Literature Piaget: Empirical Abstraction, Pseudo-empirical Abstraction, Reflective Abstraction Gray & Tall: Empirical Abstraction, Reification, Formalization MAA MathFest 2022 | August 5th 2022
Process of Abstraction Two phases: Destructive Phase Constructive Phase Criterion of Identity (Marquis) MAA MathFest 2022 | August 5th 2022
Comparing Levels of Abstraction Forgetful Functors from Category Theory B A Strictness of Criterion of Identity MAA MathFest 2022 | August 5th 2022
References Gray, Eddie, and David Tall. Abstraction as a Natural Process of Mental Compression. Mathematics Education Research Journal, 2007. Marquis, Jean-Pierre. Stairway to Heaven, 2016. MAA MathFest 2022 | August 5th 2022
