Abstraction in Mathematics: Insights from MAA MathFest 2022
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
MAA MathFest 2022 | August 5th 2022
Two phases:
•
Destructive Phase
•
Constructive Phase
Criterion of Identity (Marquis)
Comparing Levels of Abstraction
Forgetful Functors from Category
Theory
Strictness of Criterion of Identity
MAA MathFest 2022 | August 5th 2022
B
A
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
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.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
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
