Document Type
Presentation
Presentation Date
Fall 9192016
Conference Name
From Basic Cognition to Mathematical Practice
Conference Location
University of Seville, Institute of Mathematics (IMUS), Seville, Spain
Abstract
Frank Quinn (of JaffeQuinn fame, see [1]) worked out the basics of his own account of mathematical practice, an account that is informed by an analysis of contemporary mathematics and its pedagogy (see [2]). Taking this account as our starting point, we can characterize the current mathematical practice to acquire and work with new concepts as a cognitive adaptation strategy that, first, emerged to meet the challenges posed by the growing abstractness of its objects and which, second, proceeds according to the following threepronged approach:

(i) sever as many ties to ordinary language as possible and limit ordinary language explanations to an absolute minimum;

(ii) introduce axiomatic definitions and bundle them up with a sufficient num ber of examples, lemmata, propositions, etc. into small cognitive packages;

(iii) practice hard with one new cognitive package at a time.
Drawing on research in cognitive science, and especially in mathematics ed ucation, I will then show how cognitive science provides supporting evidence for the effectiveness of this mathematical practice. Time permitting, I will then complement these findings from a phenomenological perspective by exhibiting a fruitful convergence between mathematics, cognitive science, and phenomeno logical analysis.
[1] Jaffe, Arthur, Quinn, Frank. “Theoretical Mathematics: Towards a synthesis of mathematics and theoretical physics,” Bulletin of the American Mathemati cal Society NS 29:1 (1993), 113. [2] Quinn, Frank. Contributions to a Science of Mathematics, manuscript (Oc tober 2011), 98pp.
Disciplines
Cognitive Psychology  Logic and Foundations  Logic and Foundations of Mathematics  Mathematics  Philosophy  Psychology
Opus Citation
Bernd Buldt (2016).
Mathematical Practice and Human Cognition. Presented at From Basic Cognition to Mathematical Practice, University of Seville, Institute of Mathematics (IMUS), Seville, Spain.
http://opus.ipfw.edu/philos_facpres/150
Included in
Cognitive Psychology Commons, Logic and Foundations Commons, Logic and Foundations of Mathematics Commons