Document Type

Presentation

Presentation Date

Fall 9-19-2016

Conference Name

From Basic Cognition to Mathematical Practice

Conference Location

University of Seville, Institute of Mathematics (IMUS), Seville, Spain

Abstract

Frank Quinn (of Jaffe-Quinn 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 three-pronged approach:

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

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

  3. (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

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