From Basic Cognition to Mathematical Practice
University of Seville, Institute of Mathematics (IMUS), Seville, Spain
Frank Quinn (of Jaffe-Quinn fame, see ) 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 ). 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:
(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.
 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.  Quinn, Frank. Contributions to a Science of Mathematics, manuscript (Oc- tober 2011), 98pp.
Cognitive Psychology | Logic and Foundations | Logic and Foundations of Mathematics | Mathematics | Philosophy | Psychology
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.