Understanding Understanding Mathematics

Cognitive Science 2 (4):361-383 (1978)
  Copy   BIBTEX

Abstract

In this paper we look at some of the ingredients and processes involved in the understanding of mathematics. We analyze elements of mathematical knowledge, organize them in a coherent way and take note of certain classes of items that share noteworthy roles in understanding. We thus build a conceptual framework in which to talk about mathematical knowledge. We then use this representation to describe the acquisition of understanding. We also report on classroom experience with these ideas.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,571

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
How understanding makes knowledge valuable.Ayca Boylu - 2010 - Canadian Journal of Philosophy 40 (4):591-609.
Linguistic Communication versus Understanding.Xinli Wang - 2009 - Philosophia: International Journal of Philosophy (Philippine e-journal) 78 (1):71-84.
Simulation and the sense of understanding.Jaakko Kuorikoski - 2011 - In Paul Humphreys & Cyrille Imbert (eds.), Models, Simulations, and Representations. London: Routledge. pp. 168-187.
Mathematical activity.M. Giaquinto - 2005 - In Paolo Mancosu, Klaus Frovin Jørgensen & S. A. Pedersen (eds.), Visualization, Explanation and Reasoning Styles in Mathematics. Springer. pp. 75-87.
Idealizations and scientific understanding.Moti Mizrahi - 2012 - Philosophical Studies 160 (2):237-252.
The Role of Explanation in Understanding.Kareem Khalifa - 2013 - British Journal for the Philosophy of Science 64 (1):161-187.

Analytics

Added to PP
2013-11-21

Downloads
27 (#585,141)

6 months
4 (#779,041)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Genetic epistemology.Jean Piaget - 1970 - New York,: Columbia University Press.
Proofs and refutations (IV).I. Lakatos - 1963 - British Journal for the Philosophy of Science 14 (56):296-342.
Proofs and refutations (III).Imre Lakatos - 1963 - British Journal for the Philosophy of Science 14 (55):221-245.
Induction and Analogy in Mathematics.George Pólya - 1973 - Princeton University Press.

Add more references