Mathematics Education and the Objectivist Programme in HPS

Mathematics Education and the Objectivist Programme in HPS

Glas, E.

Electrical Engineering, Mathematics and Computer Science

Delft Institute of Applied Mathematics

2012-01-01

Using history of mathematics for studying concepts, methods, problems and other internal features of the discipline may give rise to a certain tension between descriptive adequacy and educational demands. Other than historians, educators are concerned with mathematics as a normatively defined discipline. Teaching cannot but be based on a pre-understanding of what mathematics ‘is’ or, in other words, on a normative (methodological, philosophical) view of the identity or nature of the discipline. Educators are primarily concerned with developments at the level of objective mathematical knowledge, that is: with the relations between successive theories, problems and proposed solutions—relations which are independent of whatever has been the role of personal or collective beliefs, convictions, traditions and other historical circumstances. Though not exactly ‘historical’ in the usual sense, I contend that this ‘objectivist’ approach does represent one among other entirely legitimate and valuable approaches to the historical development of mathematics. Its retrospective importance to current practitioners and students is illustrated by a reconstruction of the development of Eudoxus’s theory of proportionality in response to the problem of irrationality, and the way in which Dedekind some two millennia later almost literally used this ancient theory for the rigorous introduction of irrational numbers and hence of the real number continuum

http://resolver.tudelft.nl/uuid:5ce50bb8-3988-4107-8f91-cd518863acf0

https://doi.org/10.1007/s11191-011-9433-5

Springer-Verlag

1573-1901

http://link.springer.com/article/10.1007/s11191-011-9433-5

Science and Education, Jan. 2012

Institutional Repository

journal article

(c)2012 Glas, E. and Springer