@inbook {MATHEDUC.05240067,
author = {Mitchelmore, Michael and White, Paul},
title = {Abstraction in mathematics and mathematics learning.},
year = {2004},
booktitle = {Proceedings of the 28th international conference of the International Group for the Psychology of Mathematics Education, PME 28, Bergen, Norway, July 14--18, 2004},
pages = {Part III, 329-336},
publisher = {Bergen: Bergen University College},
abstract = {Summary: It is claimed that, since mathematics is essentially a self-contained system, mathematical objects may best be described as ``abstract-apart". On the other hand, fundamental mathematical ideas are closely related to the real world and their learning involves empirical concepts. These concepts may be called ``abstract-general" because they embody general properties of the real world. A discussion of the relationship between abstract-apart objects and abstract-general concepts leads to the conclusion that a key component in learning about fundamental mathematical objects is the ``formalisation" of empirical concepts. A model of the relationship between mathematics and mathematics learning is presented which also includes more advanced mathematical objects.},
msc2010 = {C30xx (E40xx E20xx A60xx)},
identifier = {2008b.00079},
}