
05240067
a
2008b.00079
Mitchelmore, Michael
White, Paul
Abstraction in mathematics and mathematics learning.
Johnsen H\o ines, Marit (ed.) et al., Proceedings of the 28th international conference of the International Group for the Psychology of Mathematics Education, PME 28, Bergen, Norway, July 1418, 2004. Bergen: Bergen University College. Part III, 329336 (2004).
2004
Bergen: Bergen University College
EN
C30
E40
E20
A60
cognitive processes
abstract reasoning
empirical abstraction
mathematical abstraction
advanced mathematical learning
thinking
emis:proceedings/PME28/RR/RR031_Mitchelmore.pdf
Summary: It is claimed that, since mathematics is essentially a selfcontained system, mathematical objects may best be described as ``abstractapart". 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 ``abstractgeneral" because they embody general properties of the real world. A discussion of the relationship between abstractapart objects and abstractgeneral 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.