H. Freudenthal. Educational Studies in Mathematics, 1 (1/2):
3-8(May 1968)Systematization is a great virtue of mathematics, and if possible, the student has to learn this virtue, too. But then I mean the activity of systematizing, not its result. Its result is a system, a beautiful closed system, closed, with no entrance and no exit. In its highest perfection it can even be handled by a machine. But for what can be performed by machines, we need no humans. What humans have to learn is not mathematics as a closed system, but rather as an activity, the process of mathematizing reality and if possible even that of mathematizing mathematics..
Systematization is a great virtue of mathematics, and if possible, the student has to learn this virtue, too. But then I mean the activity of systematizing, not its result. Its result is a system, a beautiful closed system, closed, with no entrance and no exit. In its highest perfection it can even be handled by a machine. But for what can be performed by machines, we need no humans. What humans have to learn is not mathematics as a closed system, but rather as an activity, the process of mathematizing reality and if possible even that of mathematizing mathematics.
%0 Journal Article
%1 196805
%A Freudenthal, Hans
%D 1968
%I Springer
%J Educational Studies in Mathematics
%K education learning mathematics mythesis philosophy
%N 1/2
%P 3-8
%T Why to Teach Mathematics So as to Be Useful
%U http://links.jstor.org/sici?sici=0013-1954%28196805%291%3A1%2F2%3C3%3AWTTMSA%3E2.0.CO%3B2-V
%V 1
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author = {Freudenthal, Hans},
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journal = {Educational Studies in Mathematics},
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month = may,
note = {Systematization is a great virtue of mathematics, and if possible, the student has to learn this virtue, too. But then I mean the activity of systematizing, not its result. Its result is a system, a beautiful closed system, closed, with no entrance and no exit. In its highest perfection it can even be handled by a machine. But for what can be performed by machines, we need no humans. What humans have to learn is not mathematics as a closed system, but rather as an activity, the process of mathematizing reality and if possible even that of mathematizing mathematics.},
number = {1/2},
pages = {3-8},
publisher = {Springer},
timestamp = {2008-05-30T05:47:29.000+0200},
title = {Why to Teach Mathematics So as to Be Useful},
url = {http://links.jstor.org/sici?sici=0013-1954%28196805%291%3A1%2F2%3C3%3AWTTMSA%3E2.0.CO%3B2-V},
volume = 1,
year = 1968
}