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The case of methodology is analogous though less clear. Nobody would object to the subject of methodology being science, or some pseudo science. On c… - Hans Freudenthal
" "The case of methodology is analogous though less clear. Nobody would object to the subject of methodology being science, or some pseudo science. On closer inspection, however, this agreement is no more than a verbal coincidence. It rests on what is meant by science, as reported as a subject of methodology. In fact the subject methodologists call science is more often than not different from what scientists call science. Methodologists are inclined to consider a science as a linguistic system whereas the scientist would only admit that his science has a language, not that it is a language.
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About Hans Freudenthal
Hans Freudenthal (September 17, 1905 – October 13, 1990) was a Dutch mathematician. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education.
Also Known As
Pen Names:
V. Sirolf
Alternative Names:
V. Sirlof
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H. Freudenthal
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The urn model is to be the expression of three postulates: (1) the constancy of a probability distribution, ensured by the solidity of the vessel, (2) the randomcharacter of the choice, ensured by the narrowness of the mouth, which is to prevent visibility of the contents and any consciously selective choice, (3) the independence of successive choices, whenever the drawn balls are put back into the urn. Of course in abstract probability and statistics the word " choice " can be avoided and all can be done without any reference to such a model. But as soon as the abstract theory is to be applied, random choice plays an essential role.
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No mathematical idea has ever been published in the way it was discovered. Techniques have been developed and are used, if a problem has been solved, to turn the solution procedure upside down, or if it is a larger complex of statements and theories, to turn definitions into propositions, and propositions into definitions, the hot invention into icy beauty. This then if it has affected teaching matter, is the didactical inversion, which as it happens may be anti-didactical. Rather than behaving anti-didactically, one should recognise that the learner is entitled to recapitulate in a fashion of mankind. Not in the trivial matter of an abridged version, but equally we cannot require the new generation to start at the point where their predecessors left off.
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