[The goal of developmental research is to] consciously experience, describe and justify the cyclic process of development and research so that it can… - Hans Freudenthal

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[The goal of developmental research is to] consciously experience, describe and justify the cyclic process of development and research so that it can be passed on to others in such a way that they can witness and relive the experience.

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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.

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Alternative Names: V. Sirolf V. Sirlof H. Freudenthal
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A true aphorism legitimates itself; whoever feels the need to legitimate an aphorism, admits that it is illegal. The surface of an aphorism should conceal profound truth. The claim that everybody can learn everything is superficial, but is as wrong as it can be. As a matter of fact, it is no aphorism but an advertising slogan, and the excuse that it is an aphorism, is a mere wink: in advertising you cannot do without exaggerating. But even as a wink it does not become more true.

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 statistician present at this moment will have been in doubt about the meaning of my words when I mentioned the common statistical model. It must be a stochastic device producing random results. Tossing coins or a dice or playing at cards are not flexible enough. The most general chance instrument is the urn filled with balls of different colours or with tickets bearing some ciphers or letters. This model is continuously used in our courses as a didactic tool, and in our statistical analyses as a means of translating realistic problems into mathematical ones. In statistical language " urn model " is a standard expression.

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