Frases de Hans Freudenthal

Hans Freudenthal foi um matemático de origem holandesa. Fez contribuições substanciais à topologia algébrica e também teve interesse na literatura, filosofia, história e educação matemática. Wikipedia  

✵ 17. Setembro 1905 – 13. Outubro 1990
Hans Freudenthal: 27   citações 0   Curtidas

Hans Freudenthal: Frases em inglês

“Educational technique needs a philosophy, which is a matter of faith rather than of science.”

Hans Freudenthal (1977) Weeding and Sowing: Preface to a Science of Mathematical Education. p. 33

“No scientist is as model minded as is the statistician; in no other branch of science is the word model as often and consciously used as in statistics.”

Fonte: The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961), p. 79; Part of the article "Models in applied probability", published earlier in Synthese, 12 (1960), p. 204-210.

“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.”

Fonte: The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961), p. 79; Partly cited in: Norman L. Johnson and Samuel Kotz (1977) Urn Models and Their Application: an. Approach to Modern Discrete Probability Theory http://dis.unal.edu.co/~gjhernandezp/sim/hide/Urn%20Models%20and%20Their%20Application%20-%20An%20approach%20to%20modern%20discrete%20probability%20theory_Norman%20L.Johnson(Wiley%201977%20413s).pdf, John Wiley & Sons.

“Angles are measured by arcs, such that 360° and 2π correspond to each other.”

Fonte: Mathematics as an Educational Task (1973), p. 477

“Horizontal mathematising leads from the world of life to the world of symbols.”

Fonte: Revisiting Mathematics Education (1991), p. 41

“Space and the bodies around us are early mental objects… Name-giving is a first step towards consciousness.”

Fonte: Mathematics as an Educational Task (1973), p. 63; As cited in: Anne Birgitte Fyhn (2007) Angles as Tool for Grasping Space http://munin.uit.no/bitstream/handle/10037/994/thesis.pdf?sequence=1. p. 2

“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.
Fonte: The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961), p. ix

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