All Positive Action Starts with Criticism: Hans Freudenthal by Sacha la Bastide-van Gemert, Marianne Vincken, William Third

By Sacha la Bastide-van Gemert, Marianne Vincken, William Third

This research offers a old research of Freudenthal’s didactic principles and his didactic profession. it's in part biographical, but additionally contributes to the historiography of arithmetic schooling and addresses heavily comparable questions reminiscent of: what's arithmetic and the place does it begin? Which function does arithmetic play in society and what impression does it have at the winning perspectives relating its accompanying didactics?.

Hans Freudenthal (1905–1990), professor in arithmetic, scientist, literator, yet particularly mathematics-educator, was once inextricably associated with the alterations which came about in arithmetic schooling and didactics throughout the moment half the final century. His range as a scientist and his inexhaustible efforts to set up the didactics of arithmetic as a heavily pursued technology, made Freudenthal's impact during this quarter enormous. He foresaw a necessary, useful position for arithmetic in everyone’s existence, encouraging scholars to find and create arithmetic themselves, rather than implementing a ready-made mathematical process. the speculation of arithmetic schooling hence constructed within the Netherlands might achieve international status within the following decades.

Today, within the gentle of the discussions approximately arithmetic schooling, during which the decision for `genuine’ arithmetic rather than the so-called 'kindergarten'-mathematics will be heard, Freudenthal's process appears to be like passé. even if, the result of this examine (which is especially in line with files from Freudenthal’s gigantic own archive) exhibits a extra sophisticated photograph. The direct id of 'kindergarten'-mathematics with Freudenthal’s view on arithmetic schooling isn't justified. 'Realistic arithmetic' as recommended by way of Freudenthal comprises greater than only a functional introductory and may, between different issues, constantly target at educating 'genuine' arithmetic within the end.

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J. v. 64. J. Dijksterhuis, ‘De historische behandelingswijze van de axiomatia der mechanica van Newton’, Euclides 4 (1927/28) 245–255. 52. H. v. 73. 53. D. van Dantzig, ‘Woord en werktuig. v. 91–92. 54. , 90. J. Scheltens would dispute this later in an article. According to him there certainly was a difference: physics, contrary to mathematics, returned to the experiment. However, he counted mechanics as belonging to mathematics; J. v. 268–269. 55. E. Beth, ‘Mechanica opnieuw examenvak’, Euclides 6 (1929/30) 44–48.

Hans Freudenthal in Schrijf dat op, Hans, 339. 2. nrs. 21, 141. 3. More about this literature study can be found in chapter 4. 4. In composing the following sections data have been derived from the following studies: A. Bartels, Een eeuw middelbaar onderwijs 1863–1963 (Groningen 1963); P. M. P. L. ; Joh. H. Wansink, Didactische oriëntatie voor wiskundeleraren. Delen i, ii, iii (Groningen 1971, second edition). 5. J. Idenburg, J. H. Janssen, Een eeuw middelbaar onderwijs herdacht (Groningen 1963) 5–6.

In his final reaction Dijksterhuis once again disputed the proposition that a clear representation would be necessary for understanding geometry. He wrote that it would be better to develop the pupil’s imaginative power during the systematic curriculum of geometry. To prove theorems a child found trivial did not matter and Dijksterhuis simply ignored such complaints. Een kind moet tenslotte ook leeren, zich tot gedachtenconcentratie te dwingen en het is niet altijd noodig, dat het het waarom beseft van de dingen, die men het laat doen.

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