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	Hans Freudenthal - Wikipedia, the free encyclopedia
		Hans Freudenthal (September 17, 1905 – October 13, 1990) was a Dutch mathematician born in Luckenwalde in Germany into a Jewish family.
		Freudenthal did his thesis work with Heinz Hopf and defended a thesis on the ends of topological groups in 1930.
		In 1941 Freudenthal was suspended from duties at the University of Amsterdam by the Nazis.
	en.wikipedia.org /wiki/Hans_Freudenthal (169 words)

	Portret van Hans Freudenthal (Site not responding. Last check: 2007-11-05)
		Hans Freudenthal was born in 1905 in the German town of Luckenwalde, the son of a Jewish teacher.
		In 1946 Freudenthal became a professor in Utrecht, appointed to a chair in pure and applied mathematics and the principles of mathematics.
		Hans Freudenthal, the education reformer, died on 13 October 1990.
	www.fi.uu.nl /en/freudenthal.html (415 words)

	Freudenthal
		Hans Freudenthal was born into a Jewish family, a fact which would have unfortunate consequences for him during World War II.
		In 1971 Freudenthal was appointed as the first director of the Institute for the Development of Mathematical Education in Utrecht.
		Freudenthal studied the relation between axiomatic mathematics and reality, and this study led him to contribute to intuitionism, as well as to the application of mathematics to linguistics.
	homepages.compuserve.de /thweidenfeller/mathematiker/Freudenthal.htm (1019 words)

	References for Freudenthal (Site not responding. Last check: 2007-11-05)
		J Adda, Une lumière s'est éteinte : H. Freudenthal, homo universalis, in The legacy of Hans Freudenthal (Dordrecht, 1993), 9-19.
		Hans Freudenthal, Papers dedicated to the memory of Hans Freudenthal (Dutch), Nieuw Arch.
		L Streefland, Editorial : the legacy of Freudenthal, in The legacy of Hans Freudenthal (Dordrecht, 1993) 1-7.
	turnbull.dcs.st-and.ac.uk /history/References/Freudenthal.html (243 words)

	Bruno Bassi - Were it Perfect, Would it Work Better?
		We shall examine Dr. Freudenthal's solution in some detail, and we will conclude stressing a sort of paradox that is implicit in the whole enterprise, an oscillation between a formalist and a communicative trend that makes Lincos a hybrid experiment from the point of view of the design of a perfect language.
		Freudenthal's proposal is grounded on the conviction that in order to communicate effectively we should use a language, rather than rely on other less powerful forms of communications.
		[1] Hans Freudenthal, born 1905, was at the time professor of mathematics at the University of Utrecht.
	www.brunobassi.it /scritti/lincos.html (3320 words)

	Hans Freudenthal, "RIPENSANDO L'EDUCAZIONE MATEMATICA - Lezioni tenute in Cina"
		che commenta: «Hans Freudenthal è morto nel 1990; questo libro rappresenta il suo ultimo contributo nel campo dell’educazione matematica.
		In quarta di copertina si legge: In quest’opera Freudenthal sottopone ad analisi e a revisione le idee da lui stesso espresse e sviluppate in passato; e fa questo, come egli stesso dice, non per costruire una compilazione, ma per ricercare l’essenziale nelle proprie opere precedenti, ed eliminare le eventuali contraddizioni.
		La reinvenzione, intesa da Freudenthal come appropriazione attiva di idee, strutture e procedure, comporta la messa in atto di due categorie integrative del pensiero matematico: intuizione e rigore..
	www.maecla.it /bibliotecaMatematica/af_file/FREUDENTHAL%20.htm (334 words)

	LINCOS - Freudenthal
		Hans Freudenthal made a start at one in his book, Lincos, published in 1960.
		I think it's time for version II, the all-new action-packed sequel guaranteed to have you on the edge of your seat, which is a specific structure with a flat surface perpendicular to the pull of gravity, which is a thing that, oh never mind.
		Freudenthal, Hans 1974 Cosmic Language, in T. Sebeok (ed), Current Trends in Linguirstics, vol 12, Mouton, The Hague, pp.
	people.csail.mit.edu /paulfitz/cosmic.html (583 words)

	Matemática Hoje - Educadores
		Hans Freudenthal nasceu em 1905 na cidade alemã de Luckenwalde, filho de um professor judeu.
		Em 1946 Freudenthal se tornou professor em Utrecht, designado para ocupar uma cadeira para lecionar matemáticas puras e aplicadas e os fundamentos da matemática.
		Hans Freudenthal, o reformador de educação, morreu no dia 13 de outubro 1990.
	www.matematicahoje.com.br /telas/cultura/historia/educadores.asp?aux=K (636 words)

	Mathematics In Context (Site not responding. Last check: 2007-11-05)
		Hans Freudenthal advocated mathematics as a human activity, not a subject matter to be transmitted.
		In keeping with Freudenthal's theory that 'mathematics must be connected to reality, stay close to children and be relevant to society in order to be of human value', RME uses contextual problems to constitute mathematical concepts.
		Freudenthal (1991) refers to processes of vertical and horizontal mathematization where horizontal is developing tools to solve a problem presented in a real life context and vertical is making connections between concepts and strategies, moving within a more formal world of symbols.
	s13a.math.aca.mmu.ac.uk /Student_Writings/Masters/Carol/CarolMarshall.html (5591 words)

	general information (Site not responding. Last check: 2007-11-05)
		The institute is part of Utrecht University in the Netherlands and it was founded in 1971 by the German/Dutch writer, pedagogue and mathematician, Professor Hans Freudenthal (1905-1990).
		Since 2003 an international institute for mathematics education, Freudenthal Institute - USA (Fi-US) was established in collaboration with the Wisconsin University in Madison, USA.
		The principles that underlie this approach are strongly influenced by Hans Freudenthal's concept of 'mathematics as a human activity'.
	www.freudenthal.nl /en/algemeen.html (329 words)

	[No title]
		The best known attempt to devise a universal language was made by the Dutch mathematician Hans Freudenthal.
		Lincos is rooted in mathematics and symbolic logic, augmented with a number of new symbols and three-letter words, often derived from Latin, like cur 'why' and enu 'counts' (from enumerat).
		Freudenthal shows how each word or symbol could be defined through a series of logical examples.
	www.geocities.com /monicavdv/informatie-hans/Lincos.html (536 words)

	Teaching and Learning with RME (Site not responding. Last check: 2007-11-05)
		Freudenthal's idea was that pupils should not be merely taught mathematics, but that they should be active participants in the learning process, and education should give them opportunities to reinvent maths by being able to work through the maths themselves.
		(Freudenthal Institute, b) Freudenthal also felt that for maths to be of 'human value' it should be real for children and relevant to society.
		In 1971, Freudenthal set up the IOWO (translated as the Institute for the Development of Mathematics Education), which is now called the Freudenthal Institute.
	s13a.math.aca.mmu.ac.uk /Student_Writings/TS1/KayWhiting.html (3348 words)

	www.matder.org.tr (Site not responding. Last check: 2007-11-05)
		Freudenthal' in RME için ana ilke olarak benimsediği matematikleştirme, matematik içinde bir seviye yükselmesidir.
		Freudenthal, "Matematiksel aktiviteyi konusu matematikten veya gerçek hayattan olan bir problem için çözüm arayışı, çözüm için düzenlemenin yapılması" olarak açıklıyor (Graveimeijer, 1994).
		Freudenthal, insan zihninin matematik bilgiyi nasıl elde ettiği ile ilgilenmiş ve bunun ilk basamağının gerçek hayattan problemlerle ilgilenmenin oluşturduğunu, genellemelerin farkedilmesi, notasyonların kullanılması, ve son olarak pratik problemlere tekrar dönülerek çözüm prosedürlerinin algoritmalarının elde edilmesi şeklinde bir sıra izlediğini açıklamıştır.
	www.matder.org.tr /bilim/gmeiso.asp?ID=10 (1240 words)

	The International Commission on Mathematical Instruction
		The Hans Freudenthal Medal, named for the eigth president of ICMI (1967-1970), recognizes a major cumulative program of research.
		The Hans Freudenthal Medal for 2003 is awarded to Celia Hoyles, Professor at the Institute of Education of the University of London, for
		The first Hans Freudenthal Award of the International Commission on Mathematical Instruction (ICMI) is awarded to Professor Celia Hoyles.
	www.didaktik.mathematik.uni-wuerzburg.de /gdm/aktuelles/icme_foerderpreis_2004.html (1435 words)

	denkzettel nr. 96 (Site not responding. Last check: 2007-11-05)
		Freudenthal beschreibt die “Selektion in intellektuellen Funktionen” durch das Schulfach Mathematik als einen trennscharfen und schmerzlichen Vorgang.
		In der Tat lässt sich vergleichsweise leicht und zuverlässig feststellen, ob jemand zu denen gehört, die den mathematischen Stoff nicht wirklich verstehen und den Leistungsanforderungen nicht gewachsen sind.
		Nach einer Weile fällt dann doch der Satz: “Prüfen ist eine sinnvolle Tätigkeit.” Allerdings führt Freudenthal nicht jene eben erwähnten Ärzte, Ingenieure und Piloten an, sondern macht geltend, der Unterrichtende könne “den Erfolg des Lehrprozesses nachprüfen”; außerdem hätten der Unterrichtete und die “Außenwelt” ein Recht darauf zu wissen, ob etwas gelernt worden sei.
	www.uni-flensburg.de /mathe/dzettel/0096/dz_0096.html (1097 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		the Hans Freudenthal Award, for a major program of research on mathematics education during the past 10 years,
		At each ICME, the medals and certificates of the awards given after the previous ICME will be presented at the Opening Ceremony.
		The first recipients of the Freudenthal and Klein awards, will be known by the end of the year 2003.
	olimpia.uanarino.edu.co /otros/ICMI.htm (432 words)

	Hans Freudenthal
		Hans H Schulte David Richards - Crisis and Culture in Post-Enlightenment Germany: Essays in Honour of Peter Heller - 0819186392
		This artikel Hans_Freudenthal is licensed under the GNU free Documentation License.
		This artikel Lincos is licensed under the GNU free Documentation License.
	www.bookreportforfree.com /360254_hans-freudenthal_1114520756languageoflogicwherecaniselloldbooks.html (522 words)

	[No title]
		Reinvention: roots and relation with history The notion of ‘re-invention’ was coined by Hans Freudenthal, in Chapter 6 of his Mathematics as an educational task (Freudenthal 1973).
		Freudenthal expressed himself quite critically about the place of the history of mathematics in mathematics education.
		Further research Michiel Doorman (Utrecht, Freudenthal Institute) is currently investigating “a reinvention course” about modeling movement, in which the first elements of the calculus are presented in a historical perspective (see his paper in these Proceedings).
	www.math.ntnu.edu.tw /~cyc/_private/mathedu/me1/me1_2001/jm.doc (4135 words)

	Holt, Rinehart and Winston
		MiC was collaboratively developed by the Wisconsin Center for Educational Research at the University of Wisconsin-Madison and the Freudenthal Institute of the University of Utrecht in The Netherlands.
		The Freudenthal Institute is part of Utrecht University in the Netherlands and was founded in 1971 by German/Dutch writer, pedagogue and mathematician, Professor Hans Freudenthal (1905-1990).
		Since 1971, the Freudenthal Institute has developed a theoretical approach toward the learning and teaching of mathematics known as "Realistic Mathematics Education" which incorporates views on what mathematics is, how students learn mathematics, and how mathematics should be taught.
	www.hrw.com /about/press/holtebmic.htm (795 words)

	Stadt Luckenwalde - Chronik
		Anbringung einer Tafel zur Erinnerung an den Ehrenbürger der Stadt Luckenwalde Hans Freudenthal anlässlich seines 100.
		Diese Lebenswege sind bis in die Gegenwart Vorbild und können jeden einzelnen darin bestärken, Tugenden wie Mitmenschlichkeit, Gerechtigkeit und Toleranz Wert zu schätzen, sie zu leben und den Mut aufzubringen, das, was richtig ist zu erkennen und zu tun.
		Doch bereits 1938 trafen sich Hans Winkler, Günter Samuel und Erich Schwarz, um jüdische Menschen vor der Deportation zu retten.
	www.luckenwalde.de /stadt/chronik.htm (1752 words)

	think again!
		The article asserts that 'the Netherlands has been able to transform itself into a nationwide laboratory for change in mathematics education' thanks to the Freudenthal Institute 'which conducts research into aspects of math education and how mathematics is taught.
		The institute's founder, Hans Freudenthal (picture above), 'acquired international fame and significance as the founder of realistic mathematics education, which is based on problems taken from day-to-day experiences rather than on abstract math rules.
		The article is a must read if you are interested in 'best practices' for how mathematics may be learnt and taught.
	simpler-solutions.net /pmachinefree/thinkagain/thinkagain.php?id=P936 (603 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		My purpose here is not to discuss what the appropriate balance may be, but to explore what happens when learning to ‘do mathematics’ is an essential motive in a mathematics teacher education programme, and how this learning may be facilitated.
		Theoretical Framework Hans Freudenthal asserted that mathematics education should first and foremost be about mathematics as a human activity, not as a study of existing mathematical structures.
		Freudenthal, H.: 1991, Revisiting Mathematics Education: China Lectures, Kluwer Academic Publishers, Dordrecht, the Netherlands.
	www.icme-organisers.dk /tsg23/tsg23_abstracts/rTSG23018Christiansen (3425 words)

	Footnotes (Site not responding. Last check: 2007-11-05)
		2005 note: The puzzle has been recently traced to the Dutch mathematician Hans Freudenthal.
		Freudenthal didn't publish it and didn't give a reference.
		The consensus opinion is that Freudenthal invented it.
	www-formal.stanford.edu /jmc/puzzles/footnode.html (65 words)

	ICMI Awards for 2003: THE ICMI HANS FREUDENTHAL MEDAL
		Citation for the 2003 ICMI Freudenthal Medal to Celia Hoyles
		The first Hans Freudenthal Medal of the International Commission on Mathematical Instruction (ICMI) is awarded to Professor Celia Hoyles.
		It is thanks to people like Celia Hoyles, with a clear sense of mission and the ability to build bridges between research and practice while contributing to both, that the community of mathematics education has acquired, over the years, a better-defined identity.
	www.mathunion.org /Organization/ICMI/Awards/2003/HoylesCitation.html (625 words)

	Space.com articles - Date - SETI Institute (Site not responding. Last check: 2007-11-05)
		Consider, for example, a proposal from the Dutch mathematician Hans Freudenthal.
		In Freudenthals scheme, pictures came very late in the message, and in fact, werent essential at all.
		Rather than rely on pictures, Freudenthal constructed a complex mathematical language that might be transmitted via radio signals.
	www.seti.org /site/apps/nl/content2.asp?c=ktJ2J9MMIsE&b=194993&ct=221022 (609 words)

	DeVito & Oehrle (Site not responding. Last check: 2007-11-05)
		The problem of how to communicate with the members of an alien society has been discussed by many authors but only one, Hans Freudenthal, has constructed a language for this purpose.
		Freudenthal assumes nothing other than the ability to reason as humans do and, because he assumes so little, it is necessary to communicate a great deal about the language itself before being able to communicate any interesting information.
		Since it is likely that contact between our civilization and an alien one would be via radio, potential correspondents would have a basic knowledge of science.
	www.matessa.org /~mike/devito.html (302 words)

	Gamelanmuziek voor aliens - ACHTERGROND - Mare 10, 11 november 2004
		Hij is niet de eerste die hiertoe een poging doet.
		In 1960 publiceerde de wiskundige Hans Freudenthal over hetzelfde onderwerp een studie genaamd LINCOS.
		Freudenthal wilde buitenaardse wezens zijn op wiskunde gebaseerde taal leren door eerst een basis door te zenden (cijfers, tekens als + en =) en daar vervolgens op voort te bouwen, tot de aliens steeds ingewikkeldere noties zouden begrijpen.
	www.leidenuniv.nl /mare/2004/10/11.html (1052 words)

	Institute of Education (Site not responding. Last check: 2007-11-05)
		Prof Hoyles, who is also the Institute’s dean of research, has been awarded the first ever Hans Freudenthal Medal by the International Commission on Mathematical Instruction, the world’s leading body in mathematics education.
		Prof Hoyles is being recognised for her “seminal research on instructional uses of mathematics” and will receive a medal at an official presentation ceremony at the International Congress on Mathematics Education in Copenhagen in July.
		The Hans Freudenthal Medal has been introduced by the International Commission on Mathematical Instruction to recognise a major cumulative programme of research in mathematics education.
	ioewebserver.ioe.ac.uk /ioe/cms/get.asp?cid=1397&1397_1=9535 (377 words)

	icHuddersfield - Maths award for British professor (Site not responding. Last check: 2007-11-05)
		A pioneering British maths education expert has won a major international prize just weeks after an official report highlighted the crisis engulfing the subject in schools.
		Celia Hoyles, who is professor of maths education at London University's Institute of Education is the first person to win the Hans Freudenthal Medal.
		The Hans Freudenthal medal, named after a late professor at the University of Utrecht in Holland, will be awarded every two years to someone who has conducted a "major cumulative programme of research in mathematics education".
	ichuddersfield.icnetwork.co.uk /0100news/0200nationalnews/tm_objectid=14115996&method=full&siteid=50060&headline=maths-award-for-british-professor-name_page.html (305 words)

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