Weeding and Sowing: Preface to a Science of Mathematical by Hans Freudenthal

By Hans Freudenthal

A name that seems like poetry, and a subtitle that turns out to contradict the name! however the subtitle is correct, and initially it used to be simply the name. a wierd subtitle, isn’t it? Preface to a technology of Mathematical schooling. All sciences – of their prenatal degree – have recognized this type of literature: in simple terms the time period used used to be now not ‘Preface’, yet, for example, ‘Prolegomena’, which * capacity an identical notwithstanding it sounds much less provisional. in reality such works have been thicker than the current one, by means of as much as ten occasions. there's even more that may be stated a couple of technology earlier than it comes into being than after; with the 1st effects comes modesty. this can be the preface to a e-book that may by no means be written: no longer by means of me, nor by means of anyone else. as soon as a technological know-how of mathematical schooling exists, it is going to get the preface it merits. however this preface – or what for honesty’s sake i've got labelled so – needs to fulfil a functionality: the functionality of increasing the beginning of a technology of mathematical schooling, that's heavily impeded by way of the unfounded view that such already exists. by contrast view i must argue: it rests on a incorrect estimation – either over and less than estimation while – of what's to be regarded as technology.

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The dissemination of science extends beyond geographical, political, and linguistic borders. If something is untranslatable, one may suspect that it is no science. Philosophy is different. Kant’s Kritik der reinen Vernunft has been translated into several ON E D U C A T I O N 35 languages. Are the equivalents chosen for terms like ‘Vorstellung’, An­ schauung’, ‘Empfindung’ – and also the ‘Vernunft’ of the title – good equiv­ alents? I would not know how to test it, but I do not believe that it would matter much.

Gradually Unterricht is stressed and separated from Erziehung. A problem I give one of my grandchildren or a walk I take with him, is it teaching or is it bringing up? One of my grandsons, proud of his (first male) teacher, reports that “if one of the children is naughty, the whole class gets sums in arithmetic”. That teacher certainly believes in the moral value of arithmetic lessons as did generations of teachers before him. Nobody would deny the pedagogical consequences of teaching arithmetic, although a few people would express this conviction in less positive terms.

The traces of his university study were an academic title, a philosophy for Sundays, and a learned jargon. Why do I tell this thus circumstantially? The reader knows academic professions which are at present as far advanced as medicine was two centuries ago. Greek medicine was a collection of empirical rules, bordered with a background philosophy: according to the pattern of cosmic physics with its four elements earth, water, air, and fire, the humours of the human body were divided into black bile, phlegm (lymph), yellow bile, blood, and the temperaments in melancholics, phlegmatics, cholerics, sanguinics, in order to fit pathology and therapy in that physical cosmic frame.

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