Mathematics as an Educational Task 1973rd Edition by Hans Freudenthal (PDF)

Description

Like preludes, prefaces are usually composed last. Putting them in the front of the book is a feeble reflection of what, in the style of mathe­ matics treatises and textbooks, I usually call thf didactical inversion: to be fit to print, the way to the result should be the inverse of the order in which it was found; in particular the key definitions, which were the finishing touch to the structure, are put at the front. For many years I have contrasted the didactical inversion with the thought-experiment. It is true that you should not communicate your mathematics to other people in the way it occurred to you, but rather as it could have occurred to you if you had known then what you know now, and as it would occur to the student if his learning process is being guided. This in fact is the gist of the lesson Socrates taught Meno’s slave. The thought-experi­ ment tries to find out how a student could re-invent what he is expected to learn. I said about the preface that it is a feeble reflection of the didactical inversion. Indeed, it is not a constituent part of the book. It can even be torn out. Yet it is useful. Firstly, to the reviewer who then need not read the whole work, and secondly to the author himself, who like the composer gets an opportunity to review the Leitmotivs of the book.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐When New math of SMSG swept all western country, Holland is the only one which saved itself frome all the attack and the defensive coordinator was H. Freudenthal.He tells the math-in-the making from ready-made math and explains all the educational problem of math by the property of math. This is really gem. When all american mathematician and math-educator are indulging in ‘how to let students do something’ and grading the papers, this giants reavels the ignorance and hypocricy of math education nowadays and shows the future direction. Here are some quotation :”Mathematicians who design mathematical programmes for schools they do not know and who never dreamt of anything else to be taught at schools than mathematics are of course just as narrow-minded as the computing fanatics””A teaching success with an isolated subject may be claimed but it is a cheap success, because any isolated matter can be taught successfully if it is done forcefully, in particular if the subject matter is neither unusually extensive nor profound.””Besides the future mathematician a great many others must learn mathematics. A mathematician should never forget that mathematics is too important to frame its instruction to suit more or less the needs of future mathematicians.””The greatest virtue of mathematics is its flexibility. A mathematics tailored to some applications is beside the mark, it fossilizes. While I do not urge that the pupil learns applied mathematics, I do wish that he learns how to apply mathematics. Therefore instead of applied mathematics, I would prefer to speak of ‘multi-related’ mathematics.”ps. Freudental wrote in Dutch first and translated in English himself. That’s why this book is not easy to read in English users. But if you are using English as second language (like me), that cannot be a problem but the 1st chanpter is little bit harder than the rest. You would find yourself more comfortable in 4 or 5 chapters later. I agree this volume is too expensive. Actually, I bought the used one. Fredenthal book is not common in american site. You’d better search UK or other European sites to get one.

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