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Didactics of mathematics --- Mathematics --- Mathématiques --- Study and teaching --- Etude et enseignement --- -#WWIS:AGGR --- 51 --- 371.3 --- Math --- Science --- Study and teaching. --- 51 Mathematics --- Mathématiques --- #WWIS:AGGR --- Étude et enseignement --- Mathematics - Study and teaching

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Geometry, Differential --- Lie groups --- Topology --- Géométrie différentielle --- Groupes de Lie --- Topologie --- Geometry, Differential. --- Topology. --- Lie groups. --- Géométrie différentielle

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A title that sounds like poetry, and a subtitle that seems to contradict the title! But the subtitle is right, and originally it was just the title. A strange subtitle, isn’t it? Preface to a Science of Mathematical Education. All sciences – in their prenatal stage – have known this kind of literature: only the term used was not ‘Preface’, but, for instance, ‘Prolegomena’, which * means the same though it sounds less provisional. In fact such works were thicker than the present one, by up to ten times. There is much more that can be said about a science before it comes into being than after; with the first results comes modesty. This is the preface to a book that will never be written: not by me, nor by anybody else. Once a science of mathematical education exists, it will get the preface it deserves. Nevertheless this preface – or what for honesty’s sake I have labelled so – must fulfil a function: the function of accelerating the birth of a science of mathematical education, which is seriously impeded by the unfounded view that such already exists. Against this view I have to argue: it rests on a wrong estimation – both over and under estimation at the same time – of what is to be considered as science.

Education. --- Mathematics. --- Mathematics Teaching & Research --- Mathematics --- Physical Sciences & Mathematics --- Study and teaching. --- Philosophy. --- Mathematics Education. --- 372.851 --- 372.851 Wiskundeonderwijs --(niet-universitair onderwijs) --- Wiskundeonderwijs --(niet-universitair onderwijs) --- Study and teaching --- Education --- -Science --- Natural science --- Science of science --- Sciences --- Children --- Education, Primitive --- Education of children --- Human resource development --- Instruction --- Pedagogy --- Schooling --- Students --- Youth --- Civilization --- Learning and scholarship --- Mental discipline --- Schools --- Teaching --- Training --- Math --- Science --- Didactics of mathematics --- Science. --- Natural sciences --- Mathematics—Study and teaching . --- Mathematics - Study and teaching

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This book is a product of love and respect. If that sounds rather odd I initially apologise, but let me explain why I use those words. The original manuscript was of course Freudenthal’s, but his colleagues have carried the project through to its conclusion with love for the man, and his ideas, and with a respect developed over years of communal effort. Their invitation to me to write this Preface e- bles me to pay my respects to the great man, although I am probably incurring his wrath for writing a Preface for his book without his permission! I just hope he understands the feelings of all colleagues engaged in this particular project. Hans Freudenthal died on October 13th, 1990 when this book project was well in hand. In fact he wrote to me in April 1988, saying “I am thinking about a new book. I have got the sub-title (China Lectures) though I still lack a title”. I was astonished. He had retired in 1975, but of course he kept working. Then in 1985 we had been helping him celebrate his 80th birthday, and although I said in an Editorial Statement in Educational Studies in Mathematics (ESM) at the time “we look forward to him enjoying many more years of non-retirement” I did not expect to see another lengthy manuscript.

Didactics of mathematics --- Education. --- Mathematics --- Mathematics Education. --- Study and teaching. --- Study and teaching --- Mathematics. --- Mathematics—Study and teaching . --- Mathematics - Study and teaching

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Mathematics