{"title":"Hans Freudenthal","description":null,"products":[{"product_id":"algebraical-and-topological-foundations-of-geometry-rare-book-hans-freudenthal-1675148919bab","title":"Algebraical and Topological Foundations of Geometry","description":"1962. No Edition Remarks. 208 pages. No dust jacket. Blue cloth. Well bound and clean pages, with mild tanning to text block edges. Some rub-marking and tanning to pastedowns and endpapers with inscri","brand":"WoB","offers":[{"title":"GB \/ GOOD \/ INTERNAL","offer_id":50075986493713,"sku":"1675148919BAB","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1675148919BAB_1.jpg?v=1722889084"},{"product_id":"mathematics-observed-rare-book-hans-freudenthal-1707207825bwi","title":"Mathematics Observed","description":"1967. No Edition Stated. 256 pages. White dust jacket with black lettering over blue cloth. B\u0026amp;W frontispiece. Clean pages. Minimal tanning to endpapers and page edges. Mild wear to spine, board edges","brand":"WoB","offers":[{"title":"GB \/ GOOD \/ INTERNAL","offer_id":50087586201873,"sku":"1707207825BWI","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1707207825BWI_1.jpg?v=1722930343"},{"product_id":"mathematics-as-an-educational-task-book-hans-freudenthal-9789027702357","title":"Mathematics as an Educational Task","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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52124693823761,"sku":"NLS9789027702357","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789027702357.jpg?v=1757458371"},{"product_id":"didactical-phenomenology-of-mathematical-structures-book-hans-freudenthal-9789027722614","title":"Didactical Phenomenology of Mathematical Structures","description":"The launch ofa new book series is always a challenging eventn ot only for the Editorial Board and the Publisher, but also, and more particularly, for the first author. Both the Editorial Board and the Publisher are delightedt hat the first author in this series isw ell able to meet the challenge. Professor Freudenthal needs no introduction toanyone in the Mathematics Education field and it is particularly fitting that his book should be the first in this new series because it was in 1968 that he, and Reidel, produced the first issue oft he journal Edu cational Studies in Mathematics. Breakingfresh ground is therefore nothing new to Professor Freudenthal and this book illustrates well his pleasure at such a task. To be strictly correct the 'ground' which he has broken here is not new, but aswith Mathematics as an Educational Task and Weeding and Sowing, it is rather the novelty oft he manner in which he has carried out his analysis which provides us with so many fresh perspectives. It is our intention that this new book series should provide those who work int he emerging discipline of mathematicseducation with an essential resource, and at a time of considerable concern about the whole mathematics cu rriculum this book represents just such resource. ALAN J. BISHOP Managing Editor vii A LOK BACKWARD AND A LOK FORWARD Men die, systems last.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52139280367889,"sku":"NLS9789027722614","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789027722614.jpg?v=1757568197"},{"product_id":"mathematics-as-an-educational-task-book-hans-freudenthal-9789027703224","title":"Mathematics as an Educational Task","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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52141842563345,"sku":"NLS9789027703224","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789027703224.jpg?v=1757578355"},{"product_id":"weeding-and-sowing-book-hans-freudenthal-9789027707895","title":"Weeding and Sowing","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52141871792401,"sku":"NLS9789027707895","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789027707895.jpg?v=1757578506"},{"product_id":"weeding-and-sowing-book-hans-freudenthal-9789027710727","title":"Weeding and Sowing","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52146973475089,"sku":"NLS9789027710727","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789027710727.jpg?v=1757598968"},{"product_id":"didactical-phenomenology-of-mathematical-structures-book-hans-freudenthal-9789027715357","title":"Didactical Phenomenology of Mathematical Structures","description":"The launch ofa new book series is always a challenging eventn ot only for the Editorial Board and the Publisher, but also, and more particularly, for the first author. Both the Editorial Board and the Publisher are delightedt hat the first author in this series isw ell able to meet the challenge. Professor Freudenthal needs no introduction toanyone in the Mathematics Education field and it is particularly fitting that his book should be the first in this new series because it was in 1968 that he, and Reidel, produced the first issue oft he journal Edu cational Studies in Mathematics. Breakingfresh ground is therefore nothing new to Professor Freudenthal and this book illustrates well his pleasure at such a task. To be strictly correct the 'ground' which he has broken here is not new, but aswith Mathematics as an Educational Task and Weeding and Sowing, it is rather the novelty oft he manner in which he has carried out his analysis which provides us with so many fresh perspectives. It is our intention that this new book series should provide those who work int he emerging discipline of mathematicseducation with an essential resource, and at a time of considerable concern about the whole mathematics cu rriculum this book represents just such resource. ALAN J. BISHOP Managing Editor vii A LOK BACKWARD AND A LOK FORWARD Men die, systems last.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52336022520081,"sku":"NLS9789027715357","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52763102773521,"sku":"NIN9789027715357","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789027715357.jpg?v=1758161997"},{"product_id":"revisiting-mathematics-education-book-hans-freudenthal-9780792312994","title":"Revisiting Mathematics Education","description":"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.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52336811213073,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52336811901201,"sku":"NLS9780792312994","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780792312994.jpg?v=1758164589"},{"product_id":"concept-and-the-role-of-the-model-in-mathematics-and-natural-and-social-sciences-book-hans-freudenthal-9789027700179","title":"The Concept and the Role of the Model in Mathematics and Natural and Social Sciences","description":"Proceedings of the Colloquium sponsored by the Division of  Philosophy of Sciences of the International Union of History and  Philosophy of Sciences organized at Utrecht, January 1960.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52340600176913,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52340600799505,"sku":"NLS9789027700179","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789027700179.jpg?v=1758170901"},{"product_id":"revisiting-mathematics-education-book-hans-freudenthal-9789048140930","title":"Revisiting Mathematics Education","description":"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.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52481631027473,"sku":"NLS9789048140930","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789048140930.jpg?v=1759852008"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-hans-freudenthal.oembed","provider":"World of Books ","version":"1.0","type":"link"}