Download or read book Didactical Phenomenology of Mathematical Structures written by Hans Freudenthal and published by Springer Science & Business Media. This book was released on 2005-11-28 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 LOOK BACKWARD AND A LOOK FORWARD Men die, systems last.
Download or read book Mathematics as an Educational Task written by Hans Freudenthal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Revisiting Mathematics Education written by Hans Freudenthal and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Legacy of Hans Freudenthal written by Leen Streefland and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Legacy of Freudenthal pays homage to Freudenthal and his work on mathematics, its history and education. Almost all authors were his scholars or co-workers. They testify to what they learned from him. Freudenthal himself contributes posthumously. His didactical phenomenology of the concept of force is both provocative and revealing in its originality, compared with what is usually found in physics instruction. Freudenthal is portrayed as a universal human being by Josette Adda. He made considerable contributions to mathematics itself, e.g. on homotopy theory and Lie groups in geometry. The exposition of Freudenthal's mathematical life and work is on Van Est's account. Henk Bos discusses his historical work. The essay review of the 8th edition of Hilbert's Grundlagen der Geometrie serves as a vehicle of thought. The main part of the book, however, concerns Freudenthal's work on mathematics education. Christine Keitel reviews his final book Revisiting Mathematics Education (1991). Fred Goffree describes Freudenthal's `Working on Mathematics Education' both from an historical as well as a theoretical perspective. Adrian Treffers analyses Freudenthal's influence on the development of realistic mathematics education at primary level in the Netherlands, especially his influence on the Wiskobas-project of the former IOWO. Freudenthal once predicted the disappearance of mathematics as an individual subject in education sometime around the year 2000, because it would by then have merged with integrated thematic contexts. Jan de Lange anticipates this future development and shows that Freudenthal's prediction will not come true after all. Reflective interludes unveil how he might have influenced those developments. Freudenthal contributed a wealth of ideas and conceptual tools to the development of mathematics education -- on contexts, didactical phenomenology, guided reinvention, mathematisation, the constitution of mental objects, the development of reflective thinking, levels in learning processes, the development of a mathematical attitude and so on -- but he did not design very much concrete material. Leen Streefland deals with the question of design from a theoretical point of view, while applying Freudenthal's ideas on changing perspective and shifting. For teachers, researchers, mathematics educators, mathematicians, educationalists, psychologists and policy makers.
Download or read book International Reflections on the Netherlands Didactics of Mathematics written by Marja van den Heuvel-Panhuizen and published by Springer. This book was released on 2019-08-13 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, takes readers on a journey with mathematics education researchers, developers and educators in eighteen countries, who reflect on their experiences with Realistic Mathematics Education (RME), the domain-specific instruction theory for mathematics education developed in the Netherlands since the late 1960s. Authors from outside the Netherlands discuss what aspects of RME appeal to them, their criticisms of RME and their past and current RME-based projects. It is clear that a particular approach to mathematics education cannot simply be transplanted to another country. As such, in eighteen chapters the authors describe how they have adapted RME to their individual circumstances and view on mathematics education, and tell their personal stories about how RME has influenced their thinking on mathematics education.
Download or read book Mathematicians Fleeing from Nazi Germany written by Reinhard Siegmund-Schultze and published by Princeton University Press. This book was released on 2009 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on archival sources that have never been examined before, the book discusses the preeminent emigrant mathematicians of the period, including Emmy Noether, John von Neumann, Hermann Weyl, and many others. The author explores the mechanisms of the expulsion of mathematicians from Germany, the emigrants' acculturation to their new host countries, and the fates of those mathematicians forced to stay behind. The book reveals the alienation and solidarity of the emigrants, and investigates the global development of mathematics as a consequence of their radical migration.
Download or read book The Concept and the Role of the Model in Mathematics and Natural and Social Sciences written by Hans Freudenthal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Young Mathematicians at Work written by Catherine Twomey Fosnot and published by Heinemann Educational Books. This book was released on 2001 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains how children between the ages of four and eight construct a deep understanding of numbers and the operations of addition and subtraction.
Download or read book History of Topology written by I.M. James and published by Elsevier. This book was released on 1999-08-24 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Download or read book Linear Lie Groups written by and published by Academic Press. This book was released on 2011-09-21 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Lie Groups
Download or read book All Positive Action Starts with Criticism written by Sacha la Bastide-van Gemert and published by Springer. This book was released on 2015-01-16 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study provides a historical analysis of Freudenthal’s didactic ideas and his didactic career. It is partly biographical, but also contributes to the historiography of mathematics education and addresses closely related questions such as: what is mathematics and where does it start? Which role does mathematics play in society and what influence does it have on the prevailing views concerning its accompanying didactics?. Hans Freudenthal (1905–1990), professor in mathematics, scientist, literator, but above all mathematics-educator, was inextricably linked to the changes which took place in mathematics education and didactics during the second half of the last century. His diversity as a scientist and his inexhaustible efforts to establish the didactics of mathematics as a seriously pursued science, made Freudenthal's influence in this area considerable. He foresaw an essential, practical role for mathematics in everyone’s life, encouraging students to discover and create mathematics themselves, instead of imposing a ready-made mathematical system. The theory of mathematics education thus developed in the Netherlands would gain world fame in the following decades. Today, in the light of the discussions about mathematics education, in which the call for `genuine’ mathematics instead of the so-called 'kindergarten'-mathematics can be heard, Freudenthal's approach seems to be passé. However, the outcome of this study (which is mainly based on documents from Freudenthal’s vast personal archive) shows a more refined picture. The direct identification of 'kindergarten'-mathematics with Freudenthal’s view on mathematics education is not justified. 'Realistic mathematics' as advocated by Freudenthal includes more than just a practical introductory and should, among other things, always aim at teaching 'genuine' mathematics in the end.
Download or read book Mathematicians under the Nazis written by Sanford L. Segal and published by Princeton University Press. This book was released on 2014-11-23 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contrary to popular belief--and despite the expulsion, emigration, or death of many German mathematicians--substantial mathematics was produced in Germany during 1933-1945. In this landmark social history of the mathematics community in Nazi Germany, Sanford Segal examines how the Nazi years affected the personal and academic lives of those German mathematicians who continued to work in Germany. The effects of the Nazi regime on the lives of mathematicians ranged from limitations on foreign contact to power struggles that rattled entire institutions, from changed work patterns to military draft, deportation, and death. Based on extensive archival research, Mathematicians under the Nazis shows how these mathematicians, variously motivated, reacted to the period's intense political pressures. It details the consequences of their actions on their colleagues and on the practice and organs of German mathematics, including its curricula, institutions, and journals. Throughout, Segal's focus is on the biographies of individuals, including mathematicians who resisted the injection of ideology into their profession, some who worked in concentration camps, and others (such as Ludwig Bieberbach) who used the "Aryanization" of their profession to further their own agendas. Some of the figures are no longer well known; others still tower over the field. All lived lives complicated by Nazi power. Presenting a wealth of previously unavailable information, this book is a large contribution to the history of mathematics--as well as a unique view of what it was like to live and work in Nazi Germany.
Download or read book Astrolinguistics written by Alexander Ollongren and published by Springer Science & Business Media. This book was released on 2012-11-27 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: In linguistics, one of the main areas of modern research involves the capabilities and possibilities of there being a "lingua cosmica," a LINCOS, a universal language that could be used to communicate with non-human intelligences. This book touches on the area of the development and use of a "lingua universalis" for interstellar communication, but it also presents concepts that cover a broad area of linguistics. Chomsky's paradigm on universal properties of natural languages, for a long time a leading general theory of natural languages, includes the strong assumption that humans are born with some kind of universals stored in their brains. Are there universals of this kind of language used by intelligent beings and societies elsewhere in the universe? We do not know whether such languages exist. It seems to be impossible to determine, simply because the universe is too large for an exhaustive search. Even verification will be hard to obtain, without quite a bit of luck. This book uses astrolinguistic principles in message construction and is helpful in clarifying and giving perspective to discussions on existential questions such as these.
Download or read book Mathematical Thinking written by Masami Isoda and published by World Scientific. This book was released on 2012 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties developing it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.
Download or read book All Positive Action Starts with Criticism written by Sacha La Bastide-Van Gemert and published by . This book was released on 2015-01-31 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex Cobordism and Stable Homotopy Groups of Spheres written by Douglas C. Ravenel and published by American Mathematical Soc.. This book was released on 2003-11-25 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects of the classical Adams spectral sequence and its modifications, which are the main tools topologists have to investigate the homotopy groups of spheres. Nowadays, the most efficient tools are the Brown-Peterson theory, the Adams-Novikov spectral sequence, and the chromatic spectral sequence, a device for analyzing the global structure of the stable homotopy groups of spheres and relating them to the cohomology of the Morava stabilizer groups. These topics are described in detail in Chapters 4 to 6. The revamped Chapter 7 is the computational payoff of the book, yielding a lot of information about the stable homotopy group of spheres. Appendices follow, giving self-contained accounts of the theory of formal group laws and the homological algebra associated with Hopf algebras and Hopf algebroids. The book is intended for anyone wishing to study computational stable homotopy theory. It is accessible to graduate students with a knowledge of algebraic topology and recommended to anyone wishing to venture into the frontiers of the subject.
Download or read book Japanese Lesson Study In Mathematics Its Impact Diversity And Potential For Educational Improvement written by Masami Isoda and published by World Scientific. This book was released on 2007-02-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Before It's Too Late: A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21st Century (2000) in the US, the authors quote from James Stigler's conclusions from various videotape research studies of mathematics teaching: “The key to long-term improvement [in teaching] is to figure out how to generate, accumulate, and share professional knowledge”. Japanese Lesson Study has proved to be one successful means.This book supports the growing movement of lesson study to improve the quality of mathematics education from the original viewpoints of Japanese educators who have been engaging in lesson study in mathematics for professional development and curriculum implementation. This book also illustrates several projects related to lesson study in other countries.
