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Synopsis : All Positive Action Starts with Criticism written by Sacha la Bastide-van Gemert, published by Springer which was released on 2015-01-16. Download All Positive Action Starts with Criticism Books now! Available in PDF, EPUB, Mobi Format. “...all positive action starts with criticism” Freudenthal wrote in his 'Rekendidaktiek' in 1944 . His whole life he would stick to this principle. He was critical both to himself: Mijn hele leven ben ik een slecht leermeester ... -- 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.
Type: BOOK - Published: 2015-01-16 - Publisher: Springer
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.
Type: BOOK - Published: 2020-01-06 - Publisher: Springer Nature
This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, consists of 17 chapters, in which educators from the Netherlands reflect on the teaching and learning of mathematics in their country and the role of the Dutch domain-specific instruction theory of Realistic Mathematics Education. Written by mathematics teachers, mathematics teacher educators, school advisors, and developers and researchers in the field of instructional material, textbooks, and examinations, the book offers a multitude of perspectives on important issues in Dutch mathematics education, both at primary and secondary school levels. Topics addressed include the theoretical underpinnings of the Dutch approach, the subject of mathematics in the Dutch educational system, teacher education and testing, the history of mathematics education and the use of history in teaching of mathematics, changes over time in subject matter domains and in the use of technology, and the process of innovation and how the Dutch and in particular one Dutch institute have worked on the reform.
Authors: Kristín Bjarnadóttir, Fulvia Furinghetti, Marta Menghini, Johan Prytz, Gert Schubring
Type: BOOK - Published: 2017-07-31 - Publisher: Edizioni Nuova Cultura
The Fourth International Conference on the History of Mathematics Education was hosted by Academy of Sciences and University of Turin (Italy). About 50 senior and junior researchers from 16 countries met for four days to talk about one topic: the history of mathematics education. In total 44 contributions were presented. The themes were Ideas, people and movements, Transmission of ideas, Teacher education, Geometry and textbooks, Textbooks – changes and origins, Curriculum and reform, Teaching in special institutions, and Teaching of geometry. In this volume you find 28 of the papers, all of them peer-reviewed. Since the first international conference on the history of mathematics education, the aim has been to develop this area of research, to attract more researchers and provide new insights that stimulate further “digging”. It is therefore very pleasing that so many new young researchers joined the conference, presenting results from ongoing or recently finished PhD projects. This makes us confident about a prosperous future of this research area as we look forward to the Fifth International Conference on the History of Mathematics Education, to be held in Utrecht, the Netherlands, in September 2017. Previous international conferences on the history of mathematics education: 2009 in Garðabær (Iceland) 2011 in Lisbon (Portugal) 2013 in Uppsala (Sweden)
Type: BOOK - Published: 2013-03-09 - Publisher: Springer Science & Business Media
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.
Type: BOOK - Published: 2022-04-22 - Publisher: IGI Global
Reform-based mathematics has become a popular topic in the education field as this teaching emphasizes classroom discourse and instructional goals related to student engagement and an understanding of mathematical reasoning, concepts, and procedures using instructional practices that build on students’ informal knowledge of mathematics. It also connects mathematics with other disciplines and the real world and provides opportunities for students to contribute and invent their own methods during problem-solving. Further study on the best practices, benefits, and challenges of implementing this teaching into education is required. Global Perspectives and Practices for Reform-Based Mathematics Teaching explores international perspectives on diverse reform-based practices in teaching and learning mathematics, describes challenges and issues for teachers and teacher educators, promotes reflection and academic discussion at various levels and in various educational systems, and raises questions for the field of mathematics education. Covering a range of topics such as teacher preparation programs and integrated learning spaces, this reference work is ideal for academicians, practitioners, researchers, instructors, educators, and students.
Type: BOOK - Published: 2019-08-13 - Publisher: Springer
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.
Type: BOOK - Published: 2019-12-10 - Publisher: Springer Nature
For anyone interested in the history and effects of the introduction of so-called “Modern Mathematics” (or “Mathématique Moderne,” or “New Mathematics,” etc.) this book, by Dirk De Bock and Geert Vanpaemel, is essential reading. The two authors are experienced and highly qualified Belgian scholars and the book looks carefully at events relating to school mathematics for the period from the end of World War II to 2010. Initially the book focuses on events which helped to define the modern mathematics revolution in Belgium before and during the 1960s. The book does much more than that, however, for it traces the influence of these events on national and international debates during the early phases of the reform. By providing readers with translations into English of relevant sections of key Continental documents outlining the major ideas of leading Continental scholars who contributed to the “Mathématique Moderne” movement, this book makes available to a wide readership, the theoretical, social, and political backdrops of Continental new mathematics reforms. In particular, the book focuses on the contributions made by Belgians such as Paul Libois, Willy Servais, Frédérique Lenger, and Georges Papy. The influence of modern mathematics fell away rapidly in the 1970s, however, and the authors trace the rise and fall, from that time into the 21st century, of a number of other approaches to school mathematics—in Belgium, in other Western European nations, and in North America. In summary, this is an outstanding, landmark publication displaying the fruits of deep scholarship and careful research based on extensive analyses of primary sources.
Type: BOOK - Published: 2018-12-04 - Publisher: Princeton University Press
The year’s finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2018 makes available to a wide audience many pieces not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice—and taking readers behind the scenes of today’s hottest mathematical debates. James Grime shows how to build subtly mischievous dice for playing slightly unfair games and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world—with glimpses at science, philosophy, music, art, and even crocheting. And there’s much, much more. In addition to presenting the year’s most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable pieces on mathematics. This is a must-read for anyone interested in where math has taken us—and where it is headed.
Authors: Werner Blum, Michèle Artigue, Maria Alessandra Mariotti, Rudolf Sträßer, Marja Van den Heuvel-Panhuizen
Type: BOOK - Published: 2019-02-18 - Publisher: Springer
This open access book discusses several didactic traditions in mathematics education in countries across Europe, including France, the Netherlands, Italy, Germany, the Czech and Slovakian Republics, and the Scandinavian states. It shows that while they all share common features both in the practice of learning and teaching at school and in research and development, they each have special features due to specific historical and cultural developments. The book also presents interesting historical facts about these didactic traditions, the theories and examples developed in these countries.
Authors: Jos Uffink, Giovanni Valente, Charlotte Werndl, Lena Zuchowski
Type: BOOK - Published: 2020-11-28 - Publisher: Springer Nature
This book presents a collection of essays that explore the life and works of Tatjana Afanassjewa (1876–1964), a Russian–Dutch physicist–mathematician. Readers will discover a scientist whose work on the foundations of thermodynamics significantly influenced the field itself as well as the philosophy of physics. This book highlights the philosophical consequences of her work in physics and mathematics and discusses historical aspects of her writings on the foundations of physics. In addition, it features English translations and critical reviews of key selections from her texts. First and foremost, the book highlights the numerous contributions that Afanassjewa made to the field. In particular, the authors examine her work on the foundations of thermodynamics and statistical physics, starting in the 1920s and extending to 1956, well after the untimely death of her husband in 1933. They also explore her almost entirely forgotten work on the didactics of mathematics. In addition, they discuss her influential collaboration with her husband, the Austrian physicist Paul Ehrenfest (1880–1933). The portrait that emerges is that of a highly original physicist and mathematician, whose legacy continues to influence scientists and philosophers today and whose lesser-known works deserve more attention than they have received. Readers will find a rich body of work that continues to this day to yield insights into the foundations of physics and mathematics.
Type: BOOK - Published: 2018-07-06 - Publisher: Routledge
Design Research in Education is a practical guide containing all the information required to begin a design research project. Providing an accessible background to the methodological approaches used in design research as well as addressing all the potential issues that early career researchers will encounter, the book uniquely helps the early career researcher to gain a full overview of design research and the practical skills needed to get their project off the ground. Based on extensive experience, the book also contains multiple examples of design research from both undergraduate and postgraduate students, to demonstrate possible projects to the reader. With easy to follow chapters and accessible question and response sections, Design Research in Education contains practical advice on a wide range of topics related to design research projects including: The theory of design research, what it entails, and when it is suitable The formulation of research questions How to structure a research project The quality of research and the methodological issues of validity and reliability How to write up your research The supervision of design research. Through its theoretical grounding and practical advice, Design Research in Education is the ideal introduction into the field of design based research and is essential reading for bachelor's, master's and PhD students new to the field, as well as to supervisors overseeing projects that use design research.
Authors: Évelyne Barbin, Marta Menghini, Klaus Volkert
Type: BOOK - Published: 2019-07-01 - Publisher: Springer
This book seeks to explore the history of descriptive geometry in relation to its circulation in the 19th century, which had been favoured by the transfers of the model of the École Polytechnique to other countries. The book also covers the diffusion of its teaching from higher instruction to technical and secondary teaching. In relation to that, there is analysis of the role of the institution – similar but definitely not identical in the different countries – in the field under consideration. The book contains chapters focused on different countries, areas, and institutions, written by specialists of the history of the field. Insights on descriptive geometry are provided in the context of the mathematical aspect, the aspect of teaching in particular to non-mathematicians, and the institutions themselves.