Freudenthal, Hans 19051990
Overview
Works:  268 works in 935 publications in 8 languages and 10,979 library holdings 

Genres:  Popular works Conference papers and proceedings Biography Abstracts 
Roles:  Author, Editor, Correspondent, Recipient, Other, Performer, Former owner, Translator, Conductor, Contributor 
Classifications:  QA11, 510.7 
Publication Timeline
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Most widely held works about
Hans Freudenthal
 All positive action starts with criticism : Hans Freudenthal and the didactics of mathematics by Sacha la Bastidevan Gemert( Book )
 Schrijf dat op, Hans : knipsels uit een leven by Hans Freudenthal( Book )
 Zeven grondleggers van de onderwijskunde B. Brugsma, Ph.J. Idenburg, . Freudenthal, F.W. Prins, J.W. van Hulst, L. van Gelder en C.F. van Parreren( Book )
 HF : working on mathematics education by Fred Goffree( Book )
 "Elke positieve actie begint met critiek" : Hans Freudenthal en de didactiek van de wiskunde by Sacha la Bastidevan Gemert( Book )
Most widely held works by
Hans Freudenthal
The language of logic by
Hans Freudenthal(
Book
)
54 editions published between 1961 and 1975 in 6 languages and held by 888 WorldCat member libraries worldwide
54 editions published between 1961 and 1975 in 6 languages and held by 888 WorldCat member libraries worldwide
Probability and statistics by
Hans Freudenthal(
Book
)
57 editions published between 1957 and 1981 in 6 languages and held by 749 WorldCat member libraries worldwide
57 editions published between 1957 and 1981 in 6 languages and held by 749 WorldCat member libraries worldwide
Linear lie groups by
Hans Freudenthal(
Book
)
24 editions published between 1969 and 1979 in 3 languages and held by 579 WorldCat member libraries worldwide
24 editions published between 1969 and 1979 in 3 languages and held by 579 WorldCat member libraries worldwide
Mathematics observed by
Hans Freudenthal(
Book
)
14 editions published between 1967 and 1970 in 3 languages and held by 539 WorldCat member libraries worldwide
14 editions published between 1967 and 1970 in 3 languages and held by 539 WorldCat member libraries worldwide
Mathematics as an educational task by
Hans Freudenthal(
Book
)
19 editions published between 1972 and 1973 in English and Undetermined and held by 502 WorldCat member libraries worldwide
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 thoughtexperiment. 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 thoughtexperi ment tries to find out how a student could reinvent 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
19 editions published between 1972 and 1973 in English and Undetermined and held by 502 WorldCat member libraries worldwide
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 thoughtexperiment. 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 thoughtexperi ment tries to find out how a student could reinvent 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
Weeding and sowing : preface to a science of mathematical education by
Hans Freudenthal(
Book
)
30 editions published between 1978 and 2004 in English and held by 406 WorldCat member libraries worldwide
30 editions published between 1978 and 2004 in English and held by 406 WorldCat member libraries worldwide
Didactical phenomenology of mathematical structures by
Hans Freudenthal(
Book
)
33 editions published between 1983 and 2005 in English and Undetermined and held by 393 WorldCat member libraries worldwide
33 editions published between 1983 and 2005 in English and Undetermined and held by 393 WorldCat member libraries worldwide
Lincos; design of a language for cosmic intercourse by
Hans Freudenthal(
Book
)
25 editions published in 1960 in English and Dutch and held by 326 WorldCat member libraries worldwide
25 editions published in 1960 in English and Dutch and held by 326 WorldCat member libraries worldwide
Algebraical and topological foundations of geometry; proceedings by Colloquium on Algebraic and Topological Foundations of Geometry(
Book
)
7 editions published between 1959 and 1962 in English and Undetermined and held by 321 WorldCat member libraries worldwide
7 editions published between 1959 and 1962 in English and Undetermined and held by 321 WorldCat member libraries worldwide
Revisiting mathematics education : China lectures by
Hans Freudenthal(
Book
)
30 editions published between 1991 and 2010 in English and Undetermined and held by 263 WorldCat member libraries worldwide
This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in mathematics education. The book is divided into three chapters. Chapter 1, "Mathematics Phenomenologically", explores different aspects of mathematics: What is Mathematics?; "Didactical Principles", discusses the organization of the teaching/learning processes relevant to mathematics, and is divided into four subsections: (1) Guided Reinvention; (2) Bonds with Reality; (3) Learning Processes; and (4) Longterm Learning Processes. Finally, chapter 3, "The Landscape of Mathematics Education", explores the theoretical foundations of mathematics education, and relates it to the current research and practice in the fields in three subsections: (1) Theory of Mathematics Education; (2) Research in Mathematics Education; and (3) Practice of Mathematics Education. Included is a list of the author's publications on mathematics education containing 201 entries. (Mdh)
30 editions published between 1991 and 2010 in English and Undetermined and held by 263 WorldCat member libraries worldwide
This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in mathematics education. The book is divided into three chapters. Chapter 1, "Mathematics Phenomenologically", explores different aspects of mathematics: What is Mathematics?; "Didactical Principles", discusses the organization of the teaching/learning processes relevant to mathematics, and is divided into four subsections: (1) Guided Reinvention; (2) Bonds with Reality; (3) Learning Processes; and (4) Longterm Learning Processes. Finally, chapter 3, "The Landscape of Mathematics Education", explores the theoretical foundations of mathematics education, and relates it to the current research and practice in the fields in three subsections: (1) Theory of Mathematics Education; (2) Research in Mathematics Education; and (3) Practice of Mathematics Education. Included is a list of the author's publications on mathematics education containing 201 entries. (Mdh)
Logique mathematique appliquee by
Hans Freudenthal(
Book
)
17 editions published in 1958 in 3 languages and held by 237 WorldCat member libraries worldwide
17 editions published in 1958 in 3 languages and held by 237 WorldCat member libraries worldwide
The Legacy of Hans Freudenthal by
Leen Streefland(
Book
)
6 editions published in 1993 in English and held by 130 WorldCat member libraries worldwide
The Legacy of Freudenthal pays homage to Freudenthal and his work on mathematics, its history and education. Almost all authors were his scholars or coworkers. 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 Wiskobasproject 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
6 editions published in 1993 in English and held by 130 WorldCat member libraries worldwide
The Legacy of Freudenthal pays homage to Freudenthal and his work on mathematics, its history and education. Almost all authors were his scholars or coworkers. 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 Wiskobasproject 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
Raumtheorie by
Hans Freudenthal(
Book
)
9 editions published in 1978 in German and held by 117 WorldCat member libraries worldwide
9 editions published in 1978 in German and held by 117 WorldCat member libraries worldwide
Lie groups by
Hans Freudenthal(
Book
)
13 editions published between 1960 and 1961 in English and Undetermined and held by 82 WorldCat member libraries worldwide
13 editions published between 1960 and 1961 in English and Undetermined and held by 82 WorldCat member libraries worldwide
Mathematik als pädagogische Aufgabe by
Hans Freudenthal(
Book
)
7 editions published between 1973 and 1979 in German and held by 79 WorldCat member libraries worldwide
7 editions published between 1973 and 1979 in German and held by 79 WorldCat member libraries worldwide
Collected works by
L. E. J Brouwer(
Book
)
24 editions published between 1975 and 1976 in 4 languages and held by 75 WorldCat member libraries worldwide
24 editions published between 1975 and 1976 in 4 languages and held by 75 WorldCat member libraries worldwide
Selecta by
Hans Freudenthal(
Book
)
11 editions published in 2009 in English and German and held by 71 WorldCat member libraries worldwide
Hans Freudenthal (19051990) was a Dutch mathematician, born in Luckenwalde, Germany. His scientific activities were of a rich variety. Enrolling at the University of Berlin as a student in the 1920s, he followed in the footsteps of his teachers, and became a topologist, but with a lively interest in group theory. Later in life, after a long journey through the realm of mathematics, working on almost all subjects that drew his interest, he turned towards the practical and methodological issues of the didactics of mathematics. The present Selecta are devoted to Freudenthal's mathematical oeuvre, they contain a selection of his major contributions. Included are fundamental contributions to topology such as the foundation of the theory of ends (in the thesis of 1931), the introduction (in 1937) of the suspension and its use in stability results for homotopy groups of spheres. In group theory there is work on topological groups (of the 1930s) and on various aspects of the theory of Lie groups, such as a paper on automorphisms of 1941. From the later work of the 1950s and 1960s, papers on geometric aspects of Lie theory (geometries associated to exceptional groups, space problems) have been included. Freudenthal's versatility is further demonstrated by a choice from his foundational and historical work: papers on intuitionistic logic and topology, a paper on axiomatic geometry reappraising Hilbert's Grundlagen, and a paper summarizing his development of Lincos, a universal ("cosmic") language. The book also contains a sketch of Freudenthal's life. Most of the selected papers are accompanied by brief comments
11 editions published in 2009 in English and German and held by 71 WorldCat member libraries worldwide
Hans Freudenthal (19051990) was a Dutch mathematician, born in Luckenwalde, Germany. His scientific activities were of a rich variety. Enrolling at the University of Berlin as a student in the 1920s, he followed in the footsteps of his teachers, and became a topologist, but with a lively interest in group theory. Later in life, after a long journey through the realm of mathematics, working on almost all subjects that drew his interest, he turned towards the practical and methodological issues of the didactics of mathematics. The present Selecta are devoted to Freudenthal's mathematical oeuvre, they contain a selection of his major contributions. Included are fundamental contributions to topology such as the foundation of the theory of ends (in the thesis of 1931), the introduction (in 1937) of the suspension and its use in stability results for homotopy groups of spheres. In group theory there is work on topological groups (of the 1930s) and on various aspects of the theory of Lie groups, such as a paper on automorphisms of 1941. From the later work of the 1950s and 1960s, papers on geometric aspects of Lie theory (geometries associated to exceptional groups, space problems) have been included. Freudenthal's versatility is further demonstrated by a choice from his foundational and historical work: papers on intuitionistic logic and topology, a paper on axiomatic geometry reappraising Hilbert's Grundlagen, and a paper summarizing his development of Lincos, a universal ("cosmic") language. The book also contains a sketch of Freudenthal's life. Most of the selected papers are accompanied by brief comments
Algebraical and topological foundations of geometry : proceedings of a colloquium held in Utrecht, August 1959 by
Hans Freudenthal(
Book
)
24 editions published between 1959 and 1962 in English and German and held by 63 WorldCat member libraries worldwide
Algebraical and Topological Foundations of Geometry
24 editions published between 1959 and 1962 in English and German and held by 63 WorldCat member libraries worldwide
Algebraical and Topological Foundations of Geometry
Schrijf dat op, Hans : knipsels uit een leven by
Hans Freudenthal(
Book
)
3 editions published in 1987 in Dutch and Undetermined and held by 16 WorldCat member libraries worldwide
Opstellen die een beeld geven van het leven van de hoogleraar wiskunde, columnist en journalist (1905)
3 editions published in 1987 in Dutch and Undetermined and held by 16 WorldCat member libraries worldwide
Opstellen die een beeld geven van het leven van de hoogleraar wiskunde, columnist en journalist (1905)
Ripensando l'educazione matematica : lezioni tenute in Cina by
Hans Freudenthal(
Book
)
3 editions published between 1994 and 2002 in Italian and English and held by 8 WorldCat member libraries worldwide
3 editions published between 1994 and 2002 in Italian and English and held by 8 WorldCat member libraries worldwide
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Related Identities
 Vries, H. de (Hendrik) 1932
 International Union of the History and Philosophy of Science Division of Philosophy of Sciences
 International Mathematical Union
 Bastidevan Gemert, Sacha la Author
 Third, William Translator
 Vincken, Marianne Translator
 Brouwer, L. E. J. (Luitzen Egbertus Jan) 18811966 Author
 Streefland, Leen 1939 Other Author
 Springer, T. A. (Tonny Albert) 1926 Editor
 Dalen, D. van (Dirk) 1932 Editor
Useful Links
Associated Subjects
Algebraic topology College teachers Continuous groups Education Educators Freudenthal, Hans, Geometry Geometry, Algebraic Geometry, Differential Geometry, NonEuclidean GeometryFoundations Group actions (Mathematics) Group theory Homotopy theory Humanities Information theory Languages, Artificial Lie algebras Lie groups Lincos (Artificial language) Logic, Symbolic and mathematical Mathematicians Mathematics MathematicsPhilosophy MathematicsStudy and teaching MathematicsStudy and teachingPhilosophy Netherlands NetherlandsUtrecht Parreren, Carel Frederik van Probabilities Science Semisimple Lie groups Statistics Topological groups Topology
Alternative Names
Freidental, Kh.
Freĭdentalʹ, Kh 19051990
Freĭdentalʹ, Kh. (Khans), 19051990
Freidental, Khans.
Freĭdentalʹ, Khans 19051990
Frejdentalʹ, Ch
Frejdentalʹ, Ch 19051990
Frejdental', Gans.
Frejdental', Gans 19051990
Frejdental', H.
Freudenthal, H.
Freudenthal, H. 19051990
Freudenthal, Hans
Frojdental', G.
Frojdental', G. 19051990
Frojdental', Gans.
Frojdental', Gans 19051990
Hans Freudenthal deutscher Mathematiker
Hans Freudenthal Dutch mathematician
Hans Freudenthal matemàtic neerlandès
Hans Freudenthal matemático neerlandés
Hans Freudenthal matematico tedesco
Hans Freudenthal mathématicien allemand
Sirlof, V. 19051990
Sirolf, V. 19051990
Фрейденталь, Ганс 19051990
Фрейденталь, Х.
Фрейденталь, Ханс
Фройденталь, Ханс
Ханс Фройдэнталь
הנס פרוידנטל
הנס פרוידנטל מתמטיקאי הולנדי
프로이덴탈, 한스 19051990
한스 프로이덴탈
ハンス・フロイデンタール
フロイデンタール, H
漢斯·弗洛伊登薩
漢斯·弗賴登塔爾得
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