Freudenthal, Hans 19051990
Overview
Works:  230 works in 872 publications in 9 languages and 10,151 library holdings 

Genres:  Popular works Conference papers and proceedings Biography 
Roles:  Author, Editor, Recipient, Correspondent, Performer, Other, Former owner, Translator, Contributor, Conductor 
Classifications:  QA11, 510.7 
Publication Timeline
.
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 )
 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
)
59 editions published between 1957 and 1981 in 6 languages and held by 750 WorldCat member libraries worldwide
59 editions published between 1957 and 1981 in 6 languages and held by 750 WorldCat member libraries worldwide
Linear lie groups by
Hans Freudenthal(
Book
)
37 editions published between 1960 and 1969 in 3 languages and held by 666 WorldCat member libraries worldwide
37 editions published between 1960 and 1969 in 3 languages and held by 666 WorldCat member libraries worldwide
The Concept and the role of the model in mathematics and natural and social sciences 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 by
Hans Freudenthal(
Book
)
45 editions published between 1951 and 1961 in 3 languages and held by 611 WorldCat member libraries worldwide
45 editions published between 1951 and 1961 in 3 languages and held by 611 WorldCat member libraries worldwide
Mathematics observed by
Hans Freudenthal(
Book
)
13 editions published between 1967 and 1970 in 3 languages and held by 543 WorldCat member libraries worldwide
13 editions published between 1967 and 1970 in 3 languages and held by 543 WorldCat member libraries worldwide
Mathematics as an educational task by
Hans Freudenthal(
Book
)
18 editions published between 1972 and 1973 in English and Undetermined and held by 503 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
18 editions published between 1972 and 1973 in English and Undetermined and held by 503 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
)
34 editions published between 1976 and 2004 in English and German and held by 408 WorldCat member libraries worldwide
34 editions published between 1976 and 2004 in English and German and held by 408 WorldCat member libraries worldwide
Lincos; design of a language for cosmic intercourse by
Hans Freudenthal(
Book
)
39 editions published in 1960 in 3 languages and held by 386 WorldCat member libraries worldwide
39 editions published in 1960 in 3 languages and held by 386 WorldCat member libraries worldwide
Didactical phenomenology of mathematical structures by
Hans Freudenthal(
Book
)
31 editions published between 1983 and 2005 in English and Undetermined and held by 385 WorldCat member libraries worldwide
31 editions published between 1983 and 2005 in English and Undetermined and held by 385 WorldCat member libraries worldwide
Algebraical and topological foundations of geometry; proceedings by
Hans Freudenthal(
Book
)
26 editions published between 1959 and 2014 in 3 languages and held by 366 WorldCat member libraries worldwide
Algebraical and Topological Foundations of Geometry
26 editions published between 1959 and 2014 in 3 languages and held by 366 WorldCat member libraries worldwide
Algebraical and Topological Foundations of Geometry
Revisiting mathematics education : China lectures by
Hans Freudenthal(
Book
)
32 editions published between 1991 and 2010 in 3 languages and held by 269 WorldCat member libraries worldwide
32 editions published between 1991 and 2010 in 3 languages and held by 269 WorldCat member libraries worldwide
Logique mathematique appliquee by
Hans Freudenthal(
Book
)
17 editions published in 1958 in 3 languages and held by 236 WorldCat member libraries worldwide
17 editions published in 1958 in 3 languages and held by 236 WorldCat member libraries worldwide
The Legacy of Hans Freudenthal by
Leen Streefland(
Book
)
4 editions published in 1993 in English and held by 127 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
4 editions published in 1993 in English and held by 127 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
Mathematik als pädagogische Aufgabe by
Hans Freudenthal(
Book
)
9 editions published between 1973 and 1979 in German and held by 81 WorldCat member libraries worldwide
9 editions published between 1973 and 1979 in German and held by 81 WorldCat member libraries worldwide
Mathematik in Wissenschaft und Alltag by
Hans Freudenthal(
Book
)
10 editions published between 1968 and 1977 in German and Russian and held by 68 WorldCat member libraries worldwide
10 editions published between 1968 and 1977 in German and Russian and held by 68 WorldCat member libraries worldwide
Vorrede zu einer Wissenschaft vom Mathematikunterricht by
Hans Freudenthal(
Book
)
5 editions published in 1978 in German and held by 66 WorldCat member libraries worldwide
5 editions published in 1978 in German and held by 66 WorldCat member libraries worldwide
Selecta by
Hans Freudenthal(
Book
)
7 editions published in 2009 in English and German and held by 62 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
7 editions published in 2009 in English and German and held by 62 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
Mathematik als pädagogische Aufgabe by
Hans Freudenthal(
Book
)
2 editions published in 1974 in German and held by 2 WorldCat member libraries worldwide
2 editions published in 1974 in German and held by 2 WorldCat member libraries worldwide
Schrijf dat op, Hans : knipsels uit een leven by
Hans Freudenthal(
Book
)
2 editions published in 1987 in Undetermined and Dutch and held by 1 WorldCat member library worldwide
Opstellen die een beeld geven van het leven van de hoogleraar wiskunde, columnist en journalist (1905)
2 editions published in 1987 in Undetermined and Dutch and held by 1 WorldCat member library worldwide
Opstellen die een beeld geven van het leven van de hoogleraar wiskunde, columnist en journalist (1905)
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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 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 Electromechanical analogies Geometry Geometry, Algebraic Geometry, Differential Geometry, NonEuclidean GeometryFoundations Group actions (Mathematics) Group theory Homotopy theory Humanities Lie algebras Lie groups Lincos (Artificial language) Logic, Symbolic and mathematical Mathematical models Mathematicians Mathematics MathematicsPhilosophy MathematicsStudy and teaching MathematicsStudy and teachingAudiovisual aids MathematicsStudy and teachingPhilosophy Netherlands NetherlandsUtrecht Probabilities Science ScienceMethodology SciencePhilosophy 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 matematico tedesco
Hans Freudenthal mathématicien allemand
Hans Freudenthal Nederlands wiskundige
Sirlof, V. 19051990
Sirolf, V. 19051990
Фрейденталь, Ганс 19051990
Фрейденталь, Х.
Фрейденталь, Ханс
Фройденталь, Ханс
Ханс Фройдэнталь
הנס פרוידנטל
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
Languages
English
(298)
German (86)
Dutch (21)
French (15)
Russian (5)
Italian (4)
Multiple languages (3)
Japanese (2)
Latin (2)
German (86)
Dutch (21)
French (15)
Russian (5)
Italian (4)
Multiple languages (3)
Japanese (2)
Latin (2)
Covers