WorldCat Identities

Freudenthal, Hans 1905-1990

Works: 251 works in 898 publications in 8 languages and 10,807 library holdings
Genres: Popular works  Conference papers and proceedings  Biography  Abstracts 
Roles: Author, Editor, Correspondent, Recipient, Performer, Other, Former owner, Translator, Conductor, Contributor
Classifications: QA11, 510.7
Publication Timeline
Most widely held works about Hans Freudenthal
Most widely held works by Hans Freudenthal
The language of logic by Hans Freudenthal( Book )

53 editions published between 1961 and 1975 in 6 languages and held by 891 WorldCat member libraries worldwide

Probability and statistics by Hans Freudenthal( Book )

55 editions published between 1957 and 1981 in 6 languages and held by 748 WorldCat member libraries worldwide

Linear lie groups by Hans Freudenthal( Book )

24 editions published between 1969 and 1979 in 3 languages and held by 582 WorldCat member libraries worldwide

Mathematics observed by Hans Freudenthal( Book )

14 editions published between 1967 and 1970 in 3 languages and held by 542 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 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
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 407 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 391 WorldCat member libraries worldwide

Lincos; design of a language for cosmic intercourse by Hans Freudenthal( Book )

26 editions published in 1960 in 3 languages and held by 328 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 322 WorldCat member libraries worldwide

Revisiting mathematics education : China lectures by Hans Freudenthal( Book )

33 editions published between 1991 and 2010 in 3 languages and held by 272 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) Long-term 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

The Legacy of Hans Freudenthal by Leen Streefland( Book )

6 editions published in 1993 in English and held by 129 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 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
Raumtheorie by Hans Freudenthal( Book )

9 editions published in 1978 in German and held by 117 WorldCat member libraries worldwide

Collected works by L. E. J Brouwer( Book )

28 editions published between 1975 and 1976 in 4 languages and held by 86 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

Mathematik als pädagogische Aufgabe by Hans Freudenthal( Book )

7 editions published between 1973 and 1979 in German and held by 78 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 (1905-1990) 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
Vorrede zu einer Wissenschaft vom Mathematikunterricht by Hans Freudenthal( Book )

5 editions published in 1978 in German and held by 68 WorldCat member libraries worldwide

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 65 WorldCat member libraries worldwide

Algebraical and Topological Foundations of Geometry
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Mathematics as an educational task
Alternative Names
Freidental, Kh.

Freĭdentalʹ, Kh 1905-1990

Freĭdentalʹ, Kh. (Khans), 1905-1990

Freidental, Khans.

Freĭdentalʹ, Khans 1905-1990

Frejdentalʹ, Ch

Frejdentalʹ, Ch 1905-1990

Frejdental', Gans.

Frejdental', Gans 1905-1990

Frejdental', H.

Freudenthal, H.

Freudenthal, H. 1905-1990

Freudenthal, Hans

Frojdental', G.

Frojdental', G. 1905-1990

Frojdental', Gans.

Frojdental', Gans 1905-1990

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. 1905-1990

Sirolf, V. 1905-1990

Фрейденталь, Ганс 1905-1990

Фрейденталь, Х.

Фрейденталь, Ханс

Фройденталь, Ханс

Ханс Фройдэнталь

הנס פרוידנטל

프로이덴탈, 한스 1905-1990

한스 프로이덴탈


フロイデンタール, H



Linear lie groupsMathematics as an educational taskWeeding and sowing : preface to a science of mathematical educationDidactical phenomenology of mathematical structuresRevisiting mathematics education : China lecturesThe Legacy of Hans FreudenthalSelecta