Witten a.d. Ruhr 1928 - Bielefeld 2004


A pioneer of the modern development of mathematics education

Hans Georg Steiner was one of the pioneers of the modern development of mathematics education1 and its establishment as a scientific discipline.

Hans-Georg Steiner, born on 21 November 1928, was 16 years old when World War II ended in Germany2 . He had been forced by the Nazi regime to become a member of the anti-aircraft protection forces in the last stages of the war. After the war, he completed his school education in the difficult conditions of post-war Germany. In 1949 he enrolled in mathematics and physics at the University of Münster. From his first days at university on he showed a great interest in other subjects as well and was an active participant in lectures and seminars on linguistics and literature, philosophy and pedagogy. In 1955 he graduated with his first teacher state exam, followed by the second teacher state exam in 1957. In the ensuing 2 years he worked as a research assistant of Heinrich Behnke at the Institute of Mathematics in Münster where he was responsible for the programme and content of the seminars on the didactics of mathematics held every Tuesday afternoon.
Heinrich Behnke was from 1952 - the year of re-establishment of ICMI - to 1966 a member of the ICMI Executive Committee, its President from 1955 to 1958, and later its Vice-President. Within Germany, Behnke had succeeded in establishing in 1951 at Münster - the traditional home of high quality mathematics teacher education - the first "seminar for didactics of mathematics" at a German university3. Behnke soon realised the potential of the young Steiner and involved him in the organisation of conferences while he still was an undergraduate student. The series was called Tagung zur Pflege des Zusammenhangs zwischen Höherer Schule und Universität (Münster Conferences for the Promotion of the Connection between School and University). Upon invitation by Behnke, Steiner delivered his first paper at the 1957 Zusammenhangs-Conference, on "The introduction of modern mathematical concepts to the mathematics classroom". The lecture was published as an essay (STEINER, 1959), which was later considered a key contribution to the reform of secondary mathematics education in Germany (Knoche, 1988). It provided the starting point for an extensive sequence of papers and publications on theoretical as well as classroom based topics in the field of mathematics education.
Steiner's extensive international involvement already started when he still was an undergraduate student. The international guests invited to Münster by Behnke, such as Howard Fehr and James Lighthill, brought Steiner quickly into contact with international developments. While collaborating with Behnke, Steiner became involved in the ICMI activities and in 1962 he became a member of the German ICMI subcommittee himself. In the course of the ICMI subcommittee meetings, which took place under the leadership of Heinrich Behnke at the University of Münster, Steiner met teachers and researchers interested in pedagogy, philosophy and didactics - the basis for intensive working contacts as well as personal friendships, for example with Heinz Griesel, Günter Pickert and Hans Freudenthal. While working with Behnke, Steiner attended his first international congress in 1958 - the International Mathematics Congress (ICM) of the International Mathematical Union (IMU) in Edinburgh, Scotland, where he met a number of leading US American curriculum reformers. These initial contacts were further established at the ICM 1962 in Stockholm and the ICM 1966 in Moscow.

In 1960 Hans Georg Steiner undertook his first visit to the USA where he established contacts within the rapidly developing curriculum reform-movement. He was invited to give lectures in a summer institute for mathematics teachers at Columbia University in New York. This first professional journey to the USA was followed by another series of invited lectures and workshops at several teacher colleges and universities across the country sponsored by the American Association for the Advancement of Science (AAAS). The result of these journeys was a developing cooperation with US American curriculum projects: the "Secondary School Mathematics Curriculum Improvement Study" (SSMCIS) founded at Columbia University and the "Comprehensive School Mathematics Program" (CSMP) initiated by Burt Kaufmann and supported by the "Central Midwestern Regional Educational Laboratory" (CEMREL) in St. Louis, Missouri. Steiner became the European co-director of the CSMP, which was dedicated to the development of an enhancement program for mathematically gifted students. A number of publications between the years 1967 and 1973 document the intensive and fruitful work of these two projects. Steiner's key talents -initiating, fostering and extending international relationships in the field of didactics of mathematics -were already becoming evident. At the same time, he became acquainted with educational structures in which elementary and secondary schools were not separated from each other socially and conceptually. Indeed, the curriculum work of CSMP also involved elementary schools.
School related publications during this time address:
  • the teaching of logic in middle and high school;
  • the role of algebraic games for the understanding of algebraic structure;
  • the teaching of equations and functions;
  • the teaching of geometry.
Several of these publications were fundamental analyses of lasting value. In 1964 and 1965 Steiner published two papers on a correspondence between Frege and Hilbert, which he commented on in great detail. Teaching experiments and didactical analyses on the topic of mathematization of political structures were a major focus of his mathematical as well as didactical work in the late 1960s and 1970s. Steiner's "Mathematical Theory of Voting Bodies" (Eine mathematische Theorie von Abstimmungsgebilden) was also the core of this doctoral thesis completed in 1969 at the University of Darmstadt with Detlef Laugwitz (STEINER, 1969). After his return from the USA, Steiner founded, together with Heinz Kunle, in 1968 the Zentrum für Didaktik der Mathematik in Karlsruhe. Together with the annual federal conferences on didactics of mathematics that began in 1967, the Zentrum provided a decisive means for bringing together the separate traditions of Volksschul-Methodiker and Gymnasialdidaktiker4. Later, in 1969, Steiner founded, based on the Zentrum, the Zentralblatt für Didaktik der Mathematik (ZDM), the first truly international journal on the didactics of mathematics to be established in Germany. The journal was formed with two main purposes in mind - to propagate research and to review international publications - key means for forging the scientific development of the new discipline. This probably constitutes the most salient achievement of Steiner both for the German as well as the international community.

Oberwolfach 8.12.75, Meeting preparing ICME 3, Steiner, Krygowska, Freudenthal
Oberwolfach 8.12.75, Meeting preparing ICME 3,
Steiner, Krygowska, Freudenthal
In May 1970 Steiner was appointed professor for didactics of mathematics at the Pädagogische Hochschule Bayreuth, and was thus able to apply there his concepts in teacher education. Among other projects, he was involved in a teaching project for elementary schools, "Modern Mathematics in the first and second school years". This did not aim to teach set theory, but rather to develop mathematical thinking with numbers and calculations. For the teacher trainee students, accompanying lectures offered reflections on practice and theory.

Eventually, in 1973 he was appointed as one of the three foundation professors at the IDM - the Institut für Didaktik der Mathematik at the University of Bielefeld, together with Michael Otte and Heinrich Bauersfeld, and developed there a comprehensive activity in which he was able, in particular, to further the program in which he had been engaged so far - namely, establishing a scientific didactics with internationalisation as an essential element of this process. In the structure of the IDM based on the division of labour between three main groups, Steiner led the group that concentrated upon curriculum development in the upper secondary grades. As in other aspects of the work of the IDM, this group was interdisciplinary and included mathematicians, didacticians of mathematics, sociologists and psychologists. Major projects that were undertaken included the reorganization of the upper grades of the Gymnasien, vocational education, statistics and the social role of mathematics. Following the introduction of pocket calculators and computers in the classrooms, the group's researches and developments involving the new media and technologies were both innovative and original. The third international congress on mathematics education (ICME 3, Karlsruhe, 1976) became an effective landmark in the process of the national and international disciplinary stabilization of the didactics of mathematics, following its predecessors in Lyon (1969) and Exeter (1972). Steiner, from 1975 to 1978 Vice-President of ICMI and chair of the program committee, succeeded in bringing together there the different, hitherto also institutionally separated strands and to engage them in lasting cooperation. An excellent means for realizing this was the new organization of the congress. This was built around thirteen sections which investigated central issues of mathematics instruction, and which benefited from the careful preparation of the teams which were composed internationally and had worked together well before the congress. Steiner also succeeded, by means of the extensive integration of various competencies, to diminish the initial obvious tensions between the Bielefeld institute and the didacticians of mathematics working elsewhere in the Federal Republic.

Besides his work on research and development at the IDM, it was always a central concern for Steiner to give conceptual stimulation and to help spread new ideas by organizing national and international colloquia and conferences. This stimulating function is certainly one of his most important contributions to the development of the didactics of mathematics, in particular for the Federal Republic. The series of these influential conferences first began in 1974 with the Regional ICMI-IDM Conference on the Teaching of Geometry. Of the other conferences, one should name the ICMI Symposium of 1978, The Education of Mathematics Teachers, and the larger conference of 1979: Comparative Studies of Mathematics Curricula - Change and Stability.

Steiner also gave innovative suggestions via smaller-scale working conferences, such as a series of colloquia devoted to the relation of educational history and history of mathematics. Other valuable forms for the exchange of ideas were the numerous bilateral conferences organized by him: for example, the German-Italian and the German-French symposia on recent developments in the didactics of mathematics.

The conference series that proved in the long term to be probably the most important for the development of research was the series of symposia on TME: Theories of Mathematics Education established by him in 1985. TME had originated from his conviction that - thanks to the scientific level achieved - the ulterior major task lay in the advancement of theoretical approaches. At ICME 10 in Copenhagen, many participants still spoke to me about TME and told me how essential their participation in TME conferences had been for their scientific development.

Finally, Steiner merits particular respect for having organized two conferences with participants drawn from the old Federal Republic and the GDR immediately after the "Wende" in the GDR and to have thus once again initiated communication and cooperation.

Unfortunately, it was not granted to Steiner, after having become professor emeritus in 1993, to continue and to conclude his numerous projects, because, increasingly, a protracted serious illness impaired his working possibilities.


A complete list of his publications is given in Biehler/Peter-Koop 2007. Some selected publications are mentioned here:
H.G. STEINER 1959, Das moderne mathematische Denken und die Schulmathematik, Der Mathematikunterricht, 5, 4, 5-79
H.G. STEINER 1962a, Die Verbindung von Logik und Mathematik im mathematischen Unterricht, Mathematisch-Physikalische Semesterberichte, 9, 1, 74-95
H.G. STEINER 1962b, Die Behandlung des Funktionsbegriffs in der höheren Schule, L'enseignement mathématique, 2e Série, 8, 1, 62-92
H.G. STEINER 1963, Explizite Verwendung der reellen Zahlen in der Axiomatisierung der Geometrie, Der Mathematikunterricht, 9, 4, 66-87
H.G. STEINER 1964a, Frege und die Grundlagen der Geometrie I, Mathematisch-Physikalische Semesterberichte, 10, 1, 35-47
H.G. STEINER 1964b, Moderne begriffliche Methoden bei der Behandlung der komplexen Zahlen, Der Mathematikunterricht, 10, 2, 5-35
H.G. STEINER 1964c, Elementare Beweise zum Fundamentalsatz der Algebra, Der Mathematikunterricht, 10, 2, 60-93
H.G. STEINER 1965a, Frege und die Grundlagen der Geometrie II, Mathematisch-Physikalische Semesterberichte, 10, 2, 175-186
H.G. STEINER 1965b, Wie steht es mit der Modernisierung unseres Mathematikunterrichts?, Mathematisch-Physikalische Semesterberichte, 11, 2, 186-200
H.G. STEINER 1965c, Menge, Struktur, Abbildung als Leitbegriffe für den modernen mathematischen Unterricht, Der Mathematikunterricht, 11, 1, 5-19
H.G. STEINER 1969, Eine mathematische Theorie der Abstimmungsgremien, Dissertation, Fakultät für Mathematik und Physik, Technische Universität Darmstadt
H.G. STEINER 1977, ICMI and congress recommendations. Conferences 1972-1976, in H. Athen, H. Kunle (Eds.), Proceedings of the 3rd International Congress on Mathematical Education, Karlsruhe, ZDM, 383-388
H.G. STEINER 1978, Zur Entwicklung der Didaktik der Mathematik, in H.-G. Steiner (Ed.), Didaktik der Mathematik. Wege der Forschung, Darmstadt, Wissenschaftliche Buchgesellschaft, ix-xlviii
H.G. STEINER 1979, The present situation in the development of mathematics curricula for the primary school. A critical survey, L'Insegnamento integrato delle Scienze nelle Scuola Primaria, Roma, Accademia Nazionale dei Lincei, 245-269
B. CHRISTIANSEN, H.G. STEINER (Eds.) 1979, New Trends in Mathematics Teaching, IV, Paris, UNESCO
H.G. STEINER 1985, Theory of Mathematics Education (TME): An Introduction, For the Learning of Mathematics, 5, 2, 11-17
H.G. STEINER, A. VERMANDEL (Eds.) 1988, Foundations and Methodology of the Discipline Mathematics Education (Didactics of Mathematics). Proceedings of the 2nd international TME-conference, Bielefeld, July 15-19, 1985, Bielefeld, Antwerpen
H.G. STEINER 1992, Recent and coming activities of the international study group on theory of mathematics education (TME), Zentralblatt für Didaktik der Mathematik, 24, 2, 67-68

Related Publications

R. BIEHLER, R.W. SCHOLZ, R. STRÄSSER, B. WINKELMANN (Eds.) 1994, Didactics of mathematics as a scientific discipline, Dordrecht, Kluwer.
H. GRIESEL, R. FISCHER 1988, Fachdidaktische Grundfragen des Mathematikunterrichts, Special Issue for Hans-Georg Steiner's 60th birthday, Zentralblatt für Didaktik der Mathematik, 20, 5
H. HENNING, P. BENDER (Eds.) 2003, Didaktik der Mathematik in den alten Bundesländern - Methodik des Mathematikunterichts in der DDR, Magdeburg & Paderborn, Otto-von-Guericke-Universität Magdeburg & Universität Paderborn, on-line publication:
N. KNOCHE 1988, "Hans-Georg Steiner 60 Jahre", Mathematische Semesterberichte, 35, 2, 147-161
B. WINKELMANN (Ed.) 1988, Wissenschaftliches Kolloquium Hans-Georg Steiner zu Ehren, IDM Occasional Paper 116, Bielefeld, Universität Bielefeld, IDM


R. BIEHLER, A. PETER-KOOP 2007, "Hans-Georg Steiner: a life dedicated to the development of didactics of mathematics as a scientific discipline", ZDM - The International Journal on Mathematics Education, 39, 1, 3-30
A. G. HOWSON 2004, "Hans-Georg Steiner: some personal reminiscences", ICMI-Bulletin, 55, 78-80
G. SCHUBRING 2004, "Hans-Georg Steiner (21.11.1928-14.12.2004) - A life for mathematics education", ICMI-Bulletin, 55, 73-77
G. SCHUBRING 2004, "Hans-Georg Steiner. Ein Leben für die Mathematik-Ddiaktik", Mitteilungen der Gesellschaft für Ddiaktik der Mathematik, 79, 94-98

Gert Schubring
Institut für Didaktik der Mathematik
Fakultät für Mathematik, Universität Bielefeld

I am thanking Erika-Luise Steiner for her kind authorisation to use these pictures from her late husbandís photo collection.
1In Germany - as in France and Italy, Didaktik means the scientific investigation of teaching and learning processes. However, in the Anglo-Saxon world "didactics" often has negative connotations and "mathematics education" is preferred. Since not all meanings of the German terms would be thus translated, we shall maintain the use of didactics to express the German meaning.
2For a detailed account see STEINER, 1998
3Seminare were traditional forms in German universities for specialised studies in given disciplines and for closer contact with the professors.
4The Volksschule, Realschule and Gymnasium are the components of the tripartite system of secondary education still to be found in most regions of Germany.