Hans-Georg Steiner: a life dedicated to the development of didactics of mathematics as a scientific discipline

Abstract

In our introductory paper to this special issue we follow two goals. First of all, we take on the challenge to give an account of more than 40 years of academic work by one of the leading members of our discipline by looking at Hans Georg Steiner’s contributions to the development of didactics of mathematics as a scientific discipline in Germany as well as internationally. Therefore, we try to highlight major research interests, publications and conferences during his early years in Münster, Karlsruhe and Bayreuth as well as during the 20 years at the IDM in Bielefeld. Closely linked to these periods of this life and work are specific research interests, professional contacts and friendships. Hence, the second goal of our paper is to emphasise Hans-Georg Steiner’s relationships with national and international colleagues (many of whom became friends) and their shared interests and collaborations in the development of mathematics education through a selection of invited papers that address different stages and professional foci in the life of Hans-Georg Steiner. These papers are organised in four sections: (1) Revisiting the New Math reform, (2) Developing specific research domains in didactics of mathematics, (3) Discussing theories of mathematics education (TME), and (4) Reflecting on goals and results of mathematics education.

1 Introduction

This first volume of the ‘new’ ZDM, “The International Journal on Mathematics Education (formerly Zentralblatt für Didaktik der Mathematik)” now published by Springer is dedicated to Hans-Georg Steiner, who founded the ZDM together with Heinz Kunle und Emmauel Röhrl in 1969. The context of the establishment of the ZDM was the foundation of the “Centre for Didactics of Mathematics” at the University of Karlsruhe, which is described below.

Hans-Georg Steiner passed away on December 14, 2004 after a long illness at the age of 76. Many of us remember him as a colleague who continuously fostered ties between people as well as networks across countries and disciplines. His engagement for the development of mathematics education as a discipline nationally and internationally was extraordinary. Around the world Hans-Georg Steiner is well known for his work as one of the three founding directors of the IDM (Institute for Didactics of Mathematics) at Bielefeld University.

The editors of ZDM invited us as guest editors of this special issue “In memoriam Hans-Georg Steiner”. The first author belonged to his working group at the IDM in Bielefeld from 1977 to 1993 and the second author was his last doctoral student. Our intention was to call for contributions from authors that represent the various stages of his scientific life—nationally and internationally. Fortunately, many colleagues accepted our invitation to contribute to this special issue and hence helped to document the influence of his many sparks of inspiration, advice and academic stimulus for so many of us who had the privilege to meet Hans-Georg and to work with him.

The papers in this volume reflect certain stages of his scientific life. His broad research interests and his significant contributions to the development of mathematics education are also evident in the complete list of all his publications (see Appendix 1) and a list of the conferences Hans-Georg Steiner had organized (see Appendix 2). The title of this article emphasises a most important aspect of Hans-Georg Steiner’s scientific life. Developing didactics of mathematics as a scientific discipline in an international perspective was a major concern of his work at the IDM and culminated in him creating the international TME movement (Theory of Mathematics Education). We intend to show how this concern has been emerging from his earlier work.

The papers in this volume are organised in four sections.

1.1 Revisiting the New Math reform

The contributions of his close friends and colleagues Heinz Griesel (Kassel), Hans-Joachim Vollrath (Würzburg) and Roland Scholz (Zürich) are directly related to Hans Georg’s early research and publications. Vollrath and Griesel refer to his work related to the New Math curriculum reform in the 1960s and early 1970s, in which he played a prominent role. Scholz refers to Steiner’s most favourite mathematical example, the mathematization of voting bodies. This example served as a prototype for his didactical thinking. It started as an example for making the reasons for and the value of axiomatisation in mathematics accessible to students in the 1960s. Later he used the theory of voting bodies to illustrate the social construction of mathematical knowledge (Steiner, 1969b, 1983).

1.2 Developing specific research domains in didactics of mathematics

Hans-Georg Steiner’s work at the IDM in Bielefeld is reflected in papers addressing specific research topics and working contacts from that time at an international level through the papers by Mariolina Bartolini-Bussi (Modena), Gila Hanna and Nathan Sidoli (Toronto) and Gilah Leder (Melbourne) as well as contributions from the former IDM members Hans-Niels Jahnke (Essen), Heinz Steinbring (Essen) and Gerd Schubring (Bielefeld).

1.3 Discussing theories of mathematics education

In their papers, Luciana Bazzini (Turin), Juan Godino, Carmen Batanero and Vicenç Font (Granada/Barcelona), Colette Laborde (Grenoble), David Tall (Warwick) as well as Günter Törner and Barath Sriraman (Duisburg/Montana) address aspects of Hans-Georg’s latter research interest in what he called TME, i.e. theory of mathematics education.

1.4 Reflecting on goals and results of mathematics education

During his entire life, Hans-Georg Steiner was concerned about the goals and results of mathematics education. Therefore, this special issue would have been incomplete without the contributions of Ubiratan D’Ambrosio (Sao Paulo), Rudolf Sträßer (Gießen/Luleå) and Shlomo Vinner (Beer Sheva), who look at this aspect from didactical, political, social and philosophical perspectives.

In our introduction to this special issue we aim to shine a light on Hans-Georg Steiner’s approaches, challenges, co-operations and achievements in his strive for a an international reform of mathematics teaching and learning. In doing so, we pay our respect to our academic teacher who supported not only our professional careers but who was also highly influential to many other teachers and researchers in Germany and across the globe as the papers in this volume highlight.

2 The early years: Münster–Karlsruhe–Bayreuth

Hans-Georg Steiner, born on the 21st November 1928, was 16 years old when World War II ended in Germany. He suffered from being among those children that the criminal Nazi regime forced 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 under the difficult conditions of post-war Germany (for a detailed account see Steiner, 1998). 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 following 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, a leading German mathematics professor of international renown at the University of Münster had a distinguished interest in didactics. He 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 Furtherance of the Connection between School and University] (Conference 1¹). In 1957—while still completing the second phase of teacher training—he was invited by Behnke to give a lecture at this conference. The other speakers were renowned university professors in mathematics or natural sciences and gave seminars on recent results of their disciplines. Only Hans-Georg Steiner explicitly pointed out relationships between university and school level. His eloquence, outspokenness and his distinguished style of presentation had already become evident. The title of his lecture “The introduction of modern mathematical concepts to the mathematics classroom” [Der Eingang moderner mathematischer Begriffe in den Schulunterricht] attracted many regional grammar school teachers. According to Griesel (1988, p. 167), Steiner’s audience was divided. Some questioned his authority being ‘only’ a young not yet experienced teacher, having visions not backed-up by practical experience whereas others anticipated that they were being witnesses of a prelude of a new upcoming reform.

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. The “engine of the reform” (Griesel, 1988) had started to run and ran for more than a decade. This start was courageous, ambitious and polarizing—however, not the last event of this kind in his life.

A major goal and means of improving mathematics education was the elementarization of modern concepts of mathematics as a science, making it accessible to a wide range of primary and secondary students. This reform movement was already internationally growing and it later gained in power because it met favourable societal and political conditions supporting educational reforms in general and not only in mathematics. In western countries the so-called ‘Sputnik shock’ had initiated an enormous concern and investment into the educational systems.

For envisioning the congenial intellectual and cultural climate, let us remember Jerome Bruner’s enormously influential principles of curriculum reform in those days, which came out of the legendary Woods Hole Conference on Cape Cod in 1959: “We begin with the hypothesis that any subject can be taught effectively in some intellectually honest form to any child at any stage of development” (Bruner, 1960, p. 33). Additionally, Bruner advocated the structure of the discipline as a basic orientation for all science-based school reforms and saw the spiral curriculum principle as a way to make this work.

Hans-Georg’s extensive international involvement already started at a time when he still was an undergraduate student. The International Commission of Mathematics Instruction (ICMI) had reconstituted itself as part of the International Mathematical Union (IMU) after World War II in 1951. Heinrich Behnke became a member of ICMI’s international executive committee, was its president from 1954 to 1958 and served as the president of the German subcommittee from 1951 to 1966. While collaborating with Behnke, Hans-Georg 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. It is important to note that the German Association for Didactics of Mathematics was founded not earlier than 1975 and that the German ICMI subcommittee had an important institutional function in the emerging discipline of didactics of mathematics in Germany.

While working with Heinrich Behnke, Hans-Georg 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, where Steiner was invited to give a keynote address titled “The role of axiomatics in mathematics teaching”.

In 1960 Hans-Georg Steiner made the first of many journeys to the United States being 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. Hans-Georg 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. Hans-Georg’s key talents—initiating, fostering and extending international relationships in the field of didactics of mathematics—were already becoming evident. His work as an initiator and connector was continued and further intensified during his many years as director at the “Institute for Didactics of Mathematics” (IDM) at the University of Bielefeld (see below).

Parallel to his international activities, Hans Georg Steiner’s involvement and responsibilities at the “Seminar for Didactics of Mathematics” in Münster, where he closely cooperated with Heinz Griesel, included an increasing number of invitations of interested colleagues and researchers from various countries in Europe and abroad. Quite frequently these guests together with close friends were invited to his home where he and his wife, Erika-Luise, hosted them in a most kind, charming and stimulating atmosphere. Their hospitality and generosity was greatly appreciated back then as well as later in Bielefeld by many members of our community. The special atmosphere of these visits as well as during meetings at many conferences was greatly influenced by his wife who actively took part in the discussions and contributed her personal views on didactical topics which were based on a genuine interest in the development of mathematics education and a great respect for and interest in scientific discourse in general.

But not only his nurturing of international contacts was legendary. Hans-Georg Steiner also enriched the Münster seminar series by many thought provoking presentations and topics. Behnke acknowledged his multi-faceted contributions in a documentation of the work of the didactical seminar in 1971 as follows: “H.-G. Steiner was the one who provided the most colour and innovation to the seminar. His personal academic development and that of the seminar was frequently inseparable.” [Am meisten Farbe und Neuerungen hat H.-G. Steiner dem Seminar geliefert. Seine eigene Entwicklung und die des Seminars liefen manche Jahre völlig synchron.] (Behnke, 1971).

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, as well as

• the teaching of geometry.

Several of these publications were fundamental analyses of lasting value. In 1964 and 1965 Hans Georg Steiner published two papers on a correspondence between Frege and Hilbert, which he commented on in great detail. The reform of the construction of the number system in reference to Frege is also the topic of a paper by Heinz Griesel in this volume in which he argues that Steiner’s point of view on the construction of the number system offers great potential for school mathematics (Steiner, 1964, 1965).

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. Hans-Georg Steiner’s “Mathematical Theory of Voting Bodies” [Eine mathematische Theorie von Abstimmungsgebilden] was also the core of this doctoral thesis completed 1969 at the University of Darmstadt with Detlef Laugwitz (Steiner, 1969a). Roland Scholz takes on and elaborates on the topic of voting bodies in his contribution to this special issue while Hans-Joachim Vollrath describes the historical context and Steiner’s previous controversy with Laugwitz in the context of the New Math reform.

Two years prior to his doctoral degree, Steiner took on a position at the University of Karlsruhe at the newly established Department for Didactics of Mathematics at the Institute of Geometry run by the mathematician Heinz Kunle, who—like Behnke—was greatly interested in fostering the didactics of mathematics. In 1970, Heinz Kunle became the president of the German ICMI subcommittee, a position he retained until 1990. In Karlsruhe—the later location of ICME 3—Steiner succeeded in the foundation of the “Zentrum für Didaktik der Mathematik” [Centre for Didactics of Mathematics]. This new centre was connected through intensive working contacts and co-operations to the CERMEL in St. Louis, Missouri. The foundation of the “Zentralblatt für Didaktik der Mathematik” (ZDM)—the first truly international journal on the didactics of mathematics to be established in Germany—followed in 1969 and for the coming decades Steiner remained its co-editor. The creation and development of an extensive international database with refereed publications on mathematics education (MathDi, MathEduc, http://www.emis.de:80/MATH/DI.html) was part of this process. Gerhard König became the managing editor.

In May 1970 Hans-Georg Steiner was appointed as full professor of a new chair in mathematics education at the Educational University in Bayreuth, Bavaria, but maintained the leadership of the “Centre of Didactics of Mathematics” in Karlsruhe. In 1971, he organized the “5th Annual German Conference on the Didactics of Mathematics” in Bayreuth and internationalized the conference by inviting colleagues such as Anna Zofia Krygowska (Poland), Tamás Varga (Hungary), Hans Freudenthal (The Netherlands), Georges Papy (Belgium) and Bent Christiansen (Denmark), who had been influential in the international reform movement of mathematics education.

3 Institut für Didaktik der Mathematik (IDM), Bielefeld 1973–1993

3.1 Overview

In spring 1973, Hans-Georg Steiner received an offer to become one of the three directors of the newly founded “Institut für Didaktik der Mathematik” (IDM). He accepted the offer in the fall of 1973 and served as a director of the IDM together with his colleagues Heinrich Bauersfeld and Michael Otte until he retired in 1993. The IDM was founded as a central research institute for the didactics of mathematics in Germany. Its responsibilities included the development of didactics of mathematics as a scientific discipline comprising the establishment of a national and international scientific network of scientists.

Apart from the unit for documentation and library led by Gert Schubring, the IDM mainly consisted of three working groups called F1, F2, and F3, which were directed by its three professors. “F” originally stood for “flexible working unit”. It turned out, however, that these groups became quite a stable structural element of the IDM. In the course of IDM’s development the subtitles of the groups also developed due to shifts in research interests. Nevertheless, collaboration at the IDM went beyond the borders of the working groups and two former members of F2, Hans-Niels Jahnke and Heinz Steinbring, as well as Gert Schubring, with whom Hans-Georg Steiner shared common interests in the history of mathematics and mathematics education, have contributed to this volume.

F3 started as the “Working Group for Mathematics Education at Upper Secondary Level” (i.e., grades 11–13) and this remained one of its major domains of interest at least for about the first decade of its existence. The group had an interdisciplinary character. Members had different backgrounds in mathematics, mathematics education, psychology, sociology and educational science (see Sect. 3.1).

The foundation of the ZDM, the IDM and similarly the IPN [Institute for the Pedagogy of the Natural Sciences] in Kiel can be regarded as the establishment of ‘excellence centres’ that were intended to develop scientific disciplines within a new concern for science as an engine for social and economic development. All industrialized societies increased their investments in education enormously in the late 1960s and 1970s. The “scientification” of society called for new science-based educational approaches. Didactics was not confined to optimize teaching and learning processes in school but also regarded as a reflective science concerned with knowledge in society.

When Hans-Georg Steiner started his work at the IDM, he was part of the emerging mathematics education community in Germany with whom he shared the co-operation, the visions and the disappointments in the process of the New Math reform movement. Together with German colleagues he continued to collaborate in the editorial board of three German journals for mathematics education “Mathematisch–Physikalische Semesterberichte”, “Didaktik der Mathematik” and “Zentralblatt für Didaktik der Mathematik”. He had played an early role in founding the latter two journals.

The early IDM assisted in the process of preparing ICME 3 in Karlsruhe in 1976, where Hans-Georg Steiner chaired the International Programme Committee (IPC) and Heinz Kunle chaired the Local Organizing Committee. Hans-Georg had already been a member of the IPC of ICME 1 in Lyon 1969 and ICME 2 in Exeter 1972. He had an enormous influence on the scientific structure of the 1976 congress. A major outcome of the congress was the book “New Trends in Mathematics Education” (Christiansen and Steiner, 1979), which was published and disseminated by UNESCO in addition to the proceedings (Athen and Kunle, 1977). Other than traditional proceedings with many single papers the book contains 13 chapters with survey reports attempting to summarize and identify major trends in mathematics education. These chapters were based on group work that started one year before the congress. Hans-Georg Steiner continued his collaboration with UNESCO and shared with this organization the goal of the global development of mathematics education as a practice as well as a scientific discipline with a clear responsibility of the developed countries for the developing ones.

Fig. 1

H.-G. Steiner at a conference in Oberwolfach in December 1975

Together with Benno Artmann and Arnold Kirsch, Hans-Georg Steiner had been the editor of the book series “Moderne Mathematik in elementarer Darstellung” published by Vandenhoeck and Ruprecht in Göttingen. The title of this series “Modern Mathematics in an Elementary Exposition” stands for its program, namely supporting teachers and teacher educators with elementarized modern mathematics. Volume 22 of the series was published in 1988 on the occasion of Hans-Georg Steiner’s 60th birthday. It was edited by Hans-Joachim Vollrath and contained reprints of eight of Steiner’s papers (Vollrath, 1988). The deliberate focus was Steiner’s contributions to the New Math reform (six papers from the 1960s). It further contained his 1976 paper on mathematization and a paper about philosophy and mathematics (Steiner, 1976a, 1985). The latter papers tentatively indicate a shift of his scientific interests and scientific networks, which had taken place during his work as a director of the IDM since 1973. This is also evident from the programmatic title of a new book series starting 1985 with Vandenhoeck and Ruprecht that he edited together with Michael Otte (IDM Bielefeld) and Ivo Schneider (München) called “Studien zur Wissenschafts-, Sozial- und Bildungsgeschichte der Mathematik” [Studies on the social, scientific and educational history of mathematics].

Hans-Georg Steiner fertilised the IDM with his broad international contacts and cooperations, which he extended and deepened over 20 years. Many young as well as already well-established international researchers visited the IDM. Hans-Georg was eager to communicate and popularize research results of all working groups of the IDM to a wide national and international community (see Sect. 3.3). He motivated and actively supported young researchers in the IDM and beyond to build and foster their international relations. Both authors of this paper are very grateful to him for his encouragement and assistance in this respect.

His international relations also were of great assistence when the IDM slipped into an existence crisis around 1991–1992. The national and international support for the IDM is documented in an IDM-Occasional Paper (Steiner, 1992).

In honour of his 60th birthday, Heinz Griesel (Kassel) and Roland Fischer (Klagenfurt) edited a special issue of ZDM (Griesel and Fischer, 1988). Griesel’s (1988) and Fischer’s (1988) papers on Hans-Georg Steiner as “the engine of reform”, respectively, “the engine of networking” pointedly characterize him before and after joining the IDM. Norbert Knoche (1988) in his homage concentrated on Hans-Georg Steiner’s early years and also described his later shifts of interest. More related to his IDM years, a collection of papers from a colloquium on the occasion of his birthday was also published (Winkelmann, 1988).

However, a stable interest and characteristic feature of Hans-Georg Steiner was his integrated understanding of mathematics teaching, didactics of mathematics, research and society that Fischer (1988, p. 171) characterizes as dynamic-procedural and open, pluralistic-integrative, connecting content and social aspects as well as theory and practice. This inclusive view of mathematics and its teaching and learning influenced and was obviously shared by colleagues around the world as the two papers by Ubiratan D’Ambrosio from Brazil and Shlomo Vinner from Israel in this volume indicate.

From 1984 onwards, his interest in developing and structuring the discipline of mathematics education let him create a series of international conferences and co-operations under the title of TME—“Theory of Mathematics Education” (see Sect. 3.4). Hans-Georg Steiner’s 65th birthday and retirement coincided with IDM’s 20th birthday, which gave rise to the volume “Didactics of Mathematics as a Scientific Discipline” edited by the four core members of his working group “F3” at the IDM at that time (Biehler, Scholz, Sträßer, & Winkelmann, 1994).

3.2 Working group F3: mathematics education at upper secondary level

Hans-Georg Steiner’s scientific activities related to mathematics education at upper secondary level are less well known than his outstanding contributions to the New Math reform movement and to related theories of mathematics education. The German upper secondary level consisted of two major strands. The Gymnasium [grammar school] was supposed to provide “higher general education” for those students intending to go to university. Vocational schools, which were attended by more than 75% of the students, were supposed to provide vocational education including components of higher general education.

The gap between vocational schools and general education at the Gymnasium was large, and the federal state of North-Rhine-Westfalia established a large model project [Modellversuch Kollegschule], where new types of schools were founded that were supposed to create curricula with the intention to combine general and vocational education. A central aim of these schools was to improve social mobility and contributing to participatory democratic education. Moreover, mathematics became part of the cluster mathematics/computer science/philosophy and relations between these subjects had to be reflected in the curricula. Hans-Georg Steiner became the scientific advisor for mathematics in this model project and regarded vocational education as part of the domain of his research group on upper secondary education. Rudolf Sträßer became a member of Steiner’s group at the IDM and his major responsibility was mathematical education in vocational schools (see his contribution to this volume).

In his engagement in the New Math reform movement in the 1960s, Hans-Georg Steiner had contributed many papers with didactically oriented subject matter analyses [stoffdidaktische Analysen]. His relations to the reforms of the late 1970s, however, were partly more indirect, critical, moderating, analytical and reflective than directly constructive by means of providing teaching examples, didactical analyses or didactical visions.

His evaluation of the failure of the somewhat top down New Math reform in the 1960s led him to two major consequences: recognizing a need for more fundamental research and a recognition of mathematics education from a systems perspective, including the school system, the teacher education system and didactics of mathematics at university level.

Hans-Georg Steiner became convinced that any curriculum development has to be based on fundamental research addressing questions such as

• What is mathematics, what is mathematical thinking?

• What is the role of mathematics in other sciences or in society, for people in everyday life and at their workplace?

• What were determinants of the development of mathematical curricula in the past?

• What are conditions for innovation in educational systems?

• What knowledge of mathematics and of didactics of mathematics do teachers need?

• How can mathematics education contribute to the general goals that were set up for education at upper secondary level?

• How can goals for mathematics education be justified?

These fundamental questions were related to the Zeitgeist of those years and of the IDM in particular: people felt the need for a deeper research base for supporting a scientification of the practice of curriculum design, development, implementation and evaluation.

Although one will hardly find any empirical study among Steiner’s publications, this does not imply that he was not aware of the importance of empirical research in our discipline. On the contrary, several of the young researchers that he had recruited for his group had backgrounds in empirical pedagogy and psychology, among others Roland Scholz (see his contribution to this volume as well as Scholz, 1987, 1991). Hence studies on students’ and teachers’ thinking and on empirical curriculum research became part of F3’s work.

The concrete educational context, in which the working group F3 was situated, was a national agreement between all West German federal states that had been achieved in 1972. It concerned an organizational and curricular reform of upper secondary education for all subjects. A certain specialization and differentiation of students should already start in grade 11. In two major elective subjects, the students were to learn subject matter specific scientific thinking similar to what would later be practised at university. In their minor subjects, basic scientific education [wissenschaftliche Grundbildung] was the objective. An important completely new organizational consequence was that mathematics had to be taught under very different boundary conditions: as an advanced course [Leistungskurs] or as a basic course [Grundkurs]. New curricula, text books and pedagogical approaches had to be developed. This new situation presented a great challenge for curriculum development, for research, and for the development of new didactical theories of upper secondary mathematics education.

While aiming to design a more fundamental research approach, Steiner and his group intended to give partial answers, influence the actual developments and develop a network of co-operation. A series of conferences was organized on the situation of teaching calculus and linear algebra (Conference 10), on didactics of mathematics in the education of future teachers (Conference 12) (Steiner, 1976b), general questions of mathematics education at upper secondary level (Conference 13), and specific topics such as the relation of mathematics education to philosophy (Conference 15) and information technology (Conference 14). Public interventions concerned the “Normenbuch”, i.e., the examination standards for upper secondary final examinations (Conference 9) (Luschberger, Steiner, Stowasser, & Winkelmann, 1975), and a profound critique of a public appeal by scientific organizations (including MNU and DMV) with the title “Save the quality of mathematics and science education” [Rettet die mathematisch-naturwissenschaftliche Bildung] (Steiner, 1982, 1984). Hans-Georg Steiner’s group F3 initiated the DIMGO-Project concerned with differentiation at upper secondary level, which was externally funded. It aimed at empirically researching the state of the art of basic and advanced courses in mathematics by means of analyses of curricula and textbooks, a representative survey of mathematics teachers as well as visits to exemplary classrooms (Conference 20) (Peschek & Steiner, 1982; Pfeiffer & Steiner, 1981; Reiss & Steiner, 1984). The dissertation of Hermann Pfeiffer on the social organization of knowledge in upper secondary mathematics teaching, which Hans-Georg Steiner supervised, was embedded into this work (Pfeiffer, 1981). Subsequently, Steiner’s as well as his group’s attention turned to the development of mathematical competencies at upper secondary level and a collaboration with psychologists and the group of Willibald Dörfler and Werner Peschek in Klagenfurt was established (Conference 22, 25) (Steiner, 1986).

The visible part of Hans-Georg Steiner’s year long co-operation with the ‘Kollegschulversuch’ were two conferences (Conference 14, 15) (Steiner, 1977) and some papers concerning philosophy and mathematics education, an interest that had emerged already during his studies in Münster and that was revived when a co-ordination between philosophy and mathematics curricula in the Kollegschule was put on the agenda. The focus of the second conference in September 1977 was on the relation between mathematics and information technology. Although the use of technology is not addressed in his publications, Hans-Georg regarded research in this domain as a responsibility of the IDM. He supported pertinent research and development in his working group F3 very early (see e.g. Biehler, Rach, & Winkelmann, 1988; Biehler & Winkelmann, 1988; Winkelmann, 1982) and advocated in vain that a vacant professorship at the IDM should be devoted to technology in mathematics education. The first ICMI study was devoted to the influence of computers in mathematics education and the study conference took place in Strasbourg 1985. Not only did he initiate a German preparatory conference for this study in the Mathematical Research Centre in Oberwolfach in fall 1984, but also the majority of his working group attended the conference (Biehler, Sträßer, & Winkelmann, 1986). For all three group members, research and development related to the use of technology in mathematics classrooms became a major focus of their research at a later stage. Furthermore, the contact to David Tall was established through this conference in Strasbourg (see the paper by Tall in this volume).

Hans-Georg Steiner’s engagement and support of vocational education went beyond the consultancy for the Kollegschule model project. Together with Rudolf Sträßer he succeeded in attracting financial support for a project that focussed on curriculum development and research for vocational schools (Steiner & Sträßer, 1980, 1981; see also Rudolf Sträßer’s contribution to this volume).

From about the mid 1980s onwards, Steiner’s scientific focus on upper secondary mathematics education diminished and he put his energy into developing the international TME program and into fostering collaboration in didactics of mathematics in Germany. The members of his group developed and elaborated their own fields of research and scientific networks. Despite this growing diversity, the personal collaboration, co-operation and mutual encouragement in his group F3 functioned well. While Hans-Georg Steiner did not make his working group at the IDM a ‘scientific school’ in the sense of a concise shared focus on methods and scientific objects, his extremely broad knowledge, overview and theoretical interests in the didactics of mathematics as well as his liberal personal and scientific attitude resulted in a working environment, where individual specialization and development was possible and strongly supported.

3.3 Internationalization

As has been expressed earlier, Hans-Georg Steiner supported and co-shaped the international relations of the IDM and worked for the aim of making German didactics of mathematics as a whole internationally visible and competitive. Among other institutes, the IDM was founded to develop international relations, therefore time and financial resources were available for this purpose. The conferences which Hans-Georg organized show only the most visible part of these activities. In the early years, co-operations with UNESCO and ICMI, whose vice-president he was from 1975 to 1978, were supportive of these activities.

Nowadays, when TIMSS and PISA have become very influential in educational policy (at least in Germany) it seems relevant to remember that in a certain respect, Steiner became involved in the “Second International Mathematics Study” (SIMS) (http://www.iea.nl/sims.html). Germany, however, did not participate in SIMS for reasons unclear to the authors of this paper.

The “First International Mathematics Study” had been criticized severely by Freudenthal (1975) and others with regard to curricular validity and the comparability of results. As part of SIMS and as a consequence of the critique on FIMS a broad comparative study of curricula was initiated and Steiner invited representatives of many countries, SIMS researchers and curriculum researchers to a conference on “Comparative Studies of Mathematics Curricula—Change and Stability 1960–1980” (Conference 18) and also to conferences of related topics (Conference 19, and later Conference 29), where the topic was not only discussed from the SIMS perspective but also from a more fundamental point of view of research on curriculum change (Steiner, 1980). The subtitle of the first conference was “From Royaumont to Ohrbeck”. The seminar on “New Thinking in School Mathematics” had taken place in Royaumont near Paris in September 1959 (OECD, 1961) and was considered as the signal event for the world-wide New Math reform in the 1960s (also famous for Jean Dieudonné’s legendary “Euclide must go” lecture). While the subtitle may sound a little bit overambitious today, it highlights the intention to create a science-based approach to curriculum development trying to learn from the failures of the past. Importantly, research on curriculum change and on curricular innovation was to become a research domain of its own.

With regard to a more active participation, a certain reservation against studies such as SIMS and later TIMSS was persistently shared in the IDM in those days.

Another large conference in the early years of Hans-Georg Steiner’s work at the IDM was the conference on “Co-operation between Science Teachers and Mathematics Teachers” in 1978 (Conference 17), which was organized in co-operation with ICMI and UNESCO. This conference—originally planned for developing joint teaching units—was partly transformed by him into a research conference that also discussed social and epistemological conditions for co-operation (Steiner, 1979).

From 1986 until 1992 Hans-Georg Steiner organized a series of bilateral conferences with Italian colleagues (Conference 33, 40) together with Luciana Bazzini (Bazzini & Steiner, 1989, 1994), with French researchers together with Colette Laborde (Laborde, 1988) (Conference 28) (see the contributions by Bazzini, Bartolini-Bussi and Laborde in this volume) and with colleagues from former Czechoslovakia (Conference 32, 36). He attracted financial support for these conferences from the German Research Foundation (DFG) and the respective research foundations in the other countries. At the time of writing, as we look forward to the 5th “Congress on European Research in Mathematics Education” (CERME), European scientific exchange has become well-developed. In the 1980s this was not yet the case.

Fig. 2

H.-G. Steiner at a conference in Karlovy Vary in 1988

3.4 Theory of mathematics education (TME)

In his activities and papers on TME, Hans-Georg Steiner convincingly argued for an interdisciplinary and transdisciplinary approach to the didactics of mathematics integrating the philosophy and history of mathematics, subject matter specific didactical analyses, curriculum research, research from cognitive psychology and theories of teaching and learning (Steiner, 1987, 1988). He aimed at structuring the discipline and at clarifying the relationships to other disciplines. A visible trace of Hans-Georg’s initiatives are the five TME conferences he organized between 1984 and 1991 (Conference 24, 26, 30, 35, 39) and his many related publications (e.g. see Steiner & Vermandel, 1988; Vermandel, 1988). We have already pointed out that his interest in this domain originated much earlier and was also related to the institutional function of the IDM.

Hans-Georg Steiner’s work is still influential and has been re-discovered in recent work as Törner and Sriraman describe in their contribution to this volume. The need for a meta-scientific framework for structuring, classifying and orienting the fast growing body of research in mathematics education is of ongoing relevance. The holistic and comprehensive approach that Hans-Georg Steiner courageously attempted to realize may have been historically ahead of its time. Nevertheless, we are missing his overall perspective. At the time of writing, producing scientific results in concise domains or relating research too closely to current political developments in the educational system is more en vogue than reflecting on our discipline’s development. Hans-Georg not only argued for the need for this reflection. He saw meta-scientific reflection as a difficult but crucial research duty of the community itself. This can be considered as one of the legacies of Hans-Georg Steiner’s work, which hopefully will influence the future development of our discipline.

The conferences as such and Hans-Georg’s related activities often functioned as a catalyst and encouragement of theory-aware developments and active involvement in shaping didactics of mathematics as a scientific discipline (see Gilah Leder’s contribution to this volume). The contribution of Gila Hanna, who was invited by Steiner to stay at the IDM for some weeks in the 1980s, is one of the many cases, where networks were established and elaborated (see her paper together with Nathan Sidoli in this volume). David Tall, in this volume, exemplarily describes how a visit at the IDM stimulated his theoretical orientation and Juan Godino, Carmen Batanero and Vicenç Font describe Hans-Georg’s influence on the emergence of theoretical approaches in the didactics in Spain. In 1994, Batanero, Godino, Steiner and Wenzelburger (1994) had documented international activities concerning the training of young researchers in mathematics education, where an overall perspective of TME is essential. However, although there had been long lasting discussions about establishing a postgraduate study program at the IDM itself, the decision patterns and processes were too complex for that it was realized in time.

3.5 Buildings networks and supporting research collaboration in German didactics of mathematics

Concurrently to elaborating the TME program, Hans-Georg Steiner aimed at supporting research collaboration in German didactics. Together with Heinrich Winter, who at that time was the president of the “Gesellschaft für Didaktik der Mathematik” [“Association for the Didactics of Mathematics” in German speaking countries], he organized two conferences on the relationship between didactics of mathematics and history of education and science (Conference 23, 27) (Steiner, 1990; Steiner & Winter, 1985). Later, two conferences were particularly devoted to scientific exchange and collaboration between young German researchers of that time (Conference 37, 41) (Steiner & Vollrath, 1995).

A specific concern of Hans-Georg Steiner was the promotion of co-operation between West German and East German mathematics educators. Even before the fall of the Berlin wall in 1989, Steiner managed to establish some relations with colleagues from East Germany. Soon after the border between the two German countries was open, he began to plan the first “German-German-Bilateral Conference on Didactics of Mathematics”. This fits well into his series of bilateral conferences with mathematics educators from Italy, France, and Czechoslovakia. However, it turned out that the German reunification process ran faster than the conference preparation. The conference took place in October 21–28, about three weeks after the 3rd October 1990—the day of the German reunification (Conference 37). Unfortunately, Hans-Georg had to go to hospital in the week of this conference and Bernard Winkelmann and Rolf Biehler took over responsibility and chaired the conference.

Hans-Georg Steiner resumed his interest in fostering East-West-German collaboration after his retirement. In 1996, he organized a double conference together with Werner Walsch (Conference 42) reflecting on the very different developments of didactics of mathematics in both parts of our country. His encroaching illness overshadowed the production process of the proceedings. In the early 2000s Peter Bender and Herbert Henning took over as editors, and on the occasion of his upcoming 75th birthday the proceedings (Henning & Bender, 2003) dedicated to Hans-Georg, were presented to him. At that point in time the consequences of his severe illness had already taken its toll. Fortunately, he had communicated to his wife early enough his wish that his library with numerous books, papers, journals and materials covering four decades of mathematics education be left to a university in one of the new federal states that used to belong of the former German Democratic Republic, in order to support the education of young teachers and researchers in the new states. Today, the Martin-Luther-University in Halle-Wittenberg, in particular our colleague Wilfried Herget, is taking care of this legacy.

Fig. 3

In summer 2003 when he was presented the proceedings edited by Henning & Bender

Appendices

Appendix 1

1.1 List of Hans-Georg Steiner’s Publications

• 1. Steiner, H.-G. (1956). Bewegungsgeometrische Lösung einer Dreieckskonstruktion. Mathematisch-Physikalische Semesterberichte, 5 (1/2), 132–137.

• 2. Behnke, H. & Steiner, H.-G. (1956a). Der Begriff des Vektors in der wissenschaftlichen Literatur. Teil 1. Der Mathematikunterricht, 2 (1), 5–23.

• 3. Behnke, H. & Steiner, H.-G. (1956b). Der Begriff des Vektors in der wissenschaftlichen Literatur. Teil 2. Der Mathematikunterricht, 2 (4), 65–92.

• 4. Steiner, H.-G. (1957). Einführung in die Relationstheorie. Mathematisch-Physikalische Semesterberichte, 5 (3/4), 261–271.

• 5. Pickert, G. & Steiner, H.-G. (1958). Komplexe Zahlen und Quaternionen. In H. Behnke et al. (Eds.), Grundzüge der Mathematik I (pp. 469–497). Göttingen: Vandenhoeck & Ruprecht.

• 6. Steiner, H.-G. (1959). Das moderne mathematische Denken und die Schulmathematik. Der Mathematikunterricht, 5 (4), 5–79.

• 7. Steiner, H.-G. (1959/60). Das Turmproblem als Veranschaulichung der Divergenz der harmonischen Reihe. Der mathematisch-naturwissenschaftliche Unterricht, 12 (5), 224–225.

• 8. Steiner, H.-G. (1960). Eine statische Deutung gewisser unendlicher Reihen. Mathematisch-Physikalische Semesterberichte, 7 (1), 101–107.

• 9. Freudenthal, H. & Steiner, H.-G. (1960). Gruppentheorie und Geometrie. In H. Behnke et al. (Eds.), Grundzüge der Mathematik II (pp. 403–421). Göttingen: Vandenhoeck & Ruprecht.

• 10. Steiner, H.-G. (1960/61). Ist ein Produkt Null, so ist wenigstens ein Faktor Null. Der mathematisch-naturwissenschaftliche Unterricht, 13, 408–412.

• 11. Behnke, H. & Steiner, H.-G. (1961). Der Mathematikunterricht und die Hochschulreife. Mathematisch-Physikalische Semesterberichte, 7 (2), 213–223.

• 12. Steiner, H.-G. (1961a). Logische Probleme im Mathematikunterricht: Die Gleichungslehre. Mathematisch-Physikalische Semesterberichte, 7 (2), 178–207.

• 13. Steiner, H.-G. (1961b). Ansatzpunkte für logische Betrachtungen und Übungen im Unter- und Mittelstufenunterricht. Der Mathematikunterricht, 7 (1), 79–112.

• 14. Steiner, H.-G. (1962a). Elementare Logik und Wahrscheinlichkeitstheorie. Der Mathematikunterricht, 8 (1), 16–38.

• 15. Steiner, H.-G. (1962b). Die Verbindung von Logik und Mathematik im mathematischen Unterricht. Mathematisch-Physikalische Semesterberichte, 9 (1), 74–95.

• 16. Steiner, H.-G. (1962c). Die Behandlung des Funktionsbegriffs in der höheren Schule. L’enseignement mathématique, 2 ^e Série, 8 (1), 62–92.

• 17. Steiner, H.-G. (1963). Explizite Verwendung der reellen Zahlen in der Axiomatisierung der Geometrie. Der Mathematikunterricht 9 (4), 66–87.

• 18. Steiner, H.-G. (1964a). Frege und die Grundlagen der Geometrie I. Mathematisch-Physikalische Semesterberichte, 10 (1), 35–47.

• 19. Steiner, H.-G. (1964b). Moderne begriffliche Methoden bei der Behandlung der komplexen Zahlen. Der Mathematikunterricht, 10 (2), 5–35.

• 20. Steiner, H.-G. (1964c). Elementare Beweise zum Fundamentalsatz der Algebra. Der Mathematikunterricht, 10 (2), 60–93.

• 21. Steiner, H.-G. (1964d). Kardinal- und Ordinalzahlen. In H. Behnke, R. Remmert, H.-G. Steiner & H. Tietz (Eds.) Fischer-Lexikon Mathematik I, Bd. 29 (pp. 166–196). Frankfurt: Fischer Taschenbuch Verlag.

• 22. Steiner, H.-G. (1964e). Logik und Methodologie. In H. Behnke, R. Remmert, H.-G. Steiner & H. Tietz (Eds.) Fischer-Lexikon Mathematik I, Bd. 29 (pp. 196–227). Frankfurt: Fischer Taschenbuch Verlag.

• 23. Steiner, H.-G. (1964f). Mathematische Grundlagenforschung. In H. Behnke, R. Remmert, H.-G. Steiner & H. Tietz (Eds.) Fischer-Lexikon Mathematik I, Bd. 29 (pp. 227–246). Frankfurt: Fischer Taschenbuch Verlag.

• 24. Steiner, H.-G. (1964g). Mengen, Abbildungen, Strukturen. In H. Behnke, R. Remmert, H.-G. Steiner & H. Tietz (Eds.) Fischer-Lexikon Mathematik I, Bd. 29 (pp. 246–292). Frankfurt: Fischer Taschenbuch Verlag.

• 25. Steiner, H.-G. (1964h). Relations and functions. Mathematics today. Proceedings of an International Working Session on New Teaching Methods for School Mathematics, Athens 1963 (pp. 165–181). Paris: OECD.

• 26. Steiner, H.-G. (1964i). Relations and functions. Mathematics today. The Mathematics Teacher, 57 (3), 251–257.

• 27. Steiner, H.-G. (1964/1965a). Menge und Struktur als Leitlinie für den mathematischen Unterricht I. Der mathematisch-naturwissenschaftliche Unterricht, 17 (5), 199–205.

• 28. Steiner, H.-G. (1964/1965b). Menge und Struktur als Leitlinie für den mathematischen Unterricht II. Der mathematisch-naturwissenschaftliche Unterricht, 17 (6), 259–266.

• 29. Steiner, H.-G. (1965a). Frege und die Grundlagen der Geometrie II. Mathematisch-Physikalische Semesterberichte, 10 (2), 175–186.

• 30. Steiner, H.-G. (1965b). Wie steht es mit der Modernisierung unseres Mathematikunterrichts? Mathematisch-Physikalische Semesterberichte, 11 (2), 186–200.

• 31. Steiner, H.-G. (1965c). Menge, Struktur, Abbildung als Leitbegriffe für den modernen mathematischen Unterricht. Der Mathematikunterricht, 11 (1), 5–19.

• 32. Steiner, H.-G. (1965d). Zur Didaktik der elementaren Gruppentheorie I. Der Mathematikunterricht, 11 (2), 20–39.

• 33. Steiner, H.-G. (1965e). Kalküle und Rechenautomaten im Unterricht. Der Mathematikunterricht, 11 (2), 100–109.

• 34. Steiner, H.-G. (1965f). Mathematische Grundlagenstandpunkte und Reform des Mathematikunterrichts. Mathematisch-Physikalische Semesterberichte, 12 (1), 1–22.

• 35. Steiner, H.-G. (1965g). Quadratische Gleichungen und Quadratwurzelfunktionen in Körpern. Mathematisch-Physikalische Semesterberichte, 12 (2), 211–229.

• 36. Steiner, H.-G. (1966a). Vektorraum, affine Geometrie, Abbildungen. Der Mathematikunterricht, 12 (1), 16–31.

• 37. Steiner, H.-G. (1966b). Komplexe Zahlen, Quaternionen, Vektorrechnung. Der Mathematikunterricht, 12 (1), 75–99.

• 38. Steiner, H.-G. (1966c). Anwendung der komplexen Zahlen im Physikunterricht. Der Mathematikunterricht, 12 (1), 45–54.

• 39. Steiner, H.-G. (1966d). Verschiedene Aspekte der axiomatischen Methode im Unterricht. Les Repercussions de la Recherche Mathématique sur l’Enseignement (pp. 31–70). Luxemburg.

• 40. Steiner, H.-G. (1966e). Einfache Verknüpfungsgebilde als Vorfeld der Gruppentheorie. Der Mathematikunterricht, 12 (2), 5–18.

• 41. Steiner, H.-G. (1966f). Relaciones y Funcions. Elementos Revista de Matematica para la Ensenanza media, 3 (4), 64–69.

• 42. Steiner, H.-G. (1966g). Mathematisierung und Axiomatisierung einer politischen Struktur. Der Mathematikunterricht, 12 (3), 66–86.

• 43. Steiner, H.-G. (1966h). Möglichkeiten zur Überwindung der doppelten Diskontinuität im Fachstudium der Mathematiklehrer (pp. 121–142). Düsseldorf: Universität und Studienseminar.

• 44. Steiner, H.-G. (1966i). Äquivalente Fassungen des Vollständigkeitsaxioms für die Theorie der reellen Zahlen. Mathematisch-Physikalische Semesterberichte, 13 (2), 180–201.

• 45. Steiner, H.-G. (1966j). Vorlesung über Grundlagen und Aufbau der Geometrie in didaktischer Sicht. Münster.

• 46. Steiner, H.-G. (1966k). A rigorous teacher training program. Mathematical education in the Americas II. In A report of the second Inter-American Conference on Mathematical Education, Lima, December 4–12, 1966 (pp. 246–261).

• 47. Freudenthal, H. & Steiner, H.-G. (1966). Aus der Geschichte der Wahrscheinlichkeitstheorie und der mathematischen Statistik. In H. Behnke et al. (Eds.), Grundzüge der Mathematik IV (147–195). Göttingen: Vandenhoeck & Ruprecht.

• 48. Steiner, H.-G. (1967a). Zur Behandlung des Funktionsbegriffs. In H. Behnke & H.-G. Steiner (Eds.), Mathematischer Unterricht an deutschen Universitäten und Schulen (pp. 131–171). Göttingen: Vandenhoeck & Ruprecht.

• 49. Steiner, H.-G. (1967b). Zum Aufbau einer Vorlesung über “Analysis in didaktischer Sicht”. In H. Behnke & H.-G. Steiner (Eds.), Mathematischer Unterricht an deutschen Universitäten und Schulen (pp. 265–286). Göttingen: Vandenhoeck & Ruprecht.

• 50. Steiner, H.-G. (1967c). Algebra im Unterricht der Oberstufe der Gymnasien. In H. Behnke & H.-G. Steiner (Eds.), Mathematischer Unterricht an deutschen Universitäten und Schulen (pp. 317–335). Göttingen: Vandenhoeck & Ruprecht.

• 51. Steiner, H.-G. (1967d). Compte-Rendue sur l’introduction de la notion de groupe et du calcul dans les groupes pour les 3me et 4me classe des Gymnases. Mathematica & Paedagogia, 30, 74–90.

• 52. Steiner, H.-G. (1967e). Bemerkungen zur Modernisierung des Mathematikunterrichts. Jahresbericht 1966/67 Bundesgymnasium für Mädchen in Wiener Neustadt, (pp. 12–16). Wien.

• 53. Steiner, H.-G. (1967f). Historische Bemerkungen zur vollständigen Induktion und zur Charakterisierung der natürlichen Zahlen. Der Mathematikunterricht, 13 (3), 81–97.

• 54. Steiner, H.-G. (1967g). Körper, in denen −1 nicht Quadratelement ist. Elemente der Mathematik, 22 (5), 97–102.

• 55. Steiner, H.-G. (1967h). Operational Systems and Checker Games. The Mathematics Teacher, 60 (8), 832–836.

• 56. Steiner, H.-G. (1967i). Relationstheoretische Darstellung der Aristotelischen Syllogistik. Der Mathematikunterricht, 13 (5), 23–36.

• 57. Steiner, H.-G. (1967j). Eine mathematische Theorie der Rangordnungen und Konsensus-Rangordnungen. Mathematisch-Physikalische Semesterberichte, 14 (2), 212–245.

• 58. Steiner, H.-G. (1967k). Sur l’enseignement de la théorie élémentaire des groupes et leurs applications. In International Committee of Mathematical Instruction (ICMI) (Ed.), New Trends in Mathematics Teaching, Volume I (pp. 332–348). Paris: UNESCO.

• 59. Steiner, H.-G. (1967l). Critica dei fondamenti. Matematica 1. Milano.

• 60. Steiner, H.-G. (1967m). Insiemi, rappresentazioni, strutture. Matematica 1. Milano.

• 61. Steiner, H.-G. (1967n). Logica e metodologica. Matematica 1. Milano.

• 62. Steiner, H.-G. (1967o). Numeri cardinali e ordinali. Matematica 1. Milano.

• 63. Secondary School Mathematics Curriculum in cooperation with H.-G. Steiner et al. (Ed.) (1967a). Unified Modern Mathematics, Course I, Part I. (Revised Edition). New York: Board of Trustees of Teacher College Columbia University.

• 64. Secondary School Mathematics Curriculum in cooperation with H.-G. Steiner et al. (Ed.) (1967b). Unified Modern Mathematics, Course I, Part II. (Revised Edition). New York: Board of Trustees of Teacher College Columbia University.

• 65. Secondary School Mathematics Curriculum in cooperation with H.-G Steiner et al. (Ed.) (1967c). Unified Modern Mathematics, Course II, Part I. (Revised Edition). New York: Board of Trustees of Teacher College Columbia University.

• 66. Secondary School Mathematics Curriculum in cooperation with H.-G. Steiner et al. (Ed.) (1967d). Unified Modern Mathematics, Course II, Part II. (Revised Edition). New York: Board of Trustees of Teacher College Columbia University.

• 67. Steiner, H.-G. (1968). Examples of exercises in mathematization on the secondary school level. Educational Studies in Mathematics, 1 (1/2), 181–201.

• 68. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1968). Mathematical Induction and Recursive Definition. St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 69. Steiner, H.-G. (1969a). Examples of exercises in mathematization. An extension of the theory of voting bodies. Educational Studies in Mathematics, 1 (3), 289–299.

• 70. Steiner, H.-G. (1969b). Elementare moderne Algebra. In Die Neugestaltung des Mathematikunterrichts an den höheren Schulen (pp. 48–65), Stuttgart: Klett.

• 71. Steiner, H.-G. (1969c). Geometry in school programmes. Regional Seminar Cairo (pp. 77–113). Paris: UNESCO.

• 72. Steiner, H.-G. (1969d). Aus der Geschichte des Funktionsbegriffs. Der Mathematikunterricht, 15 (3), 13–39.

• 73. Steiner, H.-G. (1969e). Eine mathematische Theorie der Abstimmungsgremien. Darmstadt: TU Darmstadt.

• 74. Steiner, H.-G. (1969f). Elaboration de la géométrie élémentaire sur la base de groupes d’applications. Mathématiques du 20e siècle, 14, 77–88.

• 75. Steiner, H.-G. (1969g). Représentation de la syllogistique aristotélicienne sur la base de la théorie des relations. Mathématiques du 20e siècle, 14, 89–102.

• 76. Steiner, H.-G. (1969h). Entwicklungstendenzen in der Didaktik der Mittelstufenalgebra. Zentralblatt für Didaktik der Mathematik, 1 (1), 2–3.

• 77. Steiner, H.-G. (1969i). Magnitudes and rational numbers—a didactical analysis. Educational Studies in Mathematics, 2 (2/3), 371–392.

• 78. Steiner, H.-G. (1969j). Checker games in operational systems as media for an inductive approach to teaching algebra. Educational Studies in Mathematics, 1 (4), 445–483.

• 79. Kaufmann, B. & Steiner, H.-G. (1969a). The CSMP approach to a content-oriented highly individualized mathematics education. Educational Studies in Mathematics, 1 (3), 312–326.

• 80. Steiner, H.-G. (1970a). Zur Wissenschaftstheorie und Philosophie der Mathematik: Mengenlehre und Platonismus. Beiträge zum mathematisch-naturwissenschaftlichen Unterricht 18, 17–26. Hannover: Franzbecker.

• 81. Steiner, H.-G. (1970b). Aufgaben und Pläne des Zentrums für Didaktik der Mathematik in Karlsruhe. Der mathematisch-naturwissenschaftliche Unterricht, 23, 183–185.

• 82. Steiner, H.-G. (1970c). Aufgaben und Pläne des Zentrums für Didaktik der Mathematik in Karlsruhe. In Beiträge zum Mathematikunterricht 1969 (pp. 71–74). Hannover: Schroedel.

• 83. Steiner, H.-G. (1970d). Some aspects of modern pedagogy of mathematics. The Mathematics Teacher 63 (5), 441–445.

• 84. Steiner, H.-G. (1970e). Quadratic equations and square root functions in fields. In International committee of mathematical instruction (ICMI) (Ed.), New Trends in Mathematics Teaching II (pp. 291–308). Paris: UNESCO.

• 85. Steiner, H.-G. (1970f). Analysen von Lehrbüchern der Geometrie für die Mittelstufe der Gymnasien. Zentralblatt für Didaktik der Mathematik, 2 (1), 11–15.

• 86. Secondary School Mathematics Curriculum in cooperation with H.-G. Steiner et al. (Ed.) (1970a). Unified Modern Mathematics, Course III, Part I. (Revised Edition). New York: Board of Trustees of Teacher College Columbia University.

• 87. Secondary School Mathematics Curriculum in cooperation with H.-G. Steiner et al. (Ed.) (1970b). Unified modern mathematics, course III, Part II. (Revised Edition). New York: Board of Trustees of Teacher College Columbia University.

• 88. Kaufmann, B. & Steiner, H.-G. (1970). Comprehensive school mathematics program (CMSP). Individualized mathematics education. In International Committee of Mathematical Instruction (ICMI) (Ed.), New Trends in Mathematics Teaching II (pp. 214–222). Paris: UNESCO.

• 89. Steiner, H.G. (Ed.) (1971a). The Teaching of Geometry at the Pre-College Level. Dordrecht: Reidel.

• 90. Steiner, H.-G. (1971b). A foundation of Euclidean geometry by means of congruence mappings. Educational Studies in Mathematics, 4 (1), 87–90.

• 91. Steiner, H.-G. (1971c). Zur Situation der Didaktik der Mathematik in der Bundesrepublik Deutschland. Die Schulwarte, 24 (10/11), 1–2.

• 92. Secondary School Mathematics Curriculum in Cooperation with H.-G. Steiner et al. (Ed.) (1971). Unified Modern Mathematics, course IV, Part I. (Revised Edition). New York: Board of Trustees of Teacher College Columbia University.

• 93. Steiner, H.-G. (1972a). Funktion. In Historisches Wörterbuch der Philosophie, Bd. 2 (Spalte 1138–1139). Basel/Stuttgart: Schwabe.

• 94. Steiner, H.-G. (1972b). Mathematik und Bildung. In H. Meschkowski (Ed.), Grundlagen der modernen Mathematik (pp. 310–340). Darmstadt: Wissenschaftliche Buchgesellschaft.

• 95. Steiner, H.-G. (1972c). Moderne algebra in de determinatiecyclus: Vierkantswortelfuncties in een willekeurig veld. Nico, 11, 97–106.

• 96. Steiner, H.-G. (1972d). Algébre moderne dans l’enseignement secondaire. Fonctions “racine-carrée” dans un champ quelconque. Nico, 12, 35–47.

• 97. Steiner, H.-G. (1972e). Mengen im Aufbau der Mathematik. Pädagogische Welt, 26 (10), 596–604.

• 98. Steiner, H.-G. (1972f). Einschränkungen zur Omnipotenz der Mengenlehre. Pädagogische Welt, 26 (12), 721–723.

• 99. Steiner, H.-G. (1972g). Mengen im mathematischen Unterricht: Eine kritische Abgrenzung. Pädagogische Welt, 26 (12), 729–736.

• 100. Secondary School Mathematics Curriculum in Cooperation with H.-G. Steiner et al. (Ed.) (1972a). Unified Modern Mathematics, Course IV, Part II. (Revised Edition). New York: Board of Trustees of Teacher College Columbia University.

• 101. Secondary School Mathematics Curriculum in cooperation with H.-G., Steiner et al (Ed.) (1972b). Unified Modern Mathematics, Course V, Part II. (Revised Edition). New York: Board of Trustees of Teacher College Columbia University

• 102. Steiner, H.-G. (1973a). Mathematik im ersten Schuljahr. In Beiträge zum Mathematikunterricht 1972/1973, (pp. 98–119). Hannover: Schroedel.

• 103. Steiner, H.-G. (1973b). “Unendlich” in Algebra und Analysis. Der Mathematikunterricht, 19 (4), 35–63.

• 104. Steiner, H.-G. (1973c). Der Minicomputer von Papy als Piagetsche Gruppierung. Didaktik der Mathematik, 1 (2), 131–142.

• 105. Steiner, H.-G. (1973d). Bemerkungen zur Wittmannschen Axiomatisierung des Gruppierungsbegriffs von J. Piaget und Hinweise auf weitere pädagogisch relevante Modelle. Die Schulwarte, 26 (8/9), 95–102.

• 106. Steiner, H.-G. (1973e). Mathematische Präzisierungen und didaktisch relevante Modelle zum Piagetschen Gruppierungsbegriffs. Didaktik der Mathematik, 1 (3), 210–225.

• 107. Steiner, H.-G. (1973f). Recent developments in pre-service and in-service training of mathematics teachers in the FRG. Zentralblatt für Didaktik der Mathematik, 5 (3), 119–120.

• 108. Steiner, H.-G. (1973g). Analyse mathématique du concept du groupement de Piaget. Le minicomputer de Papy comme groupement. Nico, 15, 77–94.

• 109. Steiner, H.-G. (1973h). Algebraische Spiele 1. Stuttgart: Klett.

• 110. Steiner, H.-G. et al. (1973). Algebra. In International Committee of Mathematical Instruction (ICMI) (Ed.), New Trends in Mathematics Teaching, Vol. III (pp. 13–24). Paris: UNESCO.

• 111. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1973a). Elements of Mathematics, Book O: Operational Systems (Chapt. 1). St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 112. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1973b). Elements of Mathematics, Book O: Sets, Subsets and Operations with Sets (Chapt. 3). St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 113. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1973c). Elements of mathematics, book O: Ordered n-tuples (Chapt. 4). St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 114. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1973d). Elements of Mathematics, Book O: Algebra in Operational Systems (Chapt. 10). St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 115. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1973e). Elements of Mathematics, Book O: Geometry: Incidence and Isometries (Chapt. 11). St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 116. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1973f). Elements of Mathematics, Book O: Algebra and Real Valued Functions. (Chapt. 13). St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 117. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1973g). Elements of Mathematics, Book 1: Introductory Logic. St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 118. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1973h). Elements of Mathematics, Book 3: Introduction to Fields. St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 119. Steiner, H.-G. (1974a). Mathematical analysis of Piaget’s grouping concept. Papy’s minicomputer as a grouping. International Journal of Mathematical Education in Science and Technology, 5, 241–250.

• 120. Steiner, H.-G. (1974b). Behandlung der reellen Zahlen im Unterricht. Mitteilungen der österreichischen mathematischen Gesellschaft. Wien.

• 121. Steiner, H.-G. (1974c). Behandlung der reellen Zahlen im Unterricht. Mitteilungen der österreichischen mathematischen Gesellschaft. Zentralblatt für Didaktik der Mathematik, 6 (3), 146–161.

• 122. Steiner, H.-G. (1974d). Qué es la matemática aplicada? In Les aplicaciones en la enceñanza y el aprendizaje de la matemética en la escuela secundaria (pp. 139–153). Montevideo: UNESCO.

• 123. Steiner, H.-G. (1974e). Elementary modern algebra as a significant component in a contemporary secondary school mathematics curriculum. In Proceedings of ICMI-JSME Regional Conference on Curriculum and Teacher Training for Mathematical Education, Tokyo, November 5–9, 1974 (pp. 44–53). Tokyo: National Institute for Educational Research.

• 124. Steiner, H.-G. (1974f). Introduction. In H. Bauersfeld, M. Otte & H.-G. Steiner (Eds.), Proceedings of the ICMI-IDM Regional Conference on the Teaching of Geometry. IDM-Schriftenreihe, Vol. 3 (pp. 5–10). Bielefeld: IDM.

• 125. Steiner, H.-G. (1974g). Bemerkungen zur Wittmannschen Axiomatisierung des Gruppierungsbegriffs von J. Piaget und Hinweise auf weitere pädagogisch relevante Modelle. In Beiträge zum Mathematikunterricht 1973 (pp. 239–246). Hannover: Schroedel.

• 126. Steiner, H.-G., Winkelmann, B. (1974). Aktuelle Probleme des Geometrieunterrichts. Diskussionspunkte während der Bielefelder Geometrie-Tagung. In H. Bauersfeld, M. Otte & H.-G. Steiner (Eds.), Proceedings of the ICM-IDM regional conference on the teaching of geometry. Bericht über die IMUK-IDM Regionaltagung zu Fragen des Geometrieunterrichts. Schriftenreihe des IDM, Band 3 (pp. 287–305). Bielefeld: IDM.

• 127. Exner, R., Karmos, J. S., Kaufmann, B., Steiner, H.-G. & Stephens, L. T. (1974). Elements of Mathematics, Book A: An Introduction to Mathematization: A Theory of Voting Bodies. St. Louis, Missouri: Central Midwestern Regional Educational Laboratory.

• 128. Steiner, H.-G. (1975a). Qué es la matemética aplicada? Conceptos de Matematica, 9 (3), 9–20.

• 129. Steiner, H.-G. (1975b). Nichtmeßbare Abstimmungsgremien. Mathematisch-Physikalische Semesterberichte, 22 (1), 53–67.

• 130. Steiner, H.-G. (1975c). Mathematisierungen, die auf metrische Räume führen. In Les applications nouvelles des mathématiques et l’enseignement secondaire (pp. 125–147). Esch-sur-Alzette (Luxembourg): Imprimerie Victor.

• 131. Steiner, H.-G. (1975d). Zum Aufbau des Instituts für Didaktik der Mathematik (IDM) in Bielefeld. Ziele und Möglichkeiten des Instituts in der gegenwärtigen Situation. Zentralblatt für Didaktik der Mathematik, 7 (2), 85–91.

• 132. Steiner, H.-G. (1975e). Zum Aufbau des Instituts für Didaktik der Mathematik (IDM) in Bielefeld. Ziele und Möglichkeiten des Instituts in der gegenwärtigen Situation (Kurzfassung). In Beiträge zum Mathematikunterricht (p. 186). Hannover: Verlag Franzbecker.

• 133. Steiner, H.-G. (1975f). Proceedings of the ICMI-IDM regional conference on the teaching of geometry (Spanish translation). Conceptos de Matematica, 36, 45–46.

• 134. Steiner, H.-G. (1975g). New ideas in the teaching of combinatorics and probability (Japanese translation). Osaka Journal of Mathematics Education, 5, 121–134.

• 135. Luschberger, H., Steiner, H.-G., Stowasser, R., Winkelmann, B. (1975). Kritische Fragen zum Normenbuch. Zentralblatt für Didaktik der Mathematik, 7 (4), 132–139.

• 136. Steiner, H.-G. (1976a). An example of the axiomatic method in instruction: The mathematization of a political structure. The Mathematics Teacher, 55, 520–528.

• 137. Steiner, H.-G. (1976b). Matematizarea si axiomatizarea unei structuri politice. Gazetta matematica (Bucuresti), Seria A, 72, 245–261.

• 138. Steiner, H.-G. (1976c). Elementary modern algebra as a significant component in a contemporary secondary school mathematics curriculum. The Japan Society of Mathematical Education, 58 (1), 2–14.

• 139. Steiner, H.-G. (1976d). Proceedings of the ICMI-IDM Regional Conference on the Teaching of Geometry (italienische Übersetzung). L’Insegnamento della Matematica, 7 (1), 27–32.

• 140. Steiner, H.-G. (1976e). Wiskundige Analyse van het Begrip Groepering van Piaget. De Minicomputer van Papy als Groepering. Niko, 20, 81–102.

• 141. Steiner, H.-G. (1976f). Mathematisierungen, die auf metrische Räume führen. Mathematisch-Physikalische Semesterberichte 23 (1), 17–58.

• 142. Steiner, H.-G. (1976g). Gegenwärtige Trends, Probleme und Aufgaben der Mathematikdidaktik. Bericht über eine Tagung vom 8. bis 12.12.1975 im Mathematischen Forschungsinstitut Oberwolfach. Zentralblatt für Didaktik der Mathematik, 8 (2), 88–92.

• 143. Steiner, H.-G. (1976h). What is applied mathematics? Indian Journal of Mathematics Teaching, 3 (1), 1–18.

• 144. Steiner, H.-G. (1976i). Finite geometries and non-measurable voting bodies. Educational Studies in Mathematics, 7 (1/2), 139–146.

• 145. Steiner, H.-G. (1976j). Programmstruktur und wissenschaftliche Schwerpunkte des 3. Internationalen Kongresses für Mathematikunterricht in Karlsruhe. In Beiträge zum Mathematikunterricht 1976 (pp. 218 – 220). Hannover: Schroedel.

• 146. Steiner, H.-G. (1976k). Mathematics curriculum development in the USA. A look at the past 20 years. Zentralblatt für Didaktik der Mathematik, 8 (3), 136–141.

• 147. Steiner, H.-G. (1976l). Isomorphie. In Historisches Wörterbuch der Philosophie, Band 4 (p. 627). Basel/Stuttgart: Schwabe.

• 148. Steiner, H.-G. (1976m). Forschung als strukturierendes Element in der Mathematikdidaktik. Mathematisch-Physikalische Semesterberichte, 23 (2), 279–286.

• 149. Steiner, H.-G. (1976n). Zur Methodik des mathematisierenden Unterrichts. In H. Dörfler & R. Fischer (Eds.), Anwendungsorientierte Mathematik in der Sekundarstufe II (pp. 211–245). Klagenfurt: Heyn.

• 150. Steiner, H.-G. (1976o). Einleitung. Zur Situation der Didaktik der Mathematik im Studium der Mathematiklehrer für die Sekundarstufe II. IDM Materialien und Studien, Band 5 (pp. 1–7). Bielefeld: IDM.

• 151. Steiner, H.-G. (1976p). Zur Entwicklungsgeschichte der Mathematiklehrerausbildung im 19. Jahrhundert bis zum Ersten Weltkrieg. In Zur Situation der Didaktik der Mathematik im Studium der Mathematiklehrer für die Sekundarstufe II. Bericht über eine Arbeitstagung vom 4.–8.10.1976 in Bielefeld. IDM - Materialien und Studien, Band 5 (pp. 10–39). Bielefeld: IDM.

• 152. Steiner, H.-G. (1977a). Günter Pickerts Beiträge zur Didaktik der Mathematik. Mathematisch-Physikalische Semesterberichte, 24 (2), 151–171.

• 153. Steiner, H.-G. (1977b). Introduction. Some aspects of mathematical education in the United Kingdom. Zentralblatt für Didaktik der Mathematik, 9 (3), 153.

• 154. Steiner, H.-G. (1977c). The Programme. In H. Athen & H. Kunle (Eds.), Proceedings of the 3rd International Congress on Mathematical Education (pp. 15–20). Karlsruhe: ZDM.

• 155. Steiner, H.-G. (1977d). ICMI and congress recommendations. Conferences 1972–1976. In H. Athen & H. Kunle (Eds.), Proceedings of the 3rd International Congress on Mathematical Education (pp. 383–388). Karlsruhe: ZDM.

• 156. Steiner, H.-G. (1977e). Einleitung. In H. Bauersfeld, M. Otte & H.-G. Steiner (Eds.), Informatik im Unterricht der Sekundarstufe II: Grundfragen, Probleme und Tendenzen mit Bezug auf allgemeine und berufsqualifizierende Ausbildungsgänge. Schriftenreihe des IDM, Band 15 (pp. v–xiii). Bielefeld: IDM.

• 157. Steiner, H.-G. (1977f). Einleitung. In H. Bauersfeld, M. Otte & H.-G. Steiner (Eds.), Übersicht zum Stand der Neugestaltung der gymnasialen Oberstufe im Mathematikunterricht in den Bundesländern. Schriftenreihe des IDM, Band 8 (pp. 2–5). Bielefeld: IDM.

• 158. Steiner, H.-G. (1977g). Zur Reform der gymnasialen Oberstufe. Skizze ihrer Entwicklung seit 1945. In H. Bauersfeld, M. Otte & H.-G. Steiner (Eds.), Übersicht zum Stand der Neugestaltung der gymnasialen Oberstufe im Mathematikunterricht in den Bundesländern. Schriftenreihe des IDM, Band 8 (pp. 7–18). Bielefeld: IDM.

• 159. Steiner, H.-G. (Ed.) (1978a). Didaktik der Mathematik. Wege der Forschung. Band 361. Darmstadt: Wissenschaftliche Buchgesellschaft.

• 160. Steiner, H.-G. (1978b). Zur Entwicklung der Didaktik der Mathematik. In: H.-G. Steiner (Ed.), Didaktik der Mathematik. Wege der Forschung (pp. ix–xlviii). Darmstadt: Wissenschaftliche Buchgesellschaft.

• 161. Steiner, H.-G. (1978c). Soziale Dimensionen von Mathematik in einer pädagogischen Neuorientierung des Mathematikunterrichts in der Sekundarstufe II. In Beiträge zum Mathematikunterricht (pp. 270–272). Hannover: Schroedel.

• 162. Steiner, H.-G. (1978d). Einleitung. In Materialien zur Linearen Algebra und Analytischen Geometrie in der Sekundarstufe II. IDM Materialien und Studien, Band 15 (pp. 1–9). Bielefeld: IDM.

• 163. Steiner, H.-G. (1979a). The present situation in the development of mathematics curricula for the primary school. A critical survey. In L’Insegnamento integrato delle Scienze nelle Scuola Primaria (pp. 245–269). Roma: Accademia Nazionale dei Lincei.

• 164. Steiner, H.-G. (Ed.) (1979b). Zum Verhältnis von Mathematik und Philosophie im Unterricht der Sekundarstufe II/Kollegschule. IDM Materialien und Studien, Band 12. Bielefeld: IDM.

• 165. Steiner, H.-G. (1979c). Einleitung. In H.-G. Steiner (Ed.), Zum Verhältnis von Mathematik und Philosophie im Unterricht der Sekundarstufe II/Kollegschule. IDM Materialien und Studien, Band 12. (pp. 1–2). Bielefeld: IDM.

• 166. Steiner, H.-G. (1979d). Zur Entwicklungsgeschichte des philosophischen Unterrichts unter besonderer Berücksichtigung der Beziehungen zur Mathematik. In H.-G. Steiner (Ed.), Zum Verhältnis von Mathematik und Philosophie im Unterricht der Sekundarstufe II/Kollegschule. IDM Materialien und Studien, Band 12 (pp. 3–57). Bielefeld: IDM.

• 167. Steiner, H.-G. (Ed.) (1979e). Cooperation Between Science Teachers and Mathematics Teachers. IDM Materialien und Studien, Band 16. Bielefeld: IDM.

• 168. Steiner, H.-G. (1979f). Introduction. Coordination of mathematics and science curricula and cooperation between mathematics teachers and science teachers. In H.-G. Steiner (Ed.), Cooperation Between Science Teachers and Mathematics Teachers. IDM Materialien und Studien, Band 16. Bielefeld: IDM.

• 169. Steiner, H.-G. (Ed.) (1979g). The Education of Mathematics Teachers. IDM Materialien und Studien, Band 15. Bielefeld: IDM.

• 170. Steiner, H.-G. (1979h). Introduction. In H.-G. Steiner (Ed.), The Education of Mathematics teachers. IDM Materialien und Studien, Band 15 (pp. 1–7). Bielefeld: IDM.

• 171. Steiner, H.-G. (1979i). Relations between elementary and advanced mathematics. In H.-G. Steiner (Ed.), The Education of Mathematics Teachers. IDM Materialien und Studien, Band 15 (pp. 90–115). Bielefeld: IDM.

• 172. Christiansen, B. & Steiner, H.-G. (Eds.) (1979a). New Trends in Mathematics Teaching, IV. Paris: UNESCO.

• 173. Christiansen, B. & Steiner, H.-G. (1979b). Introduction. In B. Christiansen & H.-G. Steiner (Eds.), New Trends in Mathematics Teaching, IV. (pp. 1–6). Paris: UNESCO.

• 174. Steiner, H.-G. (1980a). Mengenlehre. In J. Ritter & K. Gründer, Historisches Wörterbuch der Philosophie, Band 5 (Spalten 1044–1059). Basel: Schwabe.

• 175. Steiner, H.-G. (1980b). La matematica nelle sue diverse componenti e l’impostazione di un curriculo per la scuola secondaria. In C. Pontecorvo (Ed.), Quale Cultura per la Nuova Scuola Secondaria (pp. 235–276). Firenze: La Nuova Italia Editrice.

• 176. Steiner, H.-G. (1980c). School curricula and the development of science and mathematics. International Journal of Mathematical Education in Science and Technology, 11, 97–106.

• 177. Steiner, H.-G. (1980d). Philosophie und Mathematik. In Philosophische Aspekte der Bildungsinformatik II. Paderborner Arbeitspapiere FeoLL, Bd. 7 (pp. 1–55).

• 178. Steiner, H.-G. (Ed.) (1980e). Comparative studies of mathematics curricula. Change and stability, 1960–1980. IDM Materialien und Studien, Band 19. Bielefeld: IDM.

• 179. Steiner, H.-G. (1980f). Introduction. In H.-G. Steiner (Ed.), Comparative studies of mathematics curricula. Change and stability, 1960–1980. IDM Materialien und Studien, Band 19. (pp. 1–11). Bielefeld: IDM.

• 180. Steiner, H.-G. & Sträßer, R. (1980). Mathematik in der Berufsschule—Gegenwärtiger Stand, Entwicklungstendenzen, drängende Probleme. IDM Occasional Paper Nr. 7. Bielefeld: IDM.

• 181. Steiner, H.-G. (1981a). Philosophische Thematisierungen von Fragen aus der und über die Mathematik. Mathematische Semesterberichte, 28, 52–73.

• 182. Steiner, H.-G. (1981b). Zur aktuellen Problematik der neugestalteten Oberstufe. In H. Pfeiffer & H.-G. Steiner (Eds.), Vorbereitende Studien zur Differenzierung im Mathematikunterricht der neugestalteten gymnasialen Oberstufe. IDM Schriftenreihe, Band 22 (pp. i–xxii). Bielefeld: IDM.

• 183. Steiner, H.-G. (1981c). Zur Situation des Mathematikunterrichts in der Sekundarstufe II: Tendenzen, Probleme, Perspektiven. In Beiträge zum Mathematikunterricht 1981 (pp. 85–94). Hannover: Schroedel.

• 184. Steiner, H.-G. (1981d). Hans Wäsche zum Gedächtnis. Zentralblatt für Didaktik der Mathematik, 13 (1), 1–3.

• 185. Steiner, H.-G. (1981e). Erstrechnen und Rechenunterricht. In H. R. Becher (Ed.), Taschenbuch des Grundschulunterrichts (pp. 418–426). Baltmannsweiler: Schneider.

• 186. Steiner, H.-G. & Winkelmann, B. (Eds.) (1981). Fragen des Geometrieunterrichts. Köln: Aulis Verlag Deubner.

• 187. H. Bauersfeld, M. Otte & H.-G. Steiner (Eds.) (1976/1981). Beiträge zu Fragen des Analysisunterrichts in der Sekundarstufe II. IDM Schriftenreihe, Band 7. Bielefeld: IDM.

• 188. Biehler, R., Pescheck, W., Pfeiffer, H., Reiss, M., Richenhagen, G., Scholz, R.W., Steiner, H. G., Sträßer, R. & Winkelmann, B. (1976/1981). Untersuchungen zu den Analysis-Lehrplänen der gymnasialen Oberstufe in Ländern der BRD. In H.-G. Steiner (Ed.), Beiträge zu Fragen des Analysisunterrichts in der Sekundarstufe II. IDM Schriftenreihe, Band 7 (pp. 99–265). Bielefeld: IDM.

• 189. Pfeiffer, H., & Steiner, H.-G. (Eds.) (1981). Vorbereitende Studien zur Differenzierung im Mathematikunterricht der neugestalteten gymnasialen Oberstufe. IDM Materialien und Studien, Band 22. Bielefeld: IDM

• 190. Steiner, H.-G., & Sträßer, R. (1981a). Modellversuch im Bildungswesen: Modellmäßige Curriculumentwicklung in zentralen Problembereichen des mathematischen Unterrichts der beruflichen Bildung (Teilzeit-Berufsschule). In R. Sträßer (Ed.), Mathematischer Unterricht in Berufsschulen. IDM Materialien und Studien, Band 28 (pp. 9–51). Bielefeld: IDM.

• 191. Steiner, H.-G. (1982a). Eine gemeinsame Charakterisierung der Additivität von Rangordnungen auf endlichen Booleschen Verbänden und der Meßbarkeit von Abstimmungsgebilden. Mathematische Semesterberichte, 29, 21–50.

• 192. Steiner, H.-G. (1982b). Mathematisch-naturwissenschaftliche Bildung. Kritisch-konstruktive Fragen und Bemerkungen zum Aufruf einiger Fachverbände. IDM Occasional Paper Nr. 22. Bielefeld: IDM.

• 193. Steiner, H.-G. (1982c). Eine Entgegnung zu Herbert Zeitlers “Gedanken zur Mathematikdidaktik”. Didaktik der Mathematik, 10, 233–246.

• 194. Steiner, H.-G. (Ed.) (1982d). Mathematik–Philosophie–Bildung. IDM Reihe Untersuchungen zum Mathematikunterricht. Köln: Aulis Verlag Deubner.

• 195. Steiner, H.-G. (1982e). Zur Entwicklungsgeschichte des philosophischen Unterrichts unter besonderer Berücksichtigung der Beziehungen zur Mathematik. In H.-G. Steiner (Ed.). Mathematik–Philosophie–Bildung. (pp. 3–80). Köln: Aulis Verlag Deubner.

• 196. Steiner, H.-G. (1982f). Mathematikunterricht im Rahmen der NGO und ein integrativ-differenzierendes Konzept seiner Weiterentwicklung. IDM Occasional Paper Nr. 35. Bielefeld: IDM.

• 197. Steiner, H.-G. (1982g). Mathematikunterricht im Rahmen der NGO und ein integrativ-differenzierendes Konzept seiner Weiterentwicklung. In H. Pfeiffer & H.-G. Steiner (Eds.), Vorbereitende Studien zur Differenzierung im Mathematikunterricht der neugestalteten gymnasialen Oberstufe. IDM Schriftenreihe, Band 22 (pp. 68–97). Bielefeld: IDM.

• 198. Steiner, H.-G. (1982h). Aus der Geschichte des Funktionsbegriffs. In Conference on Functions. Report 1. Foundation for Curriculum Development (pp. 201–236). Enschede: SLO.

• 199. Peschek, W. & Steiner, H.-G. (Eds.) (1982). Fragen zur Differenzierung im Mathematikunterricht der gymnasialen Oberstufe. IDM Materialien und Studien Band 29. Bielefeld: IDM

• 200. Steiner, H.-G. (1983a). Mathematische Behandlung von Problemen aus der Philosophie. Mathematische Semesterberichte, 30, 194–205.

• 201. Steiner, H.-G. (1983b). Zur Diskussion um den Wissenschaftscharakter der Mathematikdidaktik. Journal für Mathematik-Didaktik, 4 (3), 245–251.

• 202. Steiner, H.-G. (1983c). Towards an education for decision behavior. In R. W. Scholz (Ed.), Decision Making under Uncertainty (pp. 413–419). Amsterdam: North-Holland.

• 203. Steiner, H.-G. (1983d). Mathematics and Experimental Sciences in the Programs of the Upper Secondary School in the Federal Republic of Germany. IDM Occasional Paper Nr. 40. Bielefeld: IDM.

• 204. Steiner, H.-G. (1983e). The process of Mathematization and the Social Dimension of Mathematics—Epistemological and Didactical Considerations. IDM Occasional Paper 41. Bielefeld: IDM.

• 205. Steiner, H.-G. (1983f). The Process of Mathematization and the Social Dimension of Mathematics—Epistemological and Didactical Considerations. Seminaire de didactique des mathématiques et de l’informatique, 44. Institut IMAG. Université Grenoble.

• 206. Steiner, H.-G. (1984a). Ordnung (Mathematik, Logik). In J. Ritter, K. Gründer (Eds.), Historisches Wörterbuch der Philsophie, Band 6 (Spalte 1303–1309). Basel/Stuttgart: Schwabe.

• 207. Steiner, H.-G. (1984b). Mathematisch-naturwissenschaftliche Bildung. In M. Reiss & H.-G. Steiner (Eds.), Mathematikkenntnisse–Leistungsmessung–Studierfähigkeit. IDM-Reihe Untersuchungen zum Mathematikunterricht, Band 9 (pp. 5–58). Köln: Aulis Verlag Deubner.

• 208. Steiner, H.-G. (1984c). Forschungs- und Orientierungsprobleme der Mathematikdidaktik. IDM Occasional Paper Nr. 47. Bielefeld: IDM.

• 209. Steiner, H.-G. (1984d). Non-Measurable Voting Bodies. A Characterization of Measurability. IDM Occasional Paper Nr. 49. Bielefeld: IDM.

• 210. Steiner, H.-G. (1984e). Philosophy of Mathematics and the Psychology of Mathematics Education. In Proceedings of the 8th international Conference for the Psychology of Mathematical Education (pp. 478–480). Sydney.

• 211. Steiner, H.-G. (1984f). Forschungs- und Orientierungsprobleme der Mathematikdidaktik. In Beiträge zum Mathematikunterricht (pp. 330–334). Bad Salzdetfurth: Franzbecker.

• 212. Steiner, H.-G. (1984g). Tendenzen und Probleme bei der Reform des Mathematikunterrichts der Oberstufe in der Bundesrepublik Deutschland. Symposium über Schulmathematik. Didaktik-Reihe der Österreichischen Mathematischen Gesellschaft, 10, 51–67.

• 213. Steiner, H.-G. (Ed.) (1984h). Theory of Mathematics Education (TME): ICME 5—Topic Area and Miniconference, Adelaide, Australia, August 30–31. IDM Occasional Paper 54. Bielefeld: IDM.

• 214. Steiner, H.-G. (1984i). Theory of Mathematics Education. In H.-G. Steiner (Ed.), Theory of Mathematics Education (TME) : ICME 5—Topic Area and Miniconference, Adelaide, Australia, August 30–31. IDM Occasional Paper 54 (pp. 16–32). Bielefeld: IDM.

• 215. Reiss, M. & Steiner, H.-G. (Eds.) (1984a). Mathematikkenntnisse–Leistungsmessung–Studierfähigkeit. IDM-Reihe Untersuchungen zum Mathematikunterricht, Band 9. Köln: Aulis Verlag Deubner.

• 216. Reiss, M. & Steiner, H.-G. (1984b). Einleitung. In M. Reiss & H.-G. Steiner (Eds.), Mathematikkenntnisse–Leistungsmessung–Studierfähigkeit. IDM Reihe Untersuchungen zum Mathematikunterricht, Band 9 (pp. 1–4). Köln: Aulis Verlag Deubner.

• 217. Steiner, H.-G. (1985a). Theorie der Mathematikdidaktik. Zentralblatt für Didaktik der Mathematik, 17 (2), 57–65.

• 218. Steiner, H.-G. (1985b). Implications for Scholarship of a Theory of Mathematics Education. IDM Occasional Paper Nr. 69. Bielefeld: IDM.

• 219. Steiner, H.-G. (1985c). Philosophie und die Bedingtheit der Mathematik. Mathematische Semesterberichte, 32, 110–130.

• 220. Steiner, H.-G. (1985d). Theory of Mathematics Education (TME): An Introduction. For the Learning of Mathematics 5 (2), 11–17.

• 221. Steiner, H.-G. (1985e). Matematica e Scienze Sperimentale nei Programmi della Scuola Secondaria Superiore nella Republica Federale Tedesca. In L’Insegnamento della Matematica e delle Scienze Sperimentali nella Scuola Secondaria Superiori. Parte Prima (pp. 67–105). Venezia: Fondazione Giorgo Cini.

• 222. Steiner, H.-G. (1985f). Philosophische Aspekte der Mathematik und ihre Wechselwirkung mit Theorie und Praxis des Mathematikunterrichts. In Beiträge zum Mathematikunterricht (pp. 305–308). Bad Salzdetfurth: Franzbecker.

• 223. Steiner, H.-G. (1985g). Recent activities related to “Theory of Mathematics Education (TME)”. Zentralblatt für Didaktik der Mathematik, 17 (5), 170–172.

• 224. Steiner, H.-G. (1985h). A Systems Approach to Mathematics Education. Journal for Research in Mathematics Education, 18 (1), 46–52.

• 225. Steiner, H.-G. & Winter, H. (Eds.) (1985a). Mathematikdidaktik–Wissenschaftsgeschichte–Bildungsgeschichte. IDM Reihe Untersuchungen zum Mathematikunterricht, Band 12 (pp. 1–5). Köln: Aulis Verlag Deubner.

• 226. Steiner, H.-G. & Winter, H. (1985b). Einleitung. In H.-G. Steiner & H. Winter (Eds.), Mathematikdidaktik–Wissenschaftsgeschichte–Bildungsgeschichte. IDM Reihe Untersuchungen zum Mathematikunterricht, Band 12 (pp. 1–5). Köln: Aulis Verlag Deubner.

• 227. Steiner, H.-G. (Ed.) (1986a). Grundfragen der Entwicklung mathematischer Fähigkeiten. Köln: Aulis Verlag Deubner.

• 228. Steiner, H.-G. (1986b). Einleitung. In H.-G. Steiner (Ed.), Grundfragen der Entwicklung mathematischer Fähigkeiten (pp. ix–xvi). Köln: Aulis Verlag Deubner.

• 229. Steiner, H.-G. (1986c). Non-Measurable Voting Bodies. A Characterization of Measurability. International Journal of Mathematical Education in Science and Technology, 17 (3), 367–376.

• 230. Steiner, H.-G. (1986d). Sonderpädagogik für testsondierte “mathematisch hochbegabte” Schüler oder offene Angebote zur integrativ-differenzierenden Förderung mathematischer Bildung. In Beiträge zum Mathematikunterricht (pp. 280–284). Bad Salzdetfurth: Franzbecker.

• 231. Steiner, H.-G. (1986e). Sonderpädagogik für testsondierte “mathematisch hochbegabte” Schüler oder offene Angebote zur integrativ-differenzierenden Förderung mathematischer Bildung. Zentralblatt für Didaktik der Mathematik, 18 (4), 130–132.

• 232. Steiner, H.-G. (1986f). Topic area: Theory of mathematics education (TME). In M. Carss (Ed.), Proceedings of the Fifth International Congress on Mathematical Education (pp. 293–299). Boston/Basel/Stuttgart: Birkhäuser

• 233. Steiner, H.-G. (1986g). Deutsch-französisches bilaterales Symposium zur Förderung des wissenschaftlichen Erfahrungsaustauschs und der Zusammenarbeit im Bereich mathematikdidaktischer Forschung. Zentralblatt für Didaktik der Mathematik, 18 (4), 148–150.

• 234. Steiner, H.-G. (1986h). Matematizzazione dei sistemi elettorali: Qualche esperienza in classe. Archimede, 38, 95–111.

• 235. Steiner, H.-G. (1986i). The process of Mathematization and the Social Dimension of Mathematics—Epistemological and Didactical Considerations. Indian Journal of Mathematics Teaching, 12 (2) 1–35.

• 236. Steiner, H.-G. (1986j). Process matemtyzacji i spoteczunywymiar matematyki–rozwazania epistemologiezne i dydaktyczne. Roczniki Polskiego Towarzystwa Matematycznego. Dydaktyka Matematyki, 175–238. (Translation by A. Sierpinska)

• 237. Steiner, H.-G. (1986k). Theory of Mathematics Education (TME) (Chinese translation). National Science Council Monthly, 14 (5), 524–534.

• 238. Fischbein, E., Skemp, R., Steiner, H.-G. et al. (1986). Relations Between Psychology of Mathematics Education (PME) and Theory of Mathematics Education (TME). IDM Occasional Paper Nr. 81. Bielefeld: IDM.

• 239. Steiner, H.-G. (1987a). Zur Geschichte der Lehrplanentwicklung für den Mathematikunterricht der Sekundarstufe. Mathematisch-Physikalische Semesterberichte, 25, 172–193.

• 240. Steiner, H.-G. (1987b). Beziehungen zwischen mathematik- und naturwissenschaftsdidaktischer Forschung. In Beiträge zum Mathematikunterricht (pp. 323–326). Bad Salzdetfurth: Franzbecker.

• 241. Steiner, H.-G. (1987c). Philosophical and epistemological aspects of mathematics and their interaction with theory and practice in mathematics education. For the Learning of Mathematics 7 (1), 7–13.

• 242. Steiner, H.-G. (1987d). Lehrerfortbildung. Vorbemerkungen. Zentralblatt für Didaktik der Mathematik, 19 (2), 43.

• 243. Steiner, H.-G. (1987e). Lehrerfortbildung 2. Vorbemerkungen. Zentralblatt für Didaktik der Mathematik, 19 (4), 135–136.

• 244. Steiner, H.-G. (1987f). Implications for scholarship of a theory of mathematics education. Zentralblatt für Didaktik der Mathematik, 19 (4), 162–167.

• 245. Steiner, H.-G. (1987g). Kierunki i problemy badawcze dydaktyki matematyki (Forschungs- und Orientierungsprobleme der Mathematikdidaktik). Roczniki Polskiego Towarzystwa Matematycznego. Dydaktyka Matematyki, V (7), 117–141.

• 246. Steiner, H.-G. (1988a). Mathematization of voting systems: some classroom experiences. International Journal of Mathematical Education in Science and Technology, 19 (2), 199–213.

• 247. Steiner, H.-G. (1988b). Theory of mathematics education and its implications for scholarship. In H.-G. Steiner & A. Vermandel (Eds.), Foundations and Methodology of the Discipline Mathematics Education (Didactics of Mathematics). Proceedings of the 2nd international TME-conference, Bielefeld, July 15–19, 1985 (pp. 5–20). Antwerp/Bielefeld.

• 248. Steiner, H.-G. (1988c). Aspects philosophiques et épistémologiques des mathématiques. Leur influence sur l’enseignement mathématique. In C. Laborde (Ed.), Actes du premier colloque franco-allemand de didactique des mathématiques et de l’informatique. La Pensée Sauvage (107–118).

• 249. Steiner, H.-G. (1988d). Über Metaphern, Modelle und Mathematik. In P. Bender (Ed.), Mathematikdidaktik: Theorie und Praxis (pp. 190–201). Berlin: Cornelsen.

• 250. Steiner, H-G. (1988e). Das mathematische Denken und die Schulmathematik. Aufsätze zur Didaktik der Mathematik. Göttingen: Vandenhoeck & Ruprecht.

• 251. Steiner, H.-G. (1988f). Topic area 15: Theory of mathematics education. In A. Hirst & K. Hirst (Eds.), Proceedings of the 6th International Congress of Mathematics Education (pp. 371–374). Budapest: Bolyai Janos Society.

• 252. Steiner, H.-G. (1988g). The two kinds of “elements” and the dialectic between synthetic-deductive and analytic-genetic approaches in mathematics. For the Learning of Mathematics, 8 (3), 7–16.

• 253. Steiner, H.-G. (1988h). Deutsch-italienisches bilaterales Symposium zur Förderung des wissenschaftlichen Erfahrungsaustauschs und der Zusammenarbeit im Bereich mathematikdidaktischer Forschung. Zentralblatt für Didaktik der Mathematik, 20 (4), 164–165.

• 254. Steiner, H.-G. & Vermandel, A. (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. Antwerpen/Bielefeld.

• 255. Steiner, H.-G. (1989a). Relations between historico-epistemological studies and research in mathematics education. In L. Bazzini, & H.-G. Steiner (Eds.), Proceedings of the 1st Italian-German Bilateral Symposium on Didactics of Mathematics, Pavia, October 4–9, 1988 (pp. 25–35). Pavia: National Research Council of Italy.

• 256. Steiner, H.-G. (1989b). Mathematization processes in class as a collective learning process. In M. Hejny & H.-G. Steiner (Eds.), Proceedings of the 1st Bratislava International Symposium on Research and Development in Mathematics Education. Bratislava, August, 3–7, 1988 (pp. 119–161). Bratislava.

• 257. Steiner, H.-G. (1989c). The nature of theoretical concepts in physics and mathematics. Implications for the fragility of knowledge in the educational context. In S. Vinner (Ed.), Proceedings of the 2nd Jerusalem Convention on Education: Science and Mathematics Education—Interaction Between Theory and Practice (pp. 387–396). Jerusalem.

• 258. Steiner, H.-G. (1989d). Cooperation between research in science education and research in mathematics education. In S. Vinner (Ed.), Proceedings of the 2nd Jerusalem Convention on Education: Science and Mathematics Education—Interaction Between Theory and Practice (pp. 73–85). Jerusalem.

• 259. Bazzini, L. & Steiner, H.-G. (Eds.) (1989). Proceedings of the 1st Italian-German Bilateral Symposium on Didactics of Mathematics, Pavia, October 4–9, 1988. Pavia: Quaderno.

• 260. Hejny, M. & Steiner, H.-G. (Eds.) (1989). Proceedings of the 1st Bratislava International Symposium on Research and Development in Mathematics Education. Bratislava, August, 3–7, 1988. Bratislava.

• 261. Steiner, H.-G. (Ed.) (1990a). Mathematikdidaktik–Bildungsgeschichte–Wissenschaftsgeschichte II. IDM-Reihe Untersuchungen zum Mathematikunterricht Band. 15. Köln: Aulis Verlag Deubner.

• 262. Steiner, H.-G. (1990b). Bemerkungen zur Geschichte des Strukturbegriffs und der impliziten Definition. In H.-G. Steiner (Ed.), Mathematikdidaktik–Bildungsgeschichte–Wissenschaftsgeschichte II (pp. 187–199). Köln: Aulis Verlag Deubner.

• 263. Steiner, H.-G. (1990c). Due tipi di “elementi” e la dialettica tra approccio deduttivo sintetico e genetico analitico in matematica. L’ insegnamento della matematica e delle educatione integrale, 13 (2), 123–151.

• 264. Steiner, H.-G. (1990d). A mathematization project in class as a collective higher order learning process. In G. Booker, P. Cobb & T. Mendicuti (Eds.), Proceedings of the 14th PME-Conference. Mexico. Vol. 2 (pp. 343–350). Mexico.

• 265. Steiner, H.-G. (1990e). Mathematization projects in class as collective higher order learning processes: The role of the teacher and reflections on teacher education: In Memorias de la Cuarta Reunion Centroamericana y del Caribe sobre Formacion de Profesores e Investigacion en Matematica Educativa (pp. 155–160). Mexico.

• 266. Steiner, H.-G. (1990f). Relations between research in mathematics education and research in science education—A theme of ICME–6 topic area 15: Theory of mathematics education (TME). introductory remarks. Zentralblatt für Didaktik der Mathematik, 22 (6), 193.

• 267. Steiner, H.-G. (1990g). Needed cooperation between science education and mathematics education. Zentralblatt für Didaktik der Mathematik, 22 (6), 194–200.

• 268. Steiner, H.-G. (1990h). Mathematisierungsprogramme im Unterricht als kollektive Lernprozesse höherer Ordnung. In Beiträge zum Mathematikunterricht (pp. 277–280). Bad Salzdetfurth: Franzbecker.

• 269. Steiner, H.-G. (1990i). Concepts and ideas from elementary algebra as sources for creative activities and discovery learning at secondary school. An outline. In Proceedings Segundo Simposio International Sobre Invest. en Educacion Matematica. Aprendizaje y Enseñanza del Algebra. Cuernavaca, Morelos, Mexico July 12–14, 1990 (pp. 105–107). Mexico.

• 270. Steiner, H.-G. (1991a). Von Osnabrück bis Osnabrück: A maximal loop? – Zur Entwicklung der Mathematikdidaktik in Deutschland in den letzten 25 Jahren. In Beiträge zum Mathematikunterricht (pp. 15–22). Bad Salzdetfurth: Franzbecker.

• 271. Steiner, H.-G. (1991b). Das IDM im Spiegel weltweiter Stellungnahmen. IDM Occasional Paper Nr. 129. Bielefeld: IDM.

• 272. Steiner, H.-G. (1991c). Laudatio zur Verleihung des Förderpreises der Gesellschaft für Didaktik der Mathematik (GDM) an Herrn Privatdozent Dr. Horst Struve (Köln) am 4. März 1991 auf der 25. Bundestagung in Osnabrück. In Beiträge zum Mathematikunterricht (pp. 7–13). Bad Salzdetfurth: Franzbecker.

• 273. Steiner, H.-G. (1991d). Vom Studienstiftler zum Professor für Mathematikdidaktik—Heinz Griesels “Münsteraner Jahre”. In H. Postel, A. Kirsch & W. Blum (Eds.), Mathematik lehren und lernen. Festschrift für Heinz Griesel (pp. 11–21). Hannover: Schroedel.

• 274. Steiner, H.-G. (1991e). Attivité Recenti ed in Preparazione del Gruppo di Studio Internazionale sulla Teoria dell’Educazione Matematica (TME). L’Insegnamento della Matematica e delle Scienze Integrate, 14 (10), 988–991.

• 275. Steiner, H.-G. (1992a). Das IDM im Spiegel weltweiter Stellungnahmen—Nationale und internationale Reaktionen auf eine drohende Schließung bzw. einschneidende Reduktion des Instituts für Didaktik der Mathematik (IDM). IDM Occasional Paper No.129. Bielefeld: IDM.

• 276. Steiner, H.-G. (1992b). Recent and coming activities of the international study group on theory of mathematics education (TME). Zentralblatt für Didaktik der Mathematik, 24 (2), 67–68.

• 277. Steiner, H.-G. (1992c). Gegenwärtige Aktivitäten der internationalen Arbeitsgruppe “Theory of Mathematics Education” (TME). In Beiträge zum Mathematikunterricht. (pp. 459–462). Bad Salzdetfurth: Franzbecker.

• 278. Steiner, H.-G. (1992d). Relation/Relationstheorie. In J. Ritter & K. Gründer (Eds.), Historisches Wörterbuch der Philosophie, Band 8 (Spalte 606–611). Basel/Stuttgart: Schwabe.

• 279. Batanero Bernabeu, M.C., Godino, J.D., Steiner, H.-G. & Wenzelburger, E. (1992). An International TME-Survey: Preparation of Researchers in Mathematics Education. Institut für Didaktik der Mathematik-Occasional Paper No. 135. Bielefeld: IDM.

• 280. Griesel, H. & Steiner, H.-G. (1992). The organization of didactics of mathematics as a professional field. Mathematics Education in the Federal Republic of Germany. Zentralblatt für Didaktik der Mathematik, 24 (7), 287–295.

• 281. Steiner, H.-G. (1993a). Die Situation der Mathematikdidaktik in den deutschsprachigen Ländern im europäischen und internationalen Vergleich. In Beiträge zum Mathematikunterricht (pp. 354–357). Bad Salzdetfurth: Franzbecker.

• 282. Steiner, H.-G. (1993b). Short Reports: 7th International Congress on Mathematics Education (ICME–7). Zentralblatt für Didaktik der Mathematik, 25 (3), 117–119.

• 283. Steiner, H.-G. (1993c). Teoria da Educação Matemática (TEM): Uma Introdução. Quadrante: Revista Teórica e de Investigação, 2 (2), 19–34.

• 284. Steiner, H.-G. (1994a). Topic group 12: Graduate programs and the formation of researchers in mathematics education. In C. Gaulin, B.R. Hodgson, D.H. Wheeler & J.C. Egsgard (Eds.), Proceedings of the 7th International Congress on Mathematical Education (Québec, August 17–23, 1992) (pp. 274–277). Sainte-Foy (Canada): Les Presses de l’Université Laval.

• 285. Steiner, H.-G. (1994b). Das zweite Jahrzehnt—Rückblick und Ausblick. In Festveranstaltung zum 20–jährigen Bestehen des Instituts für Didaktik der Mathematik (IDM). IDM-Occasional Paper Nr. 154 (pp. 80–120). Bielefeld: IDM.

• 286. Steiner, H.-G. (1994c). On metaphors, models, and mathematics. In L. Bazzini & H.-G. Steiner (Eds.), Proceedings of the 2nd Italian-German Bilateral Symposium on Didactics of Mathematics. IDM Materialien und Studien, Band 39 (pp. 175–192). Bielefeld: IDM.

• 287. Steiner, H.-G. (1994d). Mathematikdidaktik von Ideen, Begriffen und Problemen aus. Hans-Joachim Vollraths Beiträge zur Entwicklung und Konsolidierung unserer Wissenschaft. In G. Pickert & I. Weidig (Eds.): Mathematik erfahren und lehren. Festschrift für Hans-Joachim Vollrath (pp. 8–16). Stuttgart: Klett.

• 288. Steiner, H.-G. (1994e). Some notable anniversaries and some personal German-Italian memories in didactics of mathematics. On the occasion of the 25th anniversary of the foundation of Centro Ricerche Didattiche Ugo Morin, Paderno del Grappa, Italy. Zentralblatt für Didaktik der Mathematik, 26 (6), 211–214.

• 289. Steiner, H.-G. (1994f). The culture of the mathematics classroom: analysing and reflecting upon the conditions of change. Introduction to a conference report. Zentralblatt für Didaktik der Mathematik, 26 (5), 157.

• 290. Steiner, H.-G. (1994g). Didattica della Matematica: Importanti Anniversari e Memorie Italo-Germaniche. L’Insegnamento della Matematica e delle Scienze Integrate, 17A–17B (5), 426–437.

• 291. Steiner, H.-G. (1994h). Understanding: Doing or thinking? Acta Didactica Universitatis Comenianae, 3, 200–205.

• 292. Steiner, H.-G. (1994i). Institut für Didaktik der Mathematik. In P. Lundgren (Ed.), Reformuniversität Bielefeld 1969–1994. Zwischen Defensive und Innovation (pp. 308–313). Bielefeld: Verlag für Regionalgeschichte.

• 293. Batanero Bernabeu, M.C., Godino, J.D., Steiner, H.-G. & Wenzelburger, E. (1994a). The training of researchers in mathematics education—results from an international survey. Educational Studies in Mathematics, 26, 95–102.

• 294. Batanero Bernabeu, M.C., Godino, J.D., Steiner, H.-G. & Wenzelburger, E. (1994b). The training of researchers in mathematics education—Results from an international survey. Zentralblatt für Didaktik der Mathematik, 25 (6), 226–229.

• 295. Bazzini, L. & Steiner, H.-G. (Eds.) (1994). Proceedings of the Second Italian-German Bilateral Symposium on Didactics of Mathematics. IDM Materialien und Studien, Vol. 39. Bielefeld: IDM.

• 296. Schupp, H., & Steiner, H.-G. (1994). The value of national studies of mathematics education for the international community. Discussed in relation to an example from Germany. In C. Gaulin, B. Hodgson, D.H. Wheeler & J.C. Egsgard (Eds.), Proceedings of the 7th International Congress on Mathematics Education (pp. 413–415). Sainte-Foy (Canada): Les Presses de L’Université Laval.

• 297. Steiner, H.-G. (1995). Zur Bedeutung des Zusammenhangs zwischen mathematikdidaktischer Forschung und Lehre in der Lehrerbildung. In Beiträge zum Mathematikunterricht (pp. 456–459). Hildesheim: Franzbecker.

• 298. Steiner, H.-G. & Vollrath, H. J. (Eds.) (1995a). Neue problem- und praxisbezogene Forschungsansätze. IDM-Reihe Untersuchungen zum Mathematikunterricht, Band 20. Köln: Aulis Verlag Deubner.

• 299. Steiner, H.-G. & Vollrath, H. J. (1995b). Vorwort. In H.-G. Steiner & H. J. Vollrath (Eds.), Neue problem- und praxisbezogene Forschungsansätze. IDM-Reihe Untersuchungen zum Mathematikunterricht, Band 20. Köln: Aulis Verlag Deubner.

• 300. Steiner, H.-G. (1996). Vorwort. In Andrea Peter, Aktion und Reflexion—Lehrerbildung aus international vergleichender Perspektive (pp. i–iii). Weinheim: Deutscher Studienverlag.

• 301. Steiner, H.-G. (1997a). From Lyon to Sevilla. Zentralbaltt für Didaktik der Mathematik, 29 (1), 28–29.

• 302. Steiner, H.-G. (1997b). Didactics of mathematics as a scientific discipline: A sketch of its development from a personal (autobiographic) point of view. In N. Malara (Ed.), Proceedings ICME-8. WG25: Didactics of Mathematics as a Scientific Discipline. Modena: University, Department of Mathematics.

• 303. Steiner, H.-G. (1997c). In Memoriam Bent Christiansen. Zentralblatt für Didaktik der Mathematik, 29 (3), 97–111.

• 304. Steiner, H.-G. (1998). Didactics of mathematics as a scientific discipline—A sketch of its development from a personal point of view. Zentralblatt für Didaktik der Mathematik, 30 (6), 224–232.

• 305. Malara, N., Azcárate, C., Steiner, H.-G., Lerman, S. & Batanero, M. (1998). Report on working group 25 “Didactics of mathematics as a scientific discipline”. In C. Alsina et al. Proceedings of the 8th International Congress on Mathematics Education (pp. 219–223). Sevilla: SAEM Thales.

1.2 Edited Book Series

• B. Artmann, A. Kirsch & H.-G. Steiner (Eds.) Moderne Mathematik in elementarer Darstellung. Göttingen: Vandenhoeck & Ruprecht.

• H. Bauersfeld, M. Otte & H.-G. Steiner (Eds.) IDM Schriftenreihe. Bielefeld: Institut für Didaktik der Mathematik.

• M. Otte, I. Schneider & H.-G. Steiner (Eds.). Studien zur Wissenschaft-, Sozial- und Bildungsgeschichte der Mathematik. Göttingen: Vandenhoeck & Ruprecht.

Appendix 2

1.1 Organization and co-organization of congresses, conferences, workshops by Hans-Georg Steiner (co-organizers are only partly known)

• 1. Münsteraner Tagungen zur Pflege des Zusammenhangs von Schule und Universität—Münster Conferences for the Furtherance of the Connection between School and University. University of Münster, 1955–1967

• 2. Studientagungen für belgische und luxemburgische Mathematiklehrer—Study Conference for Mathematics Teachers in Belgium and Luxembourg. University of Münster, 1963, 1964, 1966, 1967

• 3. Die Neugestaltung des Mathematikunterrichts an den höheren Schulen—The Restructuring of Mathematics teaching at College-Bound High Schools. ICMI/IMUK-Regional Conference, Vienna, 1966

• 4. Arbeitstagung des Zentrums für Didaktik der Mathematik an der Universität Karlsruhe zu Fragen der Grundlagenforschung und mathematischen Logik im Unterricht—Workshop on Foundations of Mathematics and Mathematical Logic in Mathematics Instruction Conducted by the Centre of Didactics of Mathematics at the University of Karlsruhe. Oberwolfach, June 30–July 2, 1968

• 5. Arbeitstagung zum Stand der Didaktik der Algebra und zur Vorbereitung der Entwicklung eines Lese- und Arbeitsbuchs zur modernen elementaren Algebra für 12- bis 19-Jährige—Workshop on Didactics of Algebra and the Preparation of a Text Book for Modern Elementary Algebra Aimed at 12- to 19-Year-Old Students. Kassel, April 8–13, 1969

• 6. 2nd CSMP international conference: The Teaching of Geometry at the Pre-College Level. Carbondale, Illinois, March 19–28, 1970

• 7. Bundestagung für Didaktik der Mathematik—National Conference on Didactics of Mathematics. Bayreuth, April 14–16, 1971

• 8. ICMI–IDM Regional Conference on the Teaching of Geometry. Bielefeld, September 16–20, 1974

• 9. Kritische Auseinandersetzung mit dem “Normenbuch” Mathematik—Critical Analysis of the Examination Standards for Upper Secondary Final Examinations. Bielefeld, October 11–12, 1975

• 10. Zur Situation der Unterrichtsgebiete Analysis und Lineare Algebra/Analytische Geometrie—On the Situation of Teaching Analysis and Linear Algebra/Analytical Geometry. December 1974, March 1975, October 1975, December 1975, February 1976

• 11. 3rd International Congress on Mathematical Education (ICME-3). Karlsruhe, August 16 –21, 1976 (as chair of the international program committee)²

• 12. Zur Situation der Didaktik der Mathematik im Studium der Mathematiklehrer für die Sekundarstufe II—On the Situation of Didactics of Mathematics in Secondary Mathematics Teacher Preservice Education. Bielefeld, October 8–14, 1976

• 13. Tendenzen und Probleme des Mathematikunterrichts in der Sekundarstufe II—Trends and Problems in Mathematics Teaching at Upper Secondary Level. Bielefeld, December 13–15, 1976

• 14. Informatik im Unterricht der Sekundarstufe II: Grundfragen, Probleme und Tendenzen mit Bezug auf allgemeinbildende und berufsqualifizierende Ausbildungsgänge—Information Technology in Upper Secondary Classrooms: Basic Questions, Problems and Trends with Respect to General and Vocational Education. Bielefeld, September 12–14, 1977

• 15. Zum Verhältnis von Mathematik und Philosophie im Unterricht der Sekundarstufe II/Kollegschule—On the Relationship Between Mathematics and Philosophy in Upper Secondary Education. Bielefeld, December 6–7, 1977, April 26–28, 1978

• 16. The Education of Mathematics Teachers. What Knowledge, Experience, and Understanding of Mathematics should a Mathematics Teacher Have? ICMI-UNESCO-IDM Symposium at the International Mathematician Congress in Helsinki, August 15–23, 1978

• 17. Co-operation between Science Teachers and Mathematics Teachers. UNESCO-ICSU-ICPE-ICMI-IDM-Conference. Bielefeld, September 17–23, 1978

• 18. Comparative Studies of Mathematics Curricula. Change and stability 1960–1980. IDM-UNESCO-SIMS Conference. Osnabrück, January 7–11, 1980

• 19. Internationale Tagung zur Methodologie der 2. Internationalen Mathematikstudie—International Conference on the Methodology of the 2nd International Mathematics Study. Bielefeld, January 13–18, 1980

• 20. Fragen der Differenzierung im Mathematikunterricht der gymnasialen Oberstufe—Questions Concerning the Differentiation in Mathematics Teaching at the Upper Secondary Level. Osnabrück, June 1–5, 1982

• 21. What Should be the Goals and Contents of General Mathematics Education? ICMI Symposium at the International Mathematicians Congress in Warsaw, August 16–24, 1983

• 22. Arbeitstagungen zur Entwicklung mathematischer Fähigkeiten—Workshops on the Development of Mathematical Competencies. Bielefeld, November 24–25, 1983, April 2–3, 1984

• 23. Wissenschafts- und Bildungsgeschichte im Zusammenhang mit mathematikdidaktischer Forschung—History of Science and Education in the Context of Mathematics Education Research. GDM-IDM Conference. Osnabrück, May 7–12, 1984

• 24. Topic Area at ICME-5 and following international conference on “Theory of Mathematics Education” (TME-1 Conference). Adelaide, Australia, August 24–30, 1984

• 25. Grundfragen der Entwicklung mathematischer Fähigkeiten—Basic Questions with Respect to the Development of Mathematical Competencies. Osnabrück, January 7–13, 1985

• 26. International Conference on Foundations and Methodology of the Discipline Mathematics Education (Didactics of Mathematics) (TME-2 Conference). Bielefeld, July 15–19, 1985

• 27. Zweite GDM-IDM-Arbeitstagung über Wissenschafts- und Bildungsgeschichte im Zusammenhang mit mathematikdidaktischer Forschung—Second GDM-IDM Workshop on the History of Science and Education in the Context of Mathematics Education Research. Osnabrück, April 7–11, 1986

• 28. Deutsch-französisches bilaterales Symposium zur Förderung des wissenschaftlichen Erfahrungsaustauschs und der Zusammenarbeit im Bereich der mathematikdidaktischen Forschung—Bilateral German-French Symposium on the Enhancement of Scientific Exchange and Cooperation in Mathematics Education Research, Marseille-Luminy. November 16–21, 1986 (together with Colette Laborde)

• 29. International Seminar on Comparative Studies of Mathematics Curricula. Centro Europeo dell’Educazione. Frascati (Rome), May 18–23, 1987

• 30. International Conference on Investigating and Bridging the Teaching-Learning Gap. (TME-3 Conference). Antwerp, July 11–15, 1988

• 31. Topic area “Theory of Mathematics Education” on the 6^th International Congress on Mathematical Education (ICME-6). Budapest, July 23–27, 1988

• 32. International Symposium on Research and Development in Mathematics Education. Bratislava, August 3–7, 1988

• 33. First Bilateral Italian-German Symposium on Didactics of Mathematics. Pavia, October 4–9, 1988 (together with Luciana Bazzini)

• 34. Bilateral German-Israeli symposium “Logo in the Classroom: From Ideas to Implementation and Practice. Bielefeld, November 1988

• 35. Fourth International Conference on Theory of Mathematics Education (TME-4 Conference). Oaxtepec, Mexico, July 3–7, 1990

• 36. Second Bratislava International Symposium on Mathematics Education (BISME-2). Bratislava, August 22–25, 1990

• 37. Symposium zur Förderung der wissenschaftlichen Zusammenarbeit in der Mathematikdidaktik in Deutschland—Symposium on the Enhancement of the Scientific Cooperation in Didactics of Mathematics in Germany. Osnabrück, October 21–28, 1990

• 38. Arbeitstagung über „Offene Systeme und mathematisch-naturwissenschaftliche Bildung”—Workshop on Open Systems and Mathematics and Science Education. Osnabrück, March 11–15, 1991

• 39. Fifth International Conference on the Theory of Mathematics Education (TME–5). Paderno del Grappa, Italy, June 20–27, 1991

• 40. Second Bilateral Italian-German Symposium on Didactics of Mathematics. Osnabrück, April 21–26, 1992 (together with Luciana Bazzini)

• 41. Arbeitstagung „Neue problem- und praxisbezogene Forschungsansätze”—Workshop on New Problem and Practice related Research Approaches. Osnabrück, August 30–September 4, 1993 (together with Hans-Joachim Vollrath)

• 42. Komparative Forschung zur Entwicklung und Ausprägung des Mathematikunterrichts und der Mathematikdidaktik als Wissenschaftsdisziplin in der BRD und der DDR von 1945 bis 1990 und ihre Bedeutung für die gegenwärtigen und künftigen Entwicklungen in Deutschland—Comparative Research on the Development and Status-quo of Mathematics Teaching and the Didactics of Mathematics as a Scientific Discipline in the Federal Republic of Germany and the German Democratic Republic from 1945 to 1990 and their Implications for Present and Future Developments in Germany. Osnabrück 1996 and Magdeburg 1996 (together with Werner Walsch, Halle)