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ICMI-13 Video

ICMI and German Mathematics Education

The German speaking community on mathematics education has had from the outset a close relation to ICMI. Felix Klein served as the first president of ICMI, bringing in many German colleagues and inspiring international research and discussion. The German speaking countries have always been characterised by strong relations between mathematics and mathematics education, and these two different communities work closely together in many respects. This special relationship is again apparent in the strong support for ICME-13 by the German Mathematical Society.

Felix Klein being a mathematician by his background was especially interested in teacher education and his lectures for teachers, published as a book – Elementary mathematics from an advanced standpoint – set the standard for presenting mathematics to teachers. Felix Klein was active as a curriculum developer and in the syllabus developed by him – the so-called Meraner Lehrpläne – he made a plea for a balance between applications and pure mathematics in schools. This balance continues to be one characteristic of the German tradition of mathematics education, exemplified by joint seminars at the Mathematisches Forschungsinstitut Oberwolfach until today.

Through his participation in the international mathematics education community at the beginning of the twentieth century Felix Klein established strong relations to mathematics educators in other countries of the world. This was especially so in many European countries, with which Germany shares many common roots, including shared pedagogical and philosophical traditions. These strong connections are apparent in the European tradition of didactics, called Didaktik in German. This Didaktik-tradition can be found in many European countries and has as a common core a theoretical foundation of education with a strong normative orientation.

The German tradition in didactics of mathematics has many distinctive features, which will be evident during the congress and which will offer ICME-13 participants deeper insights into Continental European traditions of mathematics education. Some of these features are related to argumentation and proof, various types of proof and its role in mathematics teaching. This strand of the discussion is especially connected to a particular approach to didactics of mathematics, which is subject-bound and strongly oriented towards mathematics (so-called Stoffdidaktik). This approach was already evident in Arnold Kirsch's keynote lecture on Aspects of Simplification in Mathematics Teaching at ICME-3 in Karlsruhe and has further developed in the last 40 years. Other distinctive features are related to applications and modelling, which play a prominent role in German mathematics education with foundations going back to Felix Klein. Since that time real world examples and modelling have increased in their significance in school and teacher education and German research and discussion has evolved around these ideas. Projects on teacher education and teacher training, strongly connected to the ideas of Felix Klein, have been developed in the German speaking community, especially by our Austrian colleagues. A further area of distinctiveness is the history of mathematics and its education which has been intensively researched and many ideas originating in the history of mathematics have found their way into the mathematics education discourse in German speaking countries. Another distinctive feature is the tight connection between theory and practice in mathematics education, for example in empirical research based on socio-cultural and psychological perspectives on mathematics and its education. This illustrates the richness and variety of empirical research, which is both qualitatively and quantitatively oriented. Especially in Switzerland psychological aspects going back to the psychologists Piaget and Aebli have been promoted and further developed. Strongly connected to these empirical activities is another feature of German mathematics education, namely a focus on practical activities aimed at direct improvement of the teaching-learning process. As Erich Wittmann elaborated in his keynote lecture “Developing Mathematics Education in a Systemic Process” at ICME-9 in Tokyo/Makuhari substantial learning environments bridge the gap between theory and practice. These activities lead to many innovations in school practice, for example, by discovery learning, problem solving or, modelling and applications in mathematics education.

This variety and richness of different perspectives and approaches has its origin, in part, in the early foundation of mathematics education as an academic field at German universities. There are now about two hundred professors of mathematics education in German speaking countries and many more academic researchers. German mathematics education includes important interdisciplinary empirical research groups involving educationalists and psychologists and following high empirical standards. These research groups offer excellent research and graduate study possibilities for many young researchers.

Furthermore, the German tradition in mathematics education derives distinctiveness from its strong educational roots, in particular, in the holistic concept of Bildung. This concept, which is only partly covered by the term education, was developed by the reformer Wilhelm von Humboldt some two hundred years ago, and refers to the highest possible grade of development of a human being and personality. This educational philosophy has led to an educational system that emphasises the personal development of students as well as the demands of the society, a balance that is reflected in new developments in didactics and related discussions on school syllabi in mathematics education.

The strong international connections of the German speaking mathematics education community dates back to the time of Felix Klein, but was strengthened when ICME-3 was held in Karlsruhe in 1976. The organisation of ICME-3 reflects the German tradition of collaboration between mathematicians and mathematics educators, with the mathematics educator Hans-Georg Steiner as Chair of the International Programme Committee and mathematician Heinz Kunle as Chief Organiser of the congress. Based on his experiences with ICME-3 and other international contacts, Hans-Georg Steiner further promoted German didactics in many international contexts, for example, bilateral symposia with Italy and France in the 1980s and 1990s. Since then many international conferences have taken place in Germany, including conferences of the ICME affiliated study group ICTMA (International Community of Teachers of Mathematical Modelling and its Applications), the ICMI study conference on the teaching of mathematical modelling and applications, and conferences of the International Commission for the Study and Improvement of Mathematics Teaching (CIEAEM). The ICMI Study Group on Psychology of Mathematics Education will hold its 37th conference 2013 in Kiel, just a one hour train ride from Hamburg.

The continuing involvement of the German mathematics education community in European developments is apparent in the prominent role of German speaking researchers in the foundation of the group European Researchers in Mathematics Education (ERME), which held its first conference 1998 in Melle near Osnabrück. The first summer school for Young European Researchers in Mathematics Education took place 2002 in Klagenfurt (YESS1).

In addition, three important international conferences of the supporting societies have set milestones in the last decades. The International Congress of Mathematicians (ICM) took place in 1998 in Berlin, organised by the German Society of Mathematics, and attracted more than three thousand mathematicians and mathematics educators from all over the world. Furthermore, the European Educational Research Association held its European Conference on Educational Research in 2003 in Hamburg and in 2009 in Vienna with significant participation of European mathematics educators.

The long standing contribution of the German speaking mathematics education community to the international discourse on mathematics education is apparent in the early establishment of a review journal, the Zentralblatt für Didaktik der Mathematik (ZDM) which was founded in 1969 by Hans-Georg Steiner and Heinz Kunle, strongly influenced by the success of ICME-3 in Karlsruhe. The original ZDM was characterised by its division in two parts with distinct functions: the documentation section, reviewing the important international literature on mathematics education, and the analysis section, reflecting the current discussion in mathematics education. The analysis section is now published separately as a journal by Springer under the name ZDM – The International Journal on Mathematics Education. The review part is now strongly related to the Zentralblatt für Mathematik and is operated under the name MathEduc. It is the only database worldwide concentrating exclusively on mathematics education.

These activities have always been supported at the political level, both conceptually and financially, especially in recent decades. An important indicator for this promotion is the establishment of the Standing Office of IMU in 2011 in Berlin, which is strongly supported by the Federal State of Berlin and the Federal Ministry of Education and Research. This development is not only of high interest for the International Mathematical Union (IMU), but for ICMI as well.