Short Info



In 1985 the State of Nordrhein-Westfalen adopted a new syllabus for mathematics at the primary level (grades 1 to 4). This syllabus is essentially the work of Heinrich Winter, one of the leading German mathematics educators, who chaired the commission preparing the document.
For three reasons this syllabus marked an important turning point in the history of mathematical education in Germany:

  • The list of objectives also contains the so-called general objectives "mathematising", "exploring", "reasoning" and "communicating" which reflect basic components of doing mathematics at all levels
  • The complementarity of the structural and the applied aspect of mathematics is stated explicitly and its consequences for teaching are described in some detail
  • The principle of learning by discovery is explicitly prescribed as the basic principle of teaching and learning.
    In order to support teachers in putting this syllabus into practice the project "mathe 2000" was founded at the University of Dortmund in 1987 as a joint venture of the chairs "Didactics of Mathematics at the Primary Level" (Gerhard N. Müller) and "Foundations of Didactics of Mathematics" (Erich Ch. Wittmann). In 1993 Heinz Steinbring joined the project and brought in the missing empirical component. Since its inception "mathe 2000" has been based mainly on the brains of its members and so has been independent of funds although some of its research was funded.

Basic philosophy

According to a conception of mathematics education as a "design science" three areas of research and development are closely linked and pursued simultaneously:

  • the design of substantial learning environments and curricula,
  • empirical studies into children's thinking and into communication in the classroom
  • practical work (pre-service and in-service teacher education in both mathematics and didactics, school development, counselling).

Four principles are at the heart of the project:

  • Fundamental ideas of mathematics as a guideline (epistemological orientation)
  • Learning as a constructive and social process (socio-psychological orientation)
  • Teaching as organising learning processes (practical orientation)
  • Co-operation with teachers (systemic orientation).

The arch fathers

The roots of the present reform of mathematical education date back to at least the late 19th century. "mathe 2000" is understood as part of a historic process and draws heavily on ideas developed in the past, in particular on the achievements of four "arch fathers":

  • John Dewey (1859-1953), for his clear decision for education in a democratic society and for conceiving of theory as a guide to an enlightened societal practice at all levels (as developed, for example, in "Democracy and Education", "The Child and the Curriculum", "The Relation of Theory and Practice in Education", "The Sources of a Science of Education")
  • Johannes Kühnel (1869-1928), for his precise description of the shift from "guidance and receptivity" towards "organisation and activity" (cf., his classical books "Neubau des Rechenunterrichts" [Reconstructing the Teaching of Arithmetic] and "Die alte Schule" [The Old School])
  • Jean Piaget (1896-1980), for displaying the overwhelming importance of the learner's "constructive actitvity" in his pioneering work in genetic epistemology and psychology ("Psychology of Intelligence", "Mathematical Epistemology and Psychology", "Biology and Knowledge", "Theories and Models of Modern Education")
  • Hans Freudenthal (1905-1990), for his fundamental contributions to understanding mathematics as a human activity and as an educational task as well as for his insistence on developmental research as the core of mathematics education ("Mathematics as an Educational Task", "Weeding and Sowing", "Didactical Phenomenology of Mathematical Structures", "Revisiting Mathematics Education").


The research conducted by project members is documented in numerous articles, many in English, and some books. A special mark of almost all papers is that they are systematically related to specific learning environments.

For an overview of the research conducted by "mathe 2000" see the Report of PME Research Forum "Designing, Researching and Implementing Mathematical Learning Environments - the Research Group "mathe 2000"

The following collection of papers prepared for PME 25 is available in English:
Gerhard N. Müller, Heinz Steinbring and Erich Ch. Wittmann: Selected Papers from "mathe 2000". University of Dortmund: Project "mathe 2000", 2001.
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According to the general orientation of "mathe 2000" the design of materials for use in the classroom is one focus of the project. It was a strategic decision at the very beginning to present the basic message of "mathe 2000" in a "Handbuch produktiver Rechenübungen" [Handbook of practicing skills in a productive way] (2 vols. published in 1990 and 1992). The "Handbuch" contains a systematic epistemological analysis of arithmetic from grades 1 to 4 in the form of substantial learning environments which combine the practice of skills with higher mathematical activities.
The "Handbuch" inspired many teachers to conduct teaching experiments. These experiments were very successful. So it was teachers who demanded a new textbook consistent with the "Handbuch". In collaboration with a group of teachers the four volumes of "Das Zahlenbuch" ["The Book of Numbers"] were developed and tested from 1993 to 1997.
Since the middle of the nineties the book has spread over Germany and crossed the borders to some neighbouring countries (Switzerland, Belgium, and the Netherlands).

The textbook „Das Zahlenbuch“ is complemented by a series of boxes for early mathematical education: „Das kleine Zahlenbuch“ [The Little Book of Numbers], 2 vols., „Das kleine Formenbuch“ [The Little Book of Forms], 2 vols., and „Das kleine Denkspielbuch“ [The Little Book of Logical Games].

For teacher education a new series "Elementarmathematik als Prozess" [Elementary Mathematics as a Process] has been started which provides a novel access to the mathematical education of teachers. The series invites readers not only to do mathematics relevant for school but also to reflect on learning and teaching mathematics while learning mathematics.

Gerhard N. Müller, Heinz Steinbring & Erich Ch. Wittmann: Arithmetik als Prozess [Arithmetic as a Process] published in 2003 by Kallmeyer.

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