In 1985 the state Northrhine-Westphalia 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" that 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 inquiry–based learning 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).

Since its inception Mathe 2000 has been based mainly on the brains of its members and so has been independent of funds.

In 2012 the project was re-organized. In order to emphasize the continuation to the** secondary level **the logo was extended.

## Basic philosophy

Mathe 2000 is based on the view of mathematics education as a „design science“. Linked to this orientation is a distinct **mathematical **foundation: Mathematics as the science of (beautiful and useful) patterns is not only seen as subject matter for teaching but also as most important source for developing materials and conducting lessons.

Mathe 2000 rejects additives from other disciplines that are not in line with the nature of mathematics.

A comparison might be appropriate for illustrating this position: The movement slow food founded 1986, one year earlier than Mathe 2000, is focusing on the natural ingredients of organic food in contrast to technologically produced food that is full of artificial additives.

In order to underline the mathematical foundation of the project the logos have been chosen consciously:

For the Pythagorean brotherhood (around 550 B.C.) the representation of 10 dots in a triangular shape (in Greek “tetraktys”) served as a symbol for the harmony of the cosmos for the following reason: When a taut chord is plucked a certain tone is heard. When the chord is halved – its ratio with the original length is then 1 : 2 – we hear the octave. Two thirds of chord (ratio 2:3) lead to the quint, three fourth (ratio 3:4) to the quart, other harmonic intervals. The ratios 4:5 and 5:6 continue the series and produce the major third and the minor third.

## The arch fathers

Mathe 2000 is understood as part of a historical process and draws heavily from ideas developed in the past, in particular from the achievements of five "arch fathers", who have been chosen for good reasons:

**John Dewey (1859-1953)**, for his clear decision for a democratic society, for his genetic view of subject matter, 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 "instruction 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").

**Heinrich Winter (1928-2017)**, for his contributions to elementary mathematics (for which he received the honarary doctorate from the Dept. of Mathematics of the University of Dortmund), his profound theoretical papers on the foundations of mathematics education, and his substantial practice-oriented articles that cover the whole spectrum from the primary to the secondary level and pay attention to mathematical structures and applications in a balanced way (“Entdeckendes Lernen im Mathematikunterricht”, “Sachrechnen in der Grundschule”).

## Materials

It was a strategic decision at the very beginning to convey the basic message in a "**Handbuch produktiver Rechenübungen**" [Handbook of practicing skills in a productive way] (2 vols. published in 1990 and 1992, revised in 2017 and 2018).

The "Handbuch" contains a systematic structure-genetic 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** were developed and tested from 1993 to 1997.

Since the middle of the nineties this textbook has spread over Germany and crossed the borders to some neighboring countries (Switzerland, Belgium, the Netherlands, Luxembourg, Austria, Italy/Province Alto Adige). In 2014 an English version, **THE BOOK OF NUMBERS**, has been developed for the (so far) exclusive use in the Swiss International Schools.

**DAS ZAHLENBUCH** is complemented by a program for early math education.

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

The first volume is devoted to arithmetic:

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

For further information see the folder Program Mathe 2000 – A Unified Approach to Learning Mathematics and The Book of Numbers. Early Math Program and the description of the software “Plättchen & Co. digital”.

The philosophy of the project is also discussed in the paper: Katrin Akinwunmi, Karina Höveler & Susanne Schnell. On the Importance of Subject Matter in Mathematics Education: A Conversation with Erich Christian Wittmann. Eurasia Journal of Mathematics, Science and Technology Education 2014, 10(4), 357 - 363