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Colin Hannaford.

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It is a common belief that mathematics teaching has no political effects. However, the style of argument now used everywhere in mathematics was not developed originally only to do mathematics. Its original function was to counteract the teaching by the early Greek sophists of rhetoric. Their training gave the rich and privileged such an advantage in public speaking that democracy was being threatened. Making respectable a new form of argument in which evidence and logical structure predominated, was a very radical act of enlightened democratic education. Mathematics teaching in the form of open critical dialogue between teacher and taught remains a very powerful form of education in democratic attitudes. In the early part of this century, however, as mathematics education was again becoming universal throughout Europe, the belief arose that mathematics would eventually be completed as a monolithic structure of truth. This transformed mathematics into a very different paradigm of democracy, one in which unorthodoxy must be eliminated. Communicated implicitly if not explicitly to people everywhere, this belief increased respect for similarly monolithic political ideas from which dissent - and inevitably, dissenters -must also be eliminated. Gödel’s proof that mathematics cannot be completed came too late to prevent the conflict that ideas like these made unavoidable. Since Gödel's proof still stands, and today is better known, modern teachers can use mathematics again with confidence as a proof of the value of very different democratic attitudes and ideas. This is clearly relevant to multi-cultural education. Mathematics is ethically neutral, but the ethical principles which produced both democracy and mathematics can both be conveyed in mathematics teaching. These principles are highly relevant to the modern world. They should be understood and taught by teachers everywhere

This is the fundamental thesis of the Comenius project "Mathematics Teaching and Democratic Education" of the European Union, directed by the Landesinstitut für Erziehung und Unterricht, Stuttgart.

The Proceedings of the Comenius project Mathematics Teaching and Democratic Education [Koehler/Hannaford, A4 128 pages] currently available in English and German, ultimately also in Spanish, also contains the following contributions:

Outline of a possible approach (Koehler)

Mathematics teaching IS democratic education (Hannaford)

Correlations with other learning theories (Carpintero)

Personality structure and self-image of Mathematics teachers (Nieger)

Attitudes to Mathematics and Mathematics teaching (Thoma)

Pedagogical decisions and their consequences (Koehler)

Individualised Mathematics teaching (Darnton)

Towards a democratic culture in Mathematics teaching (Thoma)

Practical results of "Democratic" Mathematics teaching (Hannaford)

As seen by Non-Mathematicians (Camhy, Christoph, Ocana)

Remarks on Teacher Training courses (with EU project advice)

Copies may be obtained in English from LEU Stuttgart, Wiederholdstrasse 13, 70174 Stuttgart, Germany, tel.: 0049 711 1849565 or from me:

Colin Hannaford

The Institute of Democracy from Mathematics (IDM)

10 Marlborough Court,

Oxford OX2 OQT

UK

Tel.: 0044 1865 793752

Email: democracy@maths.win-uk.net