1. What is the purpose of mathematics ? ”Towards a Philosophy of Critical Mathematics Education” Ole Skovsmose(1994), Kluwer.Dordrecht

2. Critical Mathematics education why ? Mathematics has formatting power influencing both reality and minds ” We are born into a world with so many instances of prescriptive mathematics in place that we are hardly aware of them, and once, they are pointed out we can hardly imagine the world working without them. We have prescribed these systems, often for reasons only known to a few. They regulate and alter our lives and characterise our civilisation” (David & Hersh in Skovsmose 1996, p. 1268)

3. The cultural-historical origins of mathematics education ? (cf.Engeström) Mathematics as critical thinking As part of rationalism the structure of mathematics became the guideline for all science. Logical positivism – a neutral and objective science, mathematics as its language Critical thinking, logical reasoning and mathematics were united and became a pattern for other sciences

4. Mathematics as critical thinking According to logical positivism critique still meant ”logical clarification” To develop mathematics and to develop mathematics as a critical entreprise was the same thing.(enlightenment,optimism and belief in human reason)

5. Critical mathematics question the harmony and neutrality of mathematics Technological optimism has been supplemented /replaced by skepticism. ”.. Over the last 100 years we have seen advances in the development of new technologies and yet the same century has shown despicable human behavior, insecurity and irreversible destruction of the environment. Most of the means to achieve these wonders and horrors of science and technology have to do with advances in mathematics ”(D`ambrosio.In Skovsmose (1996, p. 1259)

6. Critique versus critique Mathematics has served to limit the notion of critique and encapsulated it in a cage of logic. Mathematics is no longer only the subject of critique (logical clarificaion) but also becomes the object of critique.

7. Critique of mathematics education ”While mathematics was proposed to be a subject structured by pure reason, the teaching of mathematics as a global concern developed rigorous structures far removed from any critical enterprise. Instead of being a discipline reflecting critical thinking, mathematics education became associated with domination,(anxiety), control, tests and rigid forms of communication” (Skovsmose, p. 1259)

8. Critical mathematics education Critique cannot develop solely as a philosophical task, but must also be developed as an ongoing educational task. Critique cannot be associated only with logical reasoning, but must refer to broader content matter and to social issues as well. Mathematics play a crucial role in social and technological development. Thus Mathematics education has a critical role in the distribution of power and welfare.

9. Critical Mathematics Education ” If a discussion of mathematics education is reduced to questions of content, then mathematics and mathematics education acts blindly together.” (skovsmose, p. 1260)

10. Democracy & Education In a traditional society, based on the use of manual tools, no specific technological knowledge seems needed to evaluate the acts and decisions of the people in charge. In a highly technological society. the content of democratic competence seems rapidly to acquire a tremendous complexity. On the face of it only a limited group of people seem to be able to manage this complexity, because this complexity seems to presuppose technological knowledge. And this technological knowledge is based on mathematics.

11. Critical thinking, democracy and tradition The utopian aim is to be on an equal footing with the authorities. Schools must be defended as an important public service that educates students to be critical citizens who can think, challenge, take risks and believe that their actions will make a difference in the larger society. How can this be done at all and without violating the best of traditional thinking ?

12. Democracy requires critical education A major concern of education is to prepare students for later participation in the economic processes of society, as education must distribute the skills necessary for society to function. Education must also prepare students for (political) life in society. The educational concern for democracy and critical education come to share the task of empowerment for citizenship. Critical education must assume an active role in identifying inequalities in society, in identifying causes for the emergent sociological and ecological crises and in finding ways of dealing with such problems.

13. Concerns in Critical Mathematics Education : Mathematics reproduce inequalities which might be established outside education, but nevertheless are reinforced by educational practice ? The function of mathematics as part of modern technologies and technological development ? How can mathematics be a tool for identifying and analyzing essential features of society – global as well as local ?

14. Theoretical inspiration for Critical Mathematics education Northern Europe: Critical Theory – the Frankfurter School (Adorno, Oscar Negt and others) The USA, southern Europe, Southamerica, S.A: Paolo Freire Africa : African Mathematical Union Commission on the History of Mathematics in Africa (AMUCHMA) (Skovsmose 1996,p. 1279)

15. Examples of critical mathematics practice Gutstein: ” Reading the world with mathematics”(Chicago inner city) Danish study of authentic mathematic modelling: Simulation model of the Economic Council” (Skovsmose 1996,p.1269) Borba´s work in the favelas of Brazil (Skovsmose 1996,p. 1268) ”Energy” ( Skovsmose 1994, 1996,p. 1266) …

16. Critical Mathematics education Different concepts with the same meaning Mathematics for social Justice (Gutstein, E.) Mathematics for equality and social justice (Shan, S-J and Bailey, P.(1991) Mathematical Education and Democracy( Skovsmose, O. 1990) Radical Math ( Frankenstein,M. 1989) …….

17. Questions for discussion Can education contribute in taking over the job of developing democratic competence ? Does mathematics have a special role to play in an education for democracy in a highly technological society ? Does the curriculum and current textbooks enable students to realize the above purpose ?

18. References Adorno, T.W.(1971): Erziehung zur Mündigkeit.Suhrkamp. Frankfurt Am Main Frankenstein, M.( (1989):Relearning Mathematics: A different Third R- Radical Maths. Free Association Books. London. Freire,P.(1972): Pedagogy of the Oppressed.Herder and Herder, New. York Gutstein, E.( Shan, S-J and BaileyP.(1991): Multiple Factors: Classroom Mathematics for Equality and Justice.Trentham Books, Stoke-on Trent. Skovsmose, O.(1990): Mathematical Education and Democracy. Educational Studies in Mathematics 21, 109-128 Skovsmose, O.(1994):Towards a Philosophy of Critical Mathematics Education.Kluwer. Dordrecht. Skovsmose, O & Nielsen, L.(1996): Critical Mathematics Education. In Bishop, A. et al: International Handbook of Mathematics Education. Kluwer, Dordrecht pp 1257-1287