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What is the purpose of mathematics ?

What is the purpose of mathematics ?. ” Towards a Philosophy of Critical Mathematics Education ” Ole Skovsmose (1994), Kluwer.Dordrecht. Critical Mathematics education why ?. Mathematics has formatting power influencing both reality and minds

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What is the purpose of mathematics ?

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

  2. CriticalMathematicseducationwhy ? • Mathematics has formatting power influencingboth reality and minds • ” Weareborninto a worldwith so manyinstances of prescriptivemathematics in placethatwearehardlyaware of them, and once, theyarepointed out wecanhardlyimagine the worldworkingwithoutthem. • We have prescribedthese systems , often for reasonsonlyknown to a few. Theyregulate and alter our lives and characteriseour civilisation” (David & Hersh in Skovsmose 1996, p. 1268)

  3. The cultural-historicalorigins of mathematicseducation ?(cf.Engeström) • Mathematics as criticalthinking • As part of rationalism the structure of mathematicsbecame the guideline for all science. • Logicalpositivism – a neutral and objective science, mathematics as itslanguage • Criticalthinking , logicalreasoning and mathematicswereunitedand became a pattern for othersciences

  4. Mathematics as criticalthinking • According to logicalpositivismcritique still meant ”logicalclarification” • To developmathematics and to developmathematics as a critical entreprise was the same thing.(enlightenment,optimism and belief in human reason)

  5. Criticalmathematicsquestion the harmony and neutrality of mathematics • Technologicaloptimism has beensupplemented /replaced by skepticism. • ”.. Over the last 100 yearswe have seenadvances in the development of new technologies and yet the same century has showndespicable human behavior, insecurity and irreversible destruction of the environment. • Most of the means to achievethesewonders and horrors of science and technology have to do withadvances 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 thesubject of critique(logicalclarificaion) • but alsobecomes theobject of critique.

  7. Critique of mathematicseducation • ”Whilemathematicswasproposed to be a subjectstructured by pure reason, the teaching of mathematics as a global concerndevelopedrigorousstructures far removed from anycriticalenterprise. • Instead of being a disciplinereflectingcriticalthinking , mathematicseducationbecameassociatedwithdomination,(anxiety), control, tests and rigid forms of communication”(Skovsmose, p. 1259)

  8. Criticalmathematicseducation • Critiquecannotdevelopsolely as a philosophicaltask, but must alsobedeveloped as an ongoingeducationaltask. • Critiquecannotbeassociatedonlywithlogicalreasoning, but must refer tobroadercontent matter and to social issues as well. • Mathematicsplay a crucialrole in social and technologicaldevelopment. Thus • Mathematicseducationhas a criticalrole in the distribution of power and welfare.

  9. CriticalMathematicsEducation • ” If a discussion of mathematicseducation is reduced to questions of content, thenmathematics and mathematicseducationactsblindlytogether.” (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. Criticalthinking, 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. • Howcanthisbe done at all and without violating the best of traditionalthinking ?

  12. Democracyrequirescriticaleducation • 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 findingways of dealing with such problems.

  13. Concerns in CriticalMathematicsEducation: • Mathematicsreproduceinequalitieswhichmightbeestablishedoutsideeducation, but neverthelessarereinforced by educationalpractice ? • The function of mathematics as part of moderntechnologies and technologicaldevelopment ? • Howcanmathematicsbe a tool foridentifying and analyzingessential features of society – global as well as local ?

  14. Theoretical inspiration for CriticalMathematicseducation • NorthernEurope: • CriticalTheory – the Frankfurter School (Adorno, Oscar Negtand others) • The USA, southernEurope, Southamerica, S.A: • Paolo Freire • Africa : AfricanMathematical Union Commissionon the History of Mathematics in Africa (AMUCHMA)(Skovsmose 1996,p. 1279)

  15. Examples of criticalmathematicspractice • Gutstein: ” Reading the worldwithmathematics”(Chicago inner city) • Danish study of authenticmathematicmodelling: Simulation model of the EconomicCouncil”(Skovsmose 1996,p.1269) • Borba´swork in the favelas of Brazil (Skovsmose 1996,p. 1268) • ”Energy”( Skovsmose 1994, 1996,p. 1266) • …

  16. CriticalMathematicseducationDifferentconceptswith the same meaning • Mathematics for social Justice (Gutstein, E.) • Mathematics for equality and social justice (Shan, S-J and Bailey, P.(1991) • MathematicalEducation and Democracy( Skovsmose, O. 1990) • RadicalMath ( 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):ErziehungzurMündigkeit.Suhrkamp. Frankfurt Am Main • Frankenstein, M.( (1989):RelearningMathematics: A differentThird R- RadicalMaths. 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: ClassroomMathematics for Equality and Justice.TrenthamBooks, Stoke-on Trent. • Skovsmose, O.(1990):MathematicalEducation and Democracy. Educational Studies in Mathematics 21, 109-128 • Skovsmose, O.(1994):Towards a Philosophy of CriticalMathematicsEducation.Kluwer.Dordrecht. • Skovsmose, O & Nielsen, L.(1996): CriticalMathematicsEducation.In Bishop, A. et al: International Handbook of MathematicsEducation.Kluwer, Dordrechtpp 1257-1287

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