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Critical Mathematics Education

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Part of the Kluwer International Handbooks of Education book series (SIHE,volume 4)

Abstract

Critical Mathematics education is described in terms of ‘concerns’ which cover the following issues:

  1. a)

    Citizenship identifies schooling as including the preparation of students to be an active part of political life.

  2. b)

    Mathematics may serve as a tool for identifying and analysing critical features of society, which may be global as well as having to do with the local environment of students.

  3. c)

    The students’ interest emphasises that the main focus of education cannot be the transformation of (pure) knowledge; instead educational practice must be understood in terms of acting persons.

  4. d)

    Culture and conflicts raise basic questions about discrimination. Does mathematics education reproduce inequalities which might be established by factors outside education but, nevertheless, are reinforced by educational practice?

  5. e)

    Mathematics itself might be problematic because of the function of mathematics as part of modem technology, which no longer can be reviewed with optimism. Mathematics is not only a tool for critique but also an object of critique.

  6. f)

    Critical mathematics education concentrates on life in the classroom to the extent that the communication between teacher and students can reflect power relations.

Keywords

  • Critical Thinking
  • Educational Practice
  • Mathematic Classroom
  • Project Work
  • Sociological Imagination

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  • Abraham, J. and Bibby, N.: 1988, ‘Mathematics and Society: Ethnomathematics and the Public Educator Curriculum’, For the Learning of Mathematics–, 2, 2–1l.

    Google Scholar 

  • Adorno, T. W.: 1971, Erziehung zür Miindigkeit, Suhrkamp, Frankfurt am Main.

    Google Scholar 

  • Alrø, H. and Skovsmose, O.: 1996, ‘On the Right Track’, For the Learning of Mathematics 16, 1, 2–8.

    Google Scholar 

  • Anzinger, W. and Rauch, E. (eds.): 1972, Wörterbuch Kritische Erziehung, Raith, Starnberg.

    Google Scholar 

  • Apple, M. W.: 1982, Education and Power, Routledge and Kegan, London.

    Google Scholar 

  • Bishop, A.J.: 1990, ‘Western Mathematics: The Secret Weapon of Cultural Imperialism’, Race and Class 32, 2, 51–65.

    CrossRef  Google Scholar 

  • Booss-Bavnbek, B.: 1991, ‘Against Ill-founded, Irresponsible Modelling’, in Niss, M., Blum, W. and Huntley, I. (eds.): Teaching of Mathematical Modelling and Applications, Ellis Horwood, Chichester, 70–82.

    Google Scholar 

  • Borba, M. C.: 1990, ‘Ethnomathematics in Education’, For the Learning of Mathematics 10, 1, 39–43.

    Google Scholar 

  • Borba, M. C.: 1991, ‘Freire and Ethnomathematics: An Application of Ethnomathematics: Teaching Math in a Brazilian Favela’, presented in the panel ‘Critical Math in the Classroom’, on the Institute in Honor of Paulo Freire’s 70th Birthday: Challenging Education, Creating Education, New York.

    Google Scholar 

  • Borba, M.C.: 1993, ‘Etnomatematica e a Cultura da Sala de Aula’, Educacao Matematica em Revista, 1, Blumenau, Brazil, 43–60.

    Google Scholar 

  • Borba, M. C.: 1995, Um estudo de etnomátematica: sua incorporação na elaboração de uma proposta pedagógica para o ‘Núcleo-Escola’ da Vila Nogueira-Sao Quirino, Associação de Professores de Matemática, Lisbon.

    Google Scholar 

  • Christiansen, I. M.: 1994, Classroom Interactions in Applied Mathematics Courses I–II, R-94-2045a and R-94-2045b, Department of Mathematics and Computer Science, Aalborg University.

    Google Scholar 

  • D’Ambrosio, U.: 1980, ‘Mathematics and Society: Some historical considerations pedagogical implications’, International Journal of Mathematical Education in Science and Technology 11, 4, 479–488.

    CrossRef  Google Scholar 

  • D’Ambrosio, U.: 1981, ‘Uniting Reality and Action: A Holistic approach to mathematics education’, in Steen, L. A. and Albers, D. J. (eds.): Teaching Teachers, Teaching Students, Birkhäuser, Boston, 33–42.

    CrossRef  Google Scholar 

  • D’Ambrosio, U.: 1985a, ‘Ethnomathematics and its Place in the History and Pedagogy of Mathematics’, For the Learning of Mathematics 5, 1, 44–48.

    Google Scholar 

  • D’Ambrosio, U.: 1985b, ‘Mathematics Education in a Cultural Setting’, International Journal of Mathematical Education in Science and Technology 16, 469–477.

    CrossRef  Google Scholar 

  • D’Ambrosio, U., 1990, Etnomatematica: Arte ou tecnica de explicar e conhecer, Editora Artica, Sao Paulo.

    Google Scholar 

  • D’Ambrosio, U., 1994, ‘Cultural Framing of Mathematics Teaching and Learning’, in Biehler, R. et al. (eds.): Didactics of Mathematics as a Scientific Discipline, Kluwer, Dordrecht, 443–455.

    Google Scholar 

  • Damerow, P., Elwitz, U., Keitel, C., Zimmer, J.: 1974, Elementarmathematik: Lernen für die Praxis? Ein Versuch der Bestimmungfachüberschreitender Curriculumziele, Klett, Stuttgart.

    Google Scholar 

  • Davis, P. J. and Hersh, R.: 1988, Descartes’ Dream: The World According to Mathematics, Penguin Books, London.

    Google Scholar 

  • Dewey, J.: 1966, Democracy and Education, The Free Press, New York. (First edition 1916.)

    Google Scholar 

  • Ernest, P.: 1991, The Philosophy of Mathematics Education, The Falmer Press, London.

    Google Scholar 

  • Fasheh, M.: 1993, ‘From a Dogmatic, Ready-Answer Approach of Teaching Mathematics Towards a Community-Building, process Orientated approach, in Julie et al.–, 1993, 15–19.

    Google Scholar 

  • Fischer, R.: 1993, ‘Mathematics and Social Change’, in Restivo, S. et al. (eds.): Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education, State University of New York Press, Albany, N.Y., 197–218.

    Google Scholar 

  • Frankenstein, M.: 1983, ‘Critical Mathematics Education: An Application of Paulo Freire’s Epistemology’, Journal of Education 165, 4, 315–339. (Reprinted in Shor, I. (ed.): Freire for the Classroom, Boyton and Cook Publishers, Porthmouth, New Hampshire, 1987, 180–210.)

    Google Scholar 

  • Frankenstein, M.: 1989, Relearning Mathematics: A Different Third R-Radical Maths, Free Association Books, London.

    Google Scholar 

  • Frankenstein, M.: 1990, ‘Incorporating Race, Gender, and Class Issues into a Critical Mathematical Literacy Curriculum’, Journal of Negro Education 59, 3, 336–347.

    CrossRef  Google Scholar 

  • Frankenstein, M.: 1993, ‘Teaching for Empowerment: Raising Class Consciousness in a Business/Consumer Mathematics Curriculum’, in Julie, C., Angelis, D. and Davis, Z. (eds.), 1993, Political Dimensions of Mathematics Education 2: Curriculum Reconstruction for Society in Transition, Maskew Miller Longman, Cape Town, 274–285.

    Google Scholar 

  • Frankenstein, M. and Powell, A B.: 1992, ‘Empowering Non-traditional College Students: On Social Ideology and Mathematics Education’, in B. Johnston (ed.): Reclaiming Mathematics, Canberra, Australia: Department of Employment, Education & Training, 188–195. (Originally published in 1989, Science and Nature, 9/10.)

    Google Scholar 

  • Frankenstein, M. and Powell, A B.: 1994, ‘Towards Liberatory Mathematics: Paulo Freire’s Epistemology and Ethnomathematics’, in McLaren, P. and Lankshear, C. (eds.): The Politics of Liberation: Paths from Freire, Routledge, London, 74–99.

    Google Scholar 

  • Freire, P.: 1972, Pedagogy of the Oppressed, Herder and Herder, New York.

    Google Scholar 

  • Freire, P.: 1974, Cultural Actionfor Freedom, Penguin Books, London.

    Google Scholar 

  • Gaddis, K. and Volmink, J. D.: 1993, Social, Cultural, and Political Issues in Mathematics Education: An Annotated Bibliography of Selected Writings, 1980-1990, CAS ME, Durban.

    Google Scholar 

  • Giddens, A: 1986, Sociology: A Brief but Critical Introduction, 2. Edition, MacMillan, London.

    Google Scholar 

  • Giroux, H. A.: 1989, Schooling for Democracy: Critical Pedagogy in the Modern Age, Routledge, London.

    Google Scholar 

  • Hermann, K. and Niss, M.: 1982, Beskœftigelsesmodellen i SMEC III, Nyt Nordisk Forlag Arnold Busck, Copenhagen.

    Google Scholar 

  • Hoffman, M. R. and Powell, A. B.; 1989, ‘Mathematics and Commentary Writing: Vehicles for Student Reflection and Empowerment’, in Keitel, C. et al. (eds.): Mathematics, Education, and Society, UNESCO, Division of Science, Technical and Environmental Education, Paris, 131–133.

    Google Scholar 

  • Hoffman, M. R. and Powell A. B.: 1990, ‘Gattegno and Freire: A Model for Teaching Mathematically Unprepared, Working-Class Students’, in Noss, R. et al. (eds.): Political Dimensions of Mathematics Education: Action and Critique: Proceedings of the First International Conference, 1-4 April 1990, Revised Edition, University of London, London, 205–215.

    Google Scholar 

  • Hoffmann, D.: 1978, Kritische Erziehungswissenschaft, Kohlhammer, Stuttgart.

    Google Scholar 

  • Julie, C., 1993, ‘Peoples Mathematics and the Application of Mathematics’, in Lange, J. de et al. (eds.)}: Innovations in Maths Education by Modelling and Applications}, Ellis Horwood}, Chichester}, 31–40.

    Google Scholar 

  • Julie, C., }Angelis, D. and Davis, Z. (eds.): 1993, Political Dimensions of Mathematics Education 2: Curriculum Reconstruction for Society in Transition, Maskew Miller Longman, CapeTown.

    Google Scholar 

  • Kant, I.: 1929, Critique of Pure Reason, Translated by Norman Kemp Smith, MacMillan, London. (First German edition 1781.)

    Google Scholar 

  • Keitel, C.: 1989, ‘Mathematics and Technology’, For the Learning of Mathematics 9, 1, 7–13.

    Google Scholar 

  • Keitel, C.: 1993, ‘Implicit Mathematical Models in Social Practice and Explicit Mathematics Teaching by Applications’, in de Lange, J. et al. (eds.): Innovations in Maths Education by Modelling and Applications, Ellis Horwood, Chichester, 19–30.

    Google Scholar 

  • Keitel, C. et al. (eds.): 1989, Mathematics, Education and SoCiety, UNESCO, Division of Science, Technical and Environmental Education, Paris.

    Google Scholar 

  • Keitel, C., Kotzmann, E. and Skovsmose, O.: 1993, ‘Beyond the Tunnel-Vision: Analysing the Relationship between Mathematics, Society and Technology’, in Keitel, C. and Ruthven, K. (eds.): Learning from Computers: Mathematics Education and Technology, Springer, Berlin, 243–279.

    CrossRef  Google Scholar 

  • Kibi, M.: 1993, ‘For People’s Power’, in Julie, C., Angelis, D. and Davis, Z. (eds.): Political Dimensions of Mathematics Education 2: Curriculum Reconstruction for Society in Transition, Maskew Miller Longman, Cape Town, 57–67.

    Google Scholar 

  • Knijnik, G., 1993, ‘Culture, Mathematics, Education and the Landless of Southern Brazil’, in Julie, C., Angelis, D. and Davis, Z. (eds.): Political Dimensions of Mathematics Education 2: Curriculum Reconstruction for Society in Transition, Maskew Miller Longman, Cape Town, 149–153.

    Google Scholar 

  • Mellin-Olsen, S.: 1977, Indlœring som social process, Rhodos, Copenhagen.

    Google Scholar 

  • Mellin-Olsen, S.: 1981, ‘Instrumentalism as an Educational Concept’, Educational Studies in Mathematics 12, 351–367.

    CrossRef  Google Scholar 

  • Mellin-Olsen, S.: 1987, The Politics of Mathematics Education, Reidel, Dordrecht.

    Google Scholar 

  • Mellin-Olsen, S.: 1991, Hvordan tenker lœrere om matematikkundervisning?, Bergen Lœrerhøgskole, Landås, Norway.

    Google Scholar 

  • Mills, C. W.: 1959, The Sociological Imagination, Oxford University Press, New York.

    Google Scholar 

  • Mollenhauer, K.: 1973, Erziehung und Emanzipation, Juventa Verlag, München.

    Google Scholar 

  • Münzinger, W. (ed.): 1977, Projektorientierter Mathematikunterricht, Urban und Schwarzenberg, München.

    Google Scholar 

  • Negt, O.: 1964, Soziologische Phantasie und exemplarisches Lernen, Europäische Verlagsanstalt, Frankfurt am Main.

    Google Scholar 

  • Nickson, M.: 1992, ‘The Culture of the Mathematics Classroom: An Unknown Quantity?’, in Grouws, D. W. (ed.): Handbook of Research on Mathematics Teaching and Learning, MacMillan Publishing Company, New York, 101–114.

    Google Scholar 

  • Niss, M.: 1977, ‘The ‘Crises’ in Mathematics Instruction and a new Teacher Education at Grammar School Level’, International Journal of Mathematical Education in Science and Technology 8, 303–321.

    CrossRef  Google Scholar 

  • Niss, M.: 1979, ‘Mathematische Erziehung’, in Volk, D. (ed.), Kritische Stichwörter zum Mathematikunterricht, Wilhelm Fink, München, 150–158.

    Google Scholar 

  • Niss, M.: 1983, ‘Considerations and Experiences Concerning Integrated Courses in Mathematics and Other Subjects’, in Zweng M., et al. (eds.): Proceedings of the Fourth International Congress on Mathematical Education, Birkhäuser, Boston, 247–249.

    Google Scholar 

  • Niss, M.: 1989, ‘Aims and Scope of Applications and Modelling in Mathematics Curricula’, in Blum, W. et al. (eds.): ‘Applications and Modelling in Learning and Teaching Mathematics’, Ellis Horwood, Chichester, 22–31.

    Google Scholar 

  • Niss, M.: 1994, ‘Mathematics and Society’, in Biehler, R. et al. (eds.): ‘Didactics of Mathematics as a Scientific Discipline’, Kluwer, Dordrecht, 367–378.

    Google Scholar 

  • Nissen, G. and Blomhøj, M. (eds.): 1994, Hul i kulturen, Spektrum, Copenhagen.

    Google Scholar 

  • Noddings, N.: 1993, ‘Politicizing the Mathematics Classroom’, in Restivo, S. et al. (eds.): Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education, State University of New York Press, Albany, N.Y., 150–161.

    Google Scholar 

  • Noss, R. et al. (eds.): 1990, ‘Political Dimensions of Mathematics Education: Action and Critique: Proceedings of the First International Conference’, 1-4 April 1990, Revised Edition, University of London, London.

    Google Scholar 

  • Nunes, T., Schliemann, A.D. and Carraher, D.W.: 1993, ’street Mathematics and School Mathematics’, Cambridge University Press, Cambridge.

    Google Scholar 

  • Paffrath, F. H. (ed.): 1987, Kritische Theorie und Pädagogik der Gegenwart, Deutscher Studien Verlag, Weinheim.

    Google Scholar 

  • Raith, W. (ed.): 1973, Handbuch zum Unterricht: Modelle emanzipatorischer Praxis, Hauptschule, Raith, Starnberg.

    Google Scholar 

  • Riess, F. (ed.): 1977, Kritik des mathematisch naturwissenschaftlichen Unterrichts, Päd-Extra Buchverlag, Frankfurt am Main.

    Google Scholar 

  • Shan, S.-J. and Bailey, P.: 1991, Multiple Factors: Classroom Mathematics for Equality and Justice, Trentham Books, Stoke-on-Trent.

    Google Scholar 

  • Skovsmose, O.: 1980, Forandringer i matematikundervisningen, Gyldendal, Copenhagen.

    Google Scholar 

  • Skovsmose, O.: 1981a, Matematikundervisning og kritisk pœdagogik, Gyldendal, Copenhagen.

    Google Scholar 

  • Skovsmose, O.: 1981b, Alternativer og matematikundervisning, Gyldendal, Copenhagen.

    Google Scholar 

  • Skovsmose, O.: 1985, ‘Mathematical Education versus Critical Education’, Educational Studies in Mathematics 16, 337–354.

    CrossRef  Google Scholar 

  • Skovsmose, O.: 1990, ‘Mathematical Education and Democracy’, Educational Studies in Mathematics 21, 109–128.

    CrossRef  Google Scholar 

  • Skovsmose, O.: 1992, ‘Democratic Competence and Reflective Knowing in Mathematics’, For the Learning of Mathematics 2, 2, 2–11.

    Google Scholar 

  • Skovsmose, O.: 1994, Towards a Philosophy of Critical Mathematics Education, Kluwer, Dordrecht.

    CrossRef  Google Scholar 

  • Tybl, R. and Walter, H. (eds.): 1973, Handbuch zum Unterricht: Modelle emanzipatorischer Praxis, Grundschule, Raith, Stamberg.

    Google Scholar 

  • Vithal, R., Christiansen, I.M., and Skovsmose, O.: 1995, ‘Project Work in University Mathematics Education: A Danish Experience: Aalborg University’, Educational Studies in Mathematics 29, 199–223.

    CrossRef  Google Scholar 

  • Voigt, J.: 1985, ‘Patterns and Routines in Classroom Interaction’, Recherches en Didactique des Mathématiques 6, 1, 69–118.

    Google Scholar 

  • Volk, D.: 1975, ‘Plädoyer für einen problemorientierten Mathematikunterricht in emanzipatorischer Absicht’, in Ewers, M. (ed.): Naturwissenschaftliche Didaktik zwischen Kritik und Konstruktion, Belz, Weinheim

    Google Scholar 

  • Yolk, D.: 1977, ‘Entscheidungsfreiraum in den Lehrplänen machen! Wissenschaftstheoretische Probleme der Mathematik in der Ausbildung der Mathematiklehrer aufnehmen’, in Riess, F. (ed.): Kritik des mathematisch naturwissenschaftlichen Unterrichts, Päd-Extra Buchverlag, Frankfurt am Main, 347–392.

    Google Scholar 

  • Volk, D.: 1979, ‘Handlungsorientierende Unterrichtslehre am Beispiel des Mathematikunterrichts, Band A’, Päd Extra Buchverlag, Bensheim.

    Google Scholar 

  • Yolk, D. (ed.): 1979, Kritische Stichwörter zum Mathematikunterricht, Wilhelm Fink, München.

    Google Scholar 

  • Yolk, D.: 1980, Zur Wissenschaftstheorie der Mathematik: Handlungsorientierende Unterrichtslehre, Band B, Päd Extra Buchverlag, Bensheim.

    Google Scholar 

  • Yolk, D.: 1989, ‘Mathematics Classes and Enlightenment’, in Blum, W. et al. (eds.): Applications and Modelling in Learning and Teaching Mathematics, Ellis Horwood, Chichester, 187–191.

    Google Scholar 

  • Volmink, J., 1994, ‘Mathematics by All’, in Lerman, S. (ed.): Cultural Perspectives on the Mathematics Classroom, Kluwer, Dordrecht, 51–68.

    CrossRef  Google Scholar 

  • Wagenschein, M., 1965, Ursprüngliches Verstehen und exaktes Denken I-II, Klett, Stuttgart.

    Google Scholar 

  • Wagenschein, M., 1970, Ursprüngliches Verstehen und exaktes Denken I-II, Klett, Stuttgart.

    Google Scholar 

  • Zaslavsky, C.: 1979, Africa Counts: Number and Pattern in African Culture, Lawrence Hill Books, New York.

    Google Scholar 

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Skovsmose, O., Nielsen, L. (1996). Critical Mathematics Education. In: Bishop, A.J., Clements, K., Keitel, C., Kilpatrick, J., Laborde, C. (eds) International Handbook of Mathematics Education. Kluwer International Handbooks of Education, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1465-0_36

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