Skip to main content

Advertisement

SpringerLink
Log in

Intercultural Perspectives on Mathematics Learning – Developing a Theoretical Framework

  • Published:
International Journal of Science and Mathematics Education Aims and scope Submit manuscript

Abstract

This paper explores Alan Bishop’s assumption that all formal mathematics education produces cultural conflicts between the children’s everyday culture and the culture of mathematics. Existing empirical studies support the assumption that mathematics learning indeed has some intercultural aspects which can be differentiated in language factors, effects of overlapping, divergent aims and purposes and moments of foreignness. Analysing mathematics learning in this way from an intercultural perspective allows us to integrate perspectives and results from psychological and pedagogical research on intercultural communication and intercultural learning into mathematics education research. Since these results are located on the descriptive and on the prescriptive level, they can be activated both for analysing and for arranging learning processes in an intercultural setting. Hence, in the third part, prescriptive consequences and didactical orientations are formulated for organising mathematics learning as intercultural learning.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arnold, M. (2001). Wissenschaftskulturen im Vergleich, 1–10. Zwischenergebnisse des Projekts Science as Culture. Wien: Institut für Interdisziplinäre Forschung und Fortbildung.

    Google Scholar 

  • Ashcraft, M., Kirk, E.P. & Hopko, D. (1998). On the cognitive sequences of mathematics anxiety. In Donlan (Ed.), The development of mathematical skills (pp. 175–196). Hove: Psychology Press.

    Google Scholar 

  • Auernheimer, G. (1998). Grundmotive und Arbeitsfelder interkultureller Bildung und Erziehung. In Dovermann and Reiberg (Eds.), Interkulturelles Lernen (pp. 18–28). Bonn: Bundeszentrale für politische Bildung.

    Google Scholar 

  • Baruk, S. (1985). L’âge du capitaine: de l’erreur en mathématiques. Paris: Editions du Soleil.

    Google Scholar 

  • Bauersfeld, H. (1983). Subjektive Erfahrungsbereiche als Grundlage einer Interaktionstheorie des Mathematiklernens und -lehrens. In Bauersfeld et al. (Eds.), Learnen und Lehren von Mathematik (pp. 1–56). Köln: Aulis.

    Google Scholar 

  • Becher, T. (1993). Academic tribes and territories: Intellectual enquiry and the cultures of disciplines. Buckingham: Taylor and Francis.

    Google Scholar 

  • Bishop, A.J. (1991). Mathematical enculturation. A cultural perspective on mathematics education. Dordrecht: Kluwer.

    Google Scholar 

  • Bishop, A.J. (1994). Cultural conflicts in mathematics education: Developing a research agenda. For the Learning of Mathematics, 14(2), 15–18.

    Google Scholar 

  • Bishop, A.J. (2002). Mathematical acculturation, cultural conflicts, and transition. In de Abreu et al. (Eds.), Transitions between contexts of mathematical practices (pp. 193–212). Dordrecht: Kluwer.

    Google Scholar 

  • Bolten, J. (2001). Interkulturelle Kompetenz. Erfurt: Landeszentrale für politische Bildung.

    Google Scholar 

  • Bonotto, C. (2001). How to connect school mathematics with students’ out-of-school knowledge. Zentralblatt für Didaktik der Mathematik, 33(3), 75–84.

    Google Scholar 

  • Breitenbach, D. (Ed.) (1979). Kommunikationsbarrieren in der Internationalen Jugendarbeit, Vol. 5. Saarbrücken: Fort Lauderdale.

    Google Scholar 

  • Brenner, M.J. & Moschkovich, J.N. (2002). Everyday and academic mathematics in the classroom. Reston: NCTM.

    Google Scholar 

  • Burton, L. (1995). Moving towards a feminist epistemology of mathematics. Educational Studies in Mathematics, 28(3), 275–291.

    Google Scholar 

  • Civil, M. (1998). Bridging in school mathematics and out-of-school mathematics: A reflection. In Proceedings of the Annual Meetings of the AERA. San Diego, CA.

  • Cobb, P. (Ed.) (1994). Learning mathematics. Constructivist and interaction theories of mathematical development. Educational Studies in Mathematics, 26(2–3).

  • D’Ambrosio, U. (1999). Ethnomathematics and its First International Congress. Zentralblatt für Didaktik der Mathematik, 31(2), 50–53.

    Google Scholar 

  • De Abreu, G., Bishop, A.J. & Pompeu, G. (1992). Approaches to research into cultural conflicts in mathematics learning. In Proceedings of the 16th PME Conference, University of New Hampshire, Durham (pp. 1.25–1.32).

  • De Abreu, G., Bishop, A.J. and Presmeg, N. (Eds.) (2002). Transitions between contexts of mathematical practices. Dordrecht: Kluwer.

    Google Scholar 

  • de Villiers, M. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17–24.

    Google Scholar 

  • Duit, R. (1993). Research on students’ conceptions – developments and trends. In Novak (Ed.), Proceedings of the 3rd International Seminar on Misconceptions and Educational Strategies in Science and Mathematics. Ithaca. New York: Cornell University.

    Google Scholar 

  • Duit, R., Goldberg, F.M. & Niedderer, H. (1992). Research in physics learning: Theoretical issues and empirical studies. Kiel: Institut für die Pädagogik der Naturwissenschaften.

    Google Scholar 

  • Duit, R. & von Rhöneck, C. (Eds.) (1996). Lernen in den Naturwissenschaften. Kiel: Institut für Pädagogik der Naturwissenschaften.

  • Ehlich, K. (1994). Interkulturelle Kommunikation. In H. Goebl et al. (Eds.), Kontaktlinguistik (pp. 920–931). New York.

  • Ernest, P. (1998). Social Constructivism as a Philosophy of Mathematics. New York: State University of New York Press.

    Google Scholar 

  • Ernest, P. (1999). Forms of knowledge in mathematics and mathematics education: Philosophical and rhetorical perspectives. Educational Studies in Mathematics, 38, 67–83.

    Google Scholar 

  • Evans, J. (1999). Building bridges: Reflections on the problem of transfer of learning in mathematics. Educational Studies in Mathematics, 39(1–3), 23–44.

    Google Scholar 

  • Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht: Reidel.

    Google Scholar 

  • Fischbein, E. (1989). Tacit models and mathematical reasoning. For the Learning of Mathematics, 9(2), 9–14.

    Google Scholar 

  • Fischbein, E., Deri, M., Nello, M.S. & Marino, M.S. (1985). The role of implicit models in solving problems in multiplication and division. Journal of Research in Mathematics Education, 16(1), 3–17.

    Google Scholar 

  • Fischer, R. (2001). Höhere Allgemeinbildung. In Fischer-Buck et al. (Eds.), Situation – Ursprung der Bildung (pp. 151–161). Leipzig: Universitätsverlag.

    Google Scholar 

  • Hammer, M.R. (1989). Intercultural communication competence. In Asanteet et al. (Eds.), Handbook of international and intercultural communication (pp. 247–260). Newbury Park: Sage.

    Google Scholar 

  • Hartmann, J. (2002). Schülervorstellungen und Schülerfehler im Bereich Drehungen. Eine mehrperspektivische Betrachtung. Zentralblatt für Didaktik der Mathematik, 34(2), 46–50.

    Google Scholar 

  • Haumersen, P. & Liebe, F. (1990). Eine schwierige Utopie. Der Prozess interkulturellen Lernens in deutsch-französischen Begegnungen. Berlin: Verlag für Wissenschaft und Bildung.

    Google Scholar 

  • Hawkins, J. & Pea, R.D. (1987). Tools for bridging the cultures of everyday and scientific thinking. Journal of Research in Science Teaching, 24(4), 291–307.

    Google Scholar 

  • Hefendehl-Hebeker, L. (1995). Geistige Ermutigung im Mathematikunterricht. In Biehleret et al. (Eds.), Mathematik allgemeinbildend unterrichten (pp. 83–91). Köln: Aulis.

    Google Scholar 

  • Heintz, B. (2000). Die Innenwelt der Mathematik. Zur Kultur und Praxis einer beweisenden Disziplin. New York: Springer.

    Google Scholar 

  • Hersh, R. (1997). What is mathematics, really? London: Jonathan Cape.

    Google Scholar 

  • Heymann, H.W. (1996). Allgemeinbildung und Mathematik. Weinheim: Beltz Verlag. English version (2003): Why teach math? A focus on general education. Dordrecht: Kluwer.

    Google Scholar 

  • Hoffmann, L. (1985). Kommunikationsmittel Fachsprache, 2nd edn. Tübingen: Gunter Narr Verlag.

    Google Scholar 

  • Holzbrecher, A. (1997). Wahrnehmung des Anderen. Zur Didaktik interkulturellen Lernens. Opladen: Leske und Budrich.

    Google Scholar 

  • Jablonka, E. (2003). Mathematical literacy. In Bishop et al. (Eds.), Second international handbook of mathematics education (pp. 75–102). Dordrecht: Kluwer.

    Google Scholar 

  • Kattmann, U., Duit, R. & Gropengießer, H. (1998). Educational reconstruction – bringing together issues of scientific clarification and students’ conceptions. In Bayrhuber and Brinkmann (Eds.), What, why, how? Proceedings of the 1st European Conference on Didaktik of Biology (pp. 253–262). Kiel: IPN.

    Google Scholar 

  • Keitel, C. et al. (Eds.) (1995). Mathematics (education) and common sense. The challenge of social change and technological development. In Proceedings of the 47th CIEAEM Meeting. Berlin: FU Berlin.

  • Kirsch, A. (1970). Elementare Zahlen- und Größenbereiche. Göttingen: Vandenhoeck & Ruprecht.

    Google Scholar 

  • Kitcher, P. (1984). The nature of mathematical knowledge. New York: Oxford University Press.

    Google Scholar 

  • Krämer, S. (1988). Symbolische Maschinen. Die Idee der Formalisierung im geschichtlichen Abriss. Darmstadt: Wiss. Buchgesellschaft.

    Google Scholar 

  • Leenen, W.R. & Grosch, H. (1998). Bausteine zur Grundlegung interkulturellen Lernens. In Dovermann and Reiberg (Eds.), Interkulturelles Lernen (pp. 29–47). Bonn: Bundeszentrale für politische Bildung.

    Google Scholar 

  • Lengnink, K. (2002). Wie Jugendliche über Abhängigkeit reden. Anknüpfungspunkte für eine Einführung in den Funktionsbegriff. In Beiträge zum Mathematikunterrichte (pp. 303–306). Hildesheim: Franzbecker.

    Google Scholar 

  • Lengnink, K. & Peschek, W. (2001). Das Verhältnis von Alltagsdenken und mathematischem Denken als Inhalt mathematischer Bildung. In Lengnink et al. (Eds.), Mathematik und Mensch (pp. 65–81). Mühltal: Verlag Allgemeine Wissenschaft.

    Google Scholar 

  • Lengnink, K. & Prediger, S. (2000). Mathematisches Denken in der Linearen Algebra. Zentralblatt für Didaktik der Mathematik, 32(4), 111–122.

    Google Scholar 

  • Luchtenberg, S. (1999). Interkulturelle kommunikative Kompetenz: Kommunikationsfelder in Schule und Gesellschaft. Opladen: Westdeutscher Verlag.

    Google Scholar 

  • Maier, H. & Schweiger, F. (1999). Mathematik und Sprache. Zum Verstehen und Verwenden von Fachsprache im Unterricht. Wien: oebv und hpt Verlagsgesellschaft.

    Google Scholar 

  • Maier, H. (2002). How much technical language do pupils need in mathematics education? In Weigand et al. (Eds.), Developments in mathematics education in German-speaking countries. Selected papers (pp. 55–66). Hildesheim: Franzbecker.

    Google Scholar 

  • Müller, W. (1987). Von der “Völkerverständigung” zum “Interkulturellen Lernen”. Starnberg: Studienkreis für Tourismus.

    Google Scholar 

  • Niederdrenk-Felgner, C. (1997). Mathematik als Fremdsprache, Beiträge zum Mathematikunterricht, 387–390.

  • Nunes, T., Carraher, D.W. & Schliemann, A.D. (1993). Street mathematics and school mathematics. New York: Cambridge University Press.

    Google Scholar 

  • OECD (1999). Measuring student knowledge and skills. A new framework for assessment. Paris: OECD.

    Google Scholar 

  • Prediger, S. (2002). Kommunikationsbarrieren beim Mathematiklernen. Analysen aus kulturalistischer Sicht. In Prediger et al. (Eds.), Mathematik und Kommunikation (pp. 91–106). Mühltal: Verlag Allgemeine Wissenschaft.

    Google Scholar 

  • Prediger, S. (2004). Mathematiklernen in interkultureller Perspektive. Mathematikphilosophische, deskriptive und präskriptive Betrachtungen, Klagenfurter Beiträge zur Didaktik der Mathematik, Vol. 6. München: Profil.

    Google Scholar 

  • Prediger, S. (2005). Mathematics – cultural product or epistemic exception? To appear in Löwe, B. et al. (Eds.), The history of the concept of the formal sciences. Dordrecht: Kluwer.

  • Rosnick, P. & Clement, J. (1980). Learning without understanding: The effect of tutoring strategies on algebra misconceptions. Journal of Mathematical Behaviour, 3(1), 3–27.

    Google Scholar 

  • Saxe, G.B. (1991). Culture and cognitive development: Studies in mathematical understanding. Hillsdale: Erlbaum.

    Google Scholar 

  • Strike, K.A. & Posner, G. (1982). Conceptual change and science teaching. European Journal of Science Education, 4, 231–240.

    Google Scholar 

  • Thomas, A. (1988). Interkulturelles Lernen im Schüleraustausch. Saarbrücken: Fort Lauderdale.

    Google Scholar 

  • Tomalin, B.& Stempleski, S. (1993). Cultural awareness. Oxford University Press.

  • Tymoczko, T. (Ed.) (1985). New Directions in the philosophy of mathematics. Boston: Birkhäuser.

    Google Scholar 

  • Voigt, J. (1994). Negotiation of mathematical meaning and learning mathematics. Educational Studies in Mathematics, 26(2–3), 275–298.

    Google Scholar 

  • Vollrath, H.-J. (1978). Lernschwierigkeiten, die sich aus dem umgangssprachlichen Verständnis geometrischer Begriffe ergeben. In Lorenz (Ed.), Lernschwierigkeiten: Forschung und Praxis (pp. 57–73). Köln: Aulis.

    Google Scholar 

  • vom Hofe, R. (1998). On the generation of basic ideas and individual images: Normative, descriptive and prescriptive aspects. In Sierpinska and Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity. An ICMI study, Book 2 (pp. 317–331). Dordrecht: Kluwer.

    Google Scholar 

  • White, L.A. (1947). The locus of mathematical reality: An anthropological footnote. Philosophy of Science, 14, 289–303.

    Google Scholar 

  • Wilder, R.L. (1981). Mathematics as a cultural system. Oxford: Pergamon Press.

    Google Scholar 

  • Yackel, E. & Cobb, P. (1996). Sociomath norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Group for Mathematics Education, Department of Mathematics and Computer Science, Postfach 330440, D-28215, Bremen, Germany

    Suzanne Prediger

Authors
  1. Suzanne Prediger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suzanne Prediger.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Prediger, S. Intercultural Perspectives on Mathematics Learning – Developing a Theoretical Framework. Int J Sci Math Educ 2, 377–406 (2004). https://doi.org/10.1007/s10763-004-2685-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10763-004-2685-7

Keywords

Search

Navigation