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Mathematical Thinking Styles in School and Across Cultures

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Selected Regular Lectures from the 12th International Congress on Mathematical Education

Abstract

A mathematical thinking style is the way in which an individual prefers to present, to understand and to think through, mathematical facts and connections by certain internal imaginations and/or externalized representations. In which way mathematical thinking styles (analytic, visual and integrated) are influence factors on the learning and teaching of mathematics is described on the basis of selected qualitative empirical studies from primary up to secondary school. Within the current MaTHSCu-project the styles are measured quantitatively by comparing mathematical thinking styles in eastern and western cultures. This study is introduced and first results are shown. Finally conclusions and implications for school are drawn.

I experienced myself, how mathematics can be opened by one teacher and closed by another. (Wagenschein 1983).

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Notes

  1. 1.

    Many thanks to Prof. Oh Nam Kwon and Prof. Mi-Kyung from the Seoul National University, South Korea.

  2. 2.

    Many thanks to Prof. Toshikazu Ikeda from the Yokohama National University, Japan.

  3. 3.

    In Germany primary school is from grade 1 to grade 4, ages from 6 to 10 years.

  4. 4.

    Funded by the Central Research Foundation of University of Kassel (ZFF).

  5. 5.

    See the full version of the scales of mathematical thinking styles in the appendix as well as the open tasks.

  6. 6.

    Results of the students’ questionnaire.

References

  • Biggs, J. B. (1996). Western misperceptions of the confucian-heritage learning culture. In D. A. Watkins & J. B. Biggs (Eds.), The Chinese Learner. Cultural, psychological and contextual influences (pp. 45–67). Hong Kong: Comparative Education Research Centre, The University of Hong Kong, The Australian Council for Educational Research.

    Google Scholar 

  • Borromeo Ferri, R. (2004). Mathematische denkstile. Franzbecker: Ergebnisse einer empirischen Studie. Hildesheim.

    Google Scholar 

  • Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modelling behaviour. Journal für Mathematikdidaktik, 31(1), 99–118.

    Article  Google Scholar 

  • Borromeo Ferri, R. (2011). Wege zur Innenwelt des mathematischen Modellierens—Kognitive Analysen von Modellierungsprozessen im Mathematikunterricht. Wiesbaden: Vieweg + Teubner.

    Google Scholar 

  • Borromeo Ferri, R., & Blum, W. (2009). Insight into teachers‘ unconscious behaviour in modelling contexts. In R. Lesh, et al. (Eds.), Modelling students’ modelling competencies (ICTMA13) (pp. 423–432). New York: Springer.

    Google Scholar 

  • Borromeo Ferri, R., & Kaiser, G. (2003). First results of a study of different mathematical thinking styles of schoolchildren. In L. Burton (Ed.), Which way?: Social justice in mathematics education (pp. 209–239). London: Greenwood.

    Google Scholar 

  • Burton, L. (1995). Moving towards a feminist epistemology of mathematics. Educational Studies in Mathematics, 28(2), 275–291.

    Article  Google Scholar 

  • Cai, J. (1995). A cognitive analysis of U.S. and Chinese students’ mathematical performance on tasks involving computation, simple problem solving, and complex problem solving. Journal for Research in Mathematics Education. (monograph series 7. Reston, VA, National Council of Teachers of Mathematics).

    Google Scholar 

  • Cai, J. (1998). An investigation of U.S. and Chinese students’ mathematical problem posing and problem solving. Mathematics Education Research Journal, 10, 37–50.

    Article  Google Scholar 

  • Cai, J. (2002). Assessing and understandig U.S. and Chinese students‘ mathematical thinking: Some issues from cross-national studies. Zentralblatt für Didaktik der Mathematik, 34(6), 278–290.

    Google Scholar 

  • Hadamard, J. (1945). The psychology of invention in the mathematical field. Toronto: Princeton University Press.

    Google Scholar 

  • Kühnen, U. (2003). Denken auf Asiatisch. Gehirn Geist, 3, 10–15.

    Google Scholar 

  • Leung, F. K. S. (2001). In search of an east asian identity in mathematics education. Educational Studies in Mathematics, 47(81), 35–51.

    Article  Google Scholar 

  • Masuda, T., & Nisbett, R. E. (2001). Attending holistically versus analytically. Journal of Personality and Social Psychology, 81, 922.

    Article  Google Scholar 

  • Nisbett, R. E. (2003). The geography of thought. London: Nicholas Brealey Publ. Ltd.

    Google Scholar 

  • PISA-Consortium Deutschland (Eds.) (2006). PISA 2003. Dokumentation der Erhebungsinstrumente. Münster: Waxmann.

    Google Scholar 

  • Riding, R., & Rayner, S. (1998). Cognitive styles and learning strategies. London: David Fulton.

    Google Scholar 

  • Riding. R. (2001). The nature and effects of cognitive style. In Sternberg, R., & Zhang, L (Eds.), Perspectives on thinking, learning and cognitive styles (pp. 47–72). London: Erlbaum.

    Google Scholar 

  • Schwank, I. (1996). Zur Konzeption prädikativer versus funktionaler kognitiver Strukturen und ihrer Anwendungen. Zentralblatt für Didaktik der Mathematik, 6, 168–183.

    Google Scholar 

  • Skemp, R. (1987). The psychology of learning mathematics. Hillsdale NJ: Erlbaum.

    Google Scholar 

  • Sternberg, R. (1997). Thinking styles. New York: Cambridge University Press.

    Book  Google Scholar 

  • Sternberg, R., & Grigorenko, E. (1997). Are cognitive styles still in style? American Psychologist, 52(7), 700–712.

    Article  Google Scholar 

  • Sternberg, R., & Wagner, R. (1991). MSG thinking styles inventory—manual, Yale University(Unpublished test manual).

    Google Scholar 

  • Sternberg, R., & Zhang, Li-Fang (Eds.). (2001). Perspectives on thinking learning, and cognitive styles. London: Erlbaum.

    Google Scholar 

  • Strauss, A., & Corbin, J. (1990). Basics of qualitative research. London: Sage.

    Google Scholar 

  • Tobies, R. (1987). Zur Berufungspolitik Felix Kleins. Grundsätzliche Ansichten. NTM-Schriftenreihe Geschichte, Naturwissenschaft, Technik, Medizin, 24(2), 43–52.

    Google Scholar 

  • Vollstedt, M. (2011a). On the classification of personal meaning: Theory-governed typology vs. empiricism-based clusters. In Ubuz, B. (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 321–328). Ankara, Turkey: PME.

    Google Scholar 

  • Vollstedt, M. (2011b). The impact of context and culture on the construction of personal meaning. In ERME (European Research in Mathematics Education) (Eds.), European Research in Mathematics Education VII. Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education. Rzeszów, Poland: University of Rzeszów.

    Google Scholar 

  • Wagenschein, M. (1983). Erinnerungen für morgen. Weinheim: Beltz.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Kassel, Kassel, Germany

    Rita Borromeo Ferri

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  1. Rita Borromeo Ferri
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Correspondence to Rita Borromeo Ferri .

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Editors and Affiliations

  1. Seoul National University, Seoul, Korea, Republic of (South Korea)

    Sung Je Cho

Appendix

Appendix

(Scales of mathematical thinking style inventory developed by Rita Borromeo Ferri; University of Kassel, Germany in 2012)

Explanations: the first 5 items are visual/pictorial; item in red color is a neutral item and does not belong to the scale; then 5 items for analytic/formal

Scales of the way of proceeding: wholistic (4 Items) and dissecting (5 items); item in red color is a neutral item and does not belong to the scale

Sub-scales for generating the stylistic patters: internal (4 items) and external (4 items) (types of assimilating information); item in red color is a neutral item and does not belong to the scale

Open tasks within the questionnaire with additional questions

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Borromeo Ferri, R. (2015). Mathematical Thinking Styles in School and Across Cultures. In: Cho, S. (eds) Selected Regular Lectures from the 12th International Congress on Mathematical Education. Springer, Cham. https://doi.org/10.1007/978-3-319-17187-6_9

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