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Doubtful Rationality

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Book cover Towards Equity in Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

The paper addresses the following two questions: (1) How can we conceptualise possible socio-political roles of mathematics-based rationality? (2) How can we conceptualise possible the socio-political roles of mathematics education? Together the two questions might help to shed some light on how mathematical rationality might assume different forms and become integrated into social and technological development. It is pointed out how mathematics-based rationality forms part of the fabrication of possibilities, strategies, facts, contingencies, and perspectives. There is, however, no inherent quality to be associated with such mathematics-based fabrications. It is considered to what extent the school mathematics tradition could establish a prescription readiness by submitting students to a school-mathematics absolutism; and to what extent this tradition could facilitate differentiated labelling of the students, as well as endorsement of an ethical filter. These aspects could be important functions of the school mathematics tradition in today’s knowledge society. It is considered to what extent mathematics education could prepare people for critical citizenship, which includes a potential for ‘talking back’ to authority. I do not see such preparation as being related to the school mathematics tradition, nor do I see it as linked to the very nature of mathematics. Rather, I am proposing it as a possible function of mathematics education.

This chapter is a reprint of an article published in ZDM—The International Journal on Mathematics Education (2007) 39(3), 215–224. DOI 10.1007/s11858-007-0024-5.

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Notes

  1. 1.

    It is not difficult to find contributors to such a book. There have been several studies which exaltedly emphasise the link between mathematics education and democracy. Thus, Hannaford (1998) argues that the mathematical way of arguing is intrinsically connected to democracy, by paying no attention to personal priorities, but only to matters of fact. That mathematics in an axiomatic form and Greek democracy developed in the same historical period is not seen as accidental. See also the discussion in Skovsmose (1994, 1998).

  2. 2.

    For an elaborated discussion of lifeworld see Husserl (1970).

  3. 3.

    This space of contingencies has been addressed in Skovsmose and Valero (2001, 2002) in terms of the critical nature of mathematics education. See also Skovsmose and Valero (2005).

  4. 4.

    The following presentation of mathematical fabrication draws on an insight obtained through a collaborative project including Keiko Yasukawa, Ole Ravn Christensen, and myself. See also the presentation of mathematics in action in Skovsmose (2005) and in Skovsmose and Yasukawa (2004).

  5. 5.

    ‘Bumping’ a passenger means to deny a passenger with a valid ticket access to the plane.

  6. 6.

    See in particular the essay The Assayer, which is reprinted in Galileo (1957, pp. 229–280).

  7. 7.

    I refer to this phenomenon as a mathematical transposition, which I will discuss later.

  8. 8.

    In Alrø and Skovsmose (2002), the notion of bureaucratic absolutism is suggested in order to clarify this possible aspect of the school mathematics tradition. The point is that the nature of command comes to include the pattern of communication in the classroom, and in this way comes to frame the learning of mathematics.

  9. 9.

    This exaggerated use of the right–wrong distinction has been addressed in terms of an ideology of certainty. See Borba and Skovsmose (1997).

  10. 10.

    This possibility was celebrated by logical positivism, which found Galilei’s insight important. What could be counted as ‘secondary sense qualities’, generally speaking, were secondary from a scientific point of view.

  11. 11.

    See also Valero (2002, 2004).

  12. 12.

    See also Skovsmose and Valero (2001), for a discussion of the notion of democracy.

  13. 13.

    See also Gutstein (2006).

  14. 14.

    See also Skovsmose (2006a, 2006b).

  15. 15.

    See also Christensen (2003) for a discussion of the role of reflections in university mathematics and science education, and (Vithal et al. 1995) for a discussion of project work in university-level mathematics education.

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Acknowledgements

This paper makes part of the project ‘Mathematics Education and Democracy’, which is based on a cooperation between Paola Valero, Department of Education, Learning and Philosophy, Aalborg University and me. I want to thank Anne Kepple for completing a careful language revision of the manuscript.

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Authors and Affiliations

  1. Department of Education, Learning and Philosophy, Aalborg University, Fibigerstræde 10, 9220, Aalborg East, Denmark

    Ole Skovsmose

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  1. Ole Skovsmose
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Correspondence to Ole Skovsmose .

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Editors and Affiliations

  1. Fac. Education, Monash University, Wellington Road, Clayton, 3800, Victoria, Australia

    Helen Forgasz

  2. Dept. Mathematics, San Jose State University, Washington Square 1, San Jose, 95192, California, USA

    Ferdinand Rivera

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Skovsmose, O. (2012). Doubtful Rationality. In: Forgasz, H., Rivera, F. (eds) Towards Equity in Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27702-3_32

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