De-traditionalizing Mathematics

Allan Tarp, Paola Valero, Ole Skovsmose, The Royal Danish School of Educational Studies

Abstract

Inspired by Anthony Giddens, a de-traditionalizing effort in mathematics and its teaching will ask: Which are the rituals, formulaic truth, guardians and normative content of tradition in these two practices? How does tradition avoid becoming fundamentalism? Which are the alternatives to tradition? Can mathematics and mathematics education become de-traditionalized?

Introduction

If viewed as social practices and interactions, mathematics and mathematics education can not be conceived apart from the phenomena and trends of the society of which they form a part. Therefore, the sociology of mathematics education should be connected to the analyses of our contemporary world. A relevant issue that is worth exploring is that of tradition. Resisting all attempts of change and being independent of specific contexts, traditional mathematics education is carried out extensively in the world. This is a phenomenon that has been widely described in research (Gregg, 1995; Perry et al., 1998, pp. 16-20) and which is still a preoccupation for people involved in the teaching of mathematics at different levels. But in spite of being a latent problem, the explanations of tradition are limited, mono-causal and insufficient in considering the social context where it takes place. These explanations elaborating on the uncritical copying of motherland practices given by the assumption that mathematics is culture free (the Colonial Echo Model in Clements et al., 1989, cited in Truran, 1997) do not consider the extensive social interaction that has been responsible not only for the implantation of such tradition but also for its maintenance. As a part of real attempts to undermine it, we need to deeply understand what it means and which are its mechanisms. The purpose of this symposium is to promote a collective reflection about tradition in mathematics and its education in order to suggest alternative ways of de-traditionalizing it.

According to the British sociologist Anthony Giddens, tradition involves rituals or the practical means of ensuring preservation as the continual reconstruction of the past; a formulaic truth or a kind of knowledge to which only certain people have full access and is enunciated in words or practices that the speakers or listeners can barely understand; guardians or the people believed to be the agents or mediators of the power conferred by the possession of formulaic truth; and a normative content or the binding character of tradition that depends on the moral and affective links that it builds into people to maintain it (Giddens, 1994, pp. 62-66). If it remains untouched and does not interact dialogically with its alternatives, tradition may become fundamentalism (p. 100).

To mathematics and its education, this raises the following questions:

What constitutes tradition in mathematics and mathematics education?
Which are the alternatives to this tradition?
Where can the roots of the dialogue that may prevent tradition from becoming fundamentalism be found?
How can mathematics and mathematics education be de-traditionalized?

Social constructivism and Social constructivism are two different examples of de-traditionalization, the former of mathematics education and the latter of mathematics itself. The mathematical tradition, inspired by a Platonic and realistic view, would answer to the philosophical question Are concepts part of nature or part of culture? Óthat concepts are part of nature. Accordingly, the main problem of traditional mathematics education is how to produce teacher-proof material to implant mathematics into the students heads. There are different opponents to this tradition. On the one hand, socialconstructivism states a psychological point: students construct their own cognitive version of mathematics. And on the other hand, social constructivism formulates a sociological point: mathematics itself is a social construction emerged from the social need for a number language to assign numbers to things. From this last point of view, the current tradition is the winner, or the closure (Bijker et al., 1987), of a contest between alternative solutions. Becoming debunked by problems as innumeracy, decreasing enrollment, etc., the time has come for a disclosure where tradition must try to defend itself against alternative solutions.

The symposium will begin with an introduction to the topic by the proponents, where we will present Giddens ideas about tradition and the notion of de-traditionalization in contemporary societies. Then, the participants will be invited to reflect in small groups about the meaning and the practices of tradition and de-traditionalizationin mathematics and mathematics education. The small groups for this reflection could be formed according to different criteria, for example, the level of schooling where the participants teach or the characteristics given by Giddens to tradition.And finally, a collective plenary reflection will be devoted to round up the small groupdiscussionand to suggest possible alternatives to de-traditionalize mathematics and mathematics education.

References

Bijker, W. E., Hughes, Th. P. and Pinch, T. (Eds.) (1987). The social construction of technological systems. Cambridge MA: MIT Press

Clements, M.A., Grimison, L.A. and Ellerton, N.F. ;'Colonialism and school mathematics in Australia 1788-1988'. In N.F. Ellerton and M.A. Clements (Eds). School Mathematics: the Challenge to Change (pp. 50-78). Geelong: Deakin University.

Giddens, A. (1994). 'Living in a post-traditional society'. In U. Beck, A. Giddens and S. Lash. Reflexive Modernization (pp. 56-109). Cambridge: Polity Press.

Gregg, J. (1995). 'The tensions and contradictions of the school mathematics tradition'. Journal for Research in Mathematics Education, 26(5), 442-466.

Perry, P., Valero, P., Castro, M., Gomez, C. y Agudelo, C. (1998).'Calidad de la educacion matematica en secundaria. Actores y procesos en lainstitucion educativa'.Bogota: una empresa docente.

Truran, J. M. (1997).'Re-interpreting Australian mathematics curriculum developmentusing a Broad-spectrum Ecological Model'. In Proceedings of the Australian and New Zealand History of Education Society Conference. Old Boundaries and NewFrontiers in Histories of Education, 1 (pp. 241Ð262). Newcastle, New SouthWales: ANZHES.