Paola Valero, Ole Skovsmose,
The Royal Danish
School of Educational Studies
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?
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
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
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.
What constitutes tradition in mathematics and mathematics
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?
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.
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