Gelsa Knijnik
Universidade do Vale do Rio dos Sinos – Brazil

The paper establishes connections between post-modern thinking and the field of Ethnomathematics, using as an argumentative resource some critiques that have been presented by mathematics educators regarding theoretical perspectives of Ethnomathematics. In discussing convergences and divergences of postmodernism and this field of mathematics, the centrality of introducing the category of power when analysing the social and the cultural is presented.


The time we are living in is marked by profound and frighteningly rapid changes: access to a virtual world that simultaneously brings us closer together and keeps us irretrievably apart, due to the exclusion of most of us from an increasingly sophisticated technology; the economic globalization process which simultaneously makes us feel "at home" in any supermarket of the world and fixes us definitely in our own places, due to the impossibility of transiting borders that are increasingly demarcated politically; massive access to the media that almost instantaneously and simultaneously shows us the robot arriving on planet Mars and poverty and death in the Congo, but that says little of the "misfortunes" that happen very close to home. All these changes have caused contrasting and irretrievable changes in our everyday worlds, broadening their very meaning.

Our everyday life is no longer geographically as definitively circumscribed (Has it ever been?), since it is precisely this geography that is blurred, without definitive borders as though it were always moving between here and there, wandering through times that are also undefined, between the past that is present and is already itself also tomorrow.

It is in this time so strongly marked by the "new", by relativity and by uncertainties that Education is rethinking itself, taking a fresh look at its own trajectory to account for the multiple processes that have come into our lives and with which a still puzzled school has dealt now with contempt and now with stubbornness. Even the so-called hard sciences such as Mathematics have been inexorably affected by all of this turbulence that is the hallmark of the end of this century. The rise of Ethnomathematics — an area of Mathematics Education that looks at the connections between mathematics and culture — must be seen in this globalised, cross-cultural scene, where times and spaces mix and mingle.

In this paper, it is my intention to establish connections between post-modern thinking and the field of Ethnomathematics, using as an argumentative resource some critiques that have been presented by mathematics educators regarding theoretical perspectives of Ethnomathematics. Let us begin by looking at Paul Dowling’s discussions (1993). The author’s purpose (1993) is to show that it is only apparent the non-affiliation of Ethnomathematics to the thinking of modernism. In constructing his reasoning, he refers to the existence of an "ideology of monoglossism" in the field of mathematics education of which constructivism is one of its forms. According to Dowling (1993, p. 36) a second manifestation of the "ideology of monoglossism" in mathematics education is "plural monoglossism" and here Ethnomathematics is the example par excellence. In this form of monoglossism, emphasis changes from the individual subject to the cultural subject; society is seen as constituted by a plurality of cultural communities, since in them there is complete absence of monoglossism. Thus society is considered heteroglossic, but the communities that constitute it are monoglossic. Following this rationale, Dowling concludes that Ethnomathematics is a discourse impregnated by the project of Modernity.

Using different arguments, Nick Taylor (1993) also emphasises the strong connection between Ethnomathematics and modernity, when speaking about a "profound ambiguity " in the Ethnomathematics discourse. He takes as one of the focuses of his reasoning the work of Walkerdine, whom he considers the "pre-eminent theorist of Ethnomathematics", stressing the relevance of the post-structuralist approach of the studies performed by this author in discussing questions of context and transference in the learning process. He shows the density of what he calls Walkerdine's "revolt" against the role of mathematics in the modernist project, reinforcing the concepts that

(...) there is only one objective answer to any question; that the world can be represented mathematically and controlled rationally; that universal canons exist in matters such as art, government, sexual preference and cultural norms; and that there is one mathematics which originated in Western Europe and the boundaries of which continue to be patrolled by liberal-democratic, middle class, phallocentric standards" (Taylor 1993, p.132-133). For Taylor it is from this standpoint that Walkerdine provides theoretical support to Ethnomathematics. However, he identifies the "dilemma of Ethnomathematics" precisely in the approach used by Walkerdine when she discusses context and transference. Criticising her he says: (...) the end goal in working from a specific bit of local knowledge — one metaphorical manifestation — to the underlying metonymic principle, is formal mathematics. It is hard to square this teleology with Walkerdine’s devastating attack on the role of formal mathematics as a central repressive mechanism of modernity. It is hard to reconcile the connection she draws between the metaphorical and metonymic elements of knowledge, with her postulation of a disjuncture between problems of practical and material necessity versus problems of symbolic control (ibidem, p.132). Taylor criticises Walkerdine's approach because it is eminently political and pedagogical and not epistemological, which he would consider more central. Even acknowledging that it is not easy to separate the pedagogical, political and epistemological fields in educational discourses, Taylor is interested in establishing differences between them, at least in order to problematise ethnomathematical studies. Taylor’s intention is to show that "whereas the Ethnomathematics ostensibly concerns epistemology, much of the debate revolves around the relationship between pedagogy and politics in mathematics education" (Taylor, 1993, p. 130).

The critiques by Dowling and Taylor could be problematised from different standpoints. The first of them concerns the emphasis placed by Ethnomathematics on the political and pedagogical dimension of Mathematics Education, in detriment of an epistemological approach, an argument presented especially by Taylor.

In fact, the heart of the discussion on Ethnomathematics has not been epistemology. There are at least two distinct perspectives to analyse this fact. The first of them can be summed up in the argument by D’Ambrosio (Knijnik, 1996, p. ix) when he states that the concepts of knowledge, science and education involved in Ethnomathematics have constituted alternative epistemologies and that these are the ones which must be further analysed. On the other hand, in the post-structuralist approach into which Walkerdine fits, the epistemological question is viewed from a different angle. Walkerdine (1990a, 1990b) stresses the distinction between her approach and those eminently epistemological or empirical ones connected to the thinking of Modernity. Thus, Taylor’s critique that Walkerdine's approach is more political than epistemological shows above all that the he did not understand from what "theoretical position" Walkerdine is speaking. She refuses to enter the field of epistemology as understood by Modernity. In her eyes such an epistemological approach does not make any sense because this is exactly the approach that she is opposing. If we consider Walkerdine (as Taylor suggests) the "most prominent theoretist of Ethnomathematics", we see that concerning epistemological matters, there is a close relationship between Ethnomathematics and the Post-structuralist perspective and, in a broader sense, Post-modernity.

Ethnomathematics presented by the authors concerns its affiliation (or not) to the thinking of modernity. What I want to stress here is that Ethnomathematics centrally problematises the "great narrative" which modernists consider to be academic mathematics. Indeed, in a modernist view, Academic Mathematics is the language par excellence to describe the distant as well as nearby Universes. In problematising this metanarrative, Ethnomathematics introduced a discussion that had thus far been absent from debates about Mathematics Education. Indeed, this is a most valuable contribution of Ethnomathematics to Mathematics and Mathematics Education. By legitimising as Mathematics more than just the intellectual products of academe and by considering as forms of other, non-hegemonic ways of knowing and producing mathematics, Ethnomathematics relativizes the "universality" of (academic) Mathematics and, moreover, questions its very nature.

Walkerdine (1990b, p.6) presents a significant argument when she says that:

mathematics provides a clear fantasy of omnipotent control over a calculable universe, which the mathematician Brian Rotman (1980) called Reasons Dream; a dream that things once proved stayed proved for ever, outside the confines of time and space. It is this Dream of Reason that appears to be coming to an end at the close of this millennium. The "promises" of a better life for most women and men on this planet, "promises" promised by scientific advances, by the dominance of reason over the "universe" have definitely disappeared together with the hundreds of thousands of us who continue to be persecuted by hunger, poverty, disease, death. This is a time of the Death of a failed Modernity, because it did not fulfil what it had promised since the French Revolution: fraternity, equality, liberty. In these death throes, "science is part of the problem, not its solution" (Silva, 1996, p. 144).

However, this is also a time of life to take another view of science, to redefine what is after all going to be called science, to think about its place in society, its destiny, which is, in fact, our own destiny as humanity. Ethnomathematics is centrally concerned with problematising such issues and, from this standpoint it converges with discussions proposed by post-modernity. Nevertheless, these convergences can not be constructed without paying attention to some important aspects which must be questioned, as well demonstrated by the authors I mentioned before. Let us take Dowling’s arguments concerning Ethnomathematics as an exemplar of plural monoglossism. This is a key-point to be discussed. What is at stake here is the uniformity, the homogeneity with which the Ethnomathematics perspective has often treated the culture of different social groups, "the identifiable cultural groups".

From the theoretical perspective of Ethnomathematics, the concept of culture moves away from a traditional view that expresses culture as "humanity's cultural heritage". Considering that this cultural heritage is a social construction resulting from the effort of all of us, the expression "humanity's cultural heritage" thus supports the argument that humanity as a whole has the right to access and use knowledge created by humans.

Nevertheless, from a traditional view, the expression "humanity's cultural heritage" is usually identified only with academic mathematics. It is exactly this identification that masks power relations that, in turn, legitimise one very specific mode of producing meaning — the Western, white, male, urban and heterosexual one — as "the" cultural heritage of humanity. In contrast, by providing visibility to other mathematics besides the academic one, Ethnomathematics problematises precisely this apparent "consensus" as to what counts as "humanity's cultural heritage". But, in moving away from this position it also ends up by producing a sort of homogenisation, although many-hued; for Ethnomathematics, each "identifiable" group is identified by what is the same in its members, and, in this sense, similarly to the previous perspective I have just mentioned, the differences, the asymmetries which after all provide the kernel of this very group are silenced.

In ethnomathematics approaches there has often been a "forgetting" of the power relations produced within each cultural group, such as those configured, for instance by gender, race and ethnic relations. Everything happens as though each "identifiable" group were "free" of such power relations, which certainly points to a simplified, not to say naive view, of how social identities are constituted, how people organise their daily lives and give meaning to their life experiences. This is precisely what Skovsmose & Vithal (1997) argue about the lack of discussion regarding relations between culture and power in the research developed by Ethnomathematics. The authors write:

The ethnomathematical practice, generated by a particular cultural group, is not only the result of interactions with the natural and social environment but also subjected to interactions with the power relations both among and within cultural groups. ethnomathematical studies have demonstrated how this has been played out between the Eurocentrism of academic mathematics and the mathematics of identifiable cultural groups, but have not equally applied this analysis to an analogous situation that occurs within an identified cultural group (Skovsmose & Vithal, 1997, p.11). As long as ethnomathematical studies do not pay careful attention to these issues, Ethnomathematics will fluctuate ambivalently between Modernity and Post-modernity. My most recent efforts have been directed at developing empirical projects with the Landless People which lead me to theorise more emphatically the power relations produced within that social movement, projects that allow me to examine the processes established in the dispute to define what knowledges among those practised by their members are instituted as regimes of truth, in the words of Foucault. To analyse such power relations will provide us with better conditions to politicise the field of Ethnomathematics in a post-modern approach.


I am indebted to Arthur Powell for his critical comments of this paper.


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