Authors: Alexandre Pais and Mônica Mesquita
The push to marry off local and school knowledge has been a growing concern within educational sciences, particularly in mathematics education where a field of studies by the name of ethnomathematics has been producing research around the uses people do of mathematics outside school’s walls. Notwithstanding the good will of educational agents in bringing to schools local knowledges, criticisms have been made on the sometimes naive way in which such a bridge is theorized and implemented. After a brief description of these criticisms, we present the Urban Boundaries Project as an attempt to avoid the inconsistencies of schooling, and the promotion of a non-scholarized ethnomathematics.
Introduction
A significant part of ethnomathematics research has educational aims (Borba, 1990; Gerdes, 1995; Barton, 1996; Powell & Frankenstein, 1997; Knijnik, 2004), seeking to bring to the schools or other formal educational environments (like indigenous schools) the knowledge and the mathematical practices of cultural groups of people. This makes ethnomathematics research part of a multicultural approach in education that during the last 30 years has aimed to open schools to the cultural diversity that characterizes our current societies. However, notwithstanding the good will of well intentioned agents, the ways in which the “bridge” between local knowledge and school knowledge is made has been the target of a strong criticism (e.g., Skovsmose & Renuka, 1997; Rowlands & Carson, 2002; Pais, 2011), and some authors have called attention for the problems involved in bringing local knowledge into school settings (e.g., Dowling, 1998; Duarte, 2004; Pais, 2011). At stake in these criticisms is the ethnomathematical assumption that by bringing local knowledge into schools a multicultural education can be achieved. In this article we start by exploring these criticisms. They call our attention to the specific character of schooling, and how the ethnomathematical push to marry off local knowledge and schooling can very well ending up conveying and idea of culture where the Other is squeezed from its otherness (Pais, 2011). Afterwards, we introduce the Urban Boundaries Project—a project based in Portugal and funded by the Fundação para a Ciência e Tecnologia—as an example of an ethnomathematical project that is not concerned with bringing local knowledge into schools, but rather to problematise within the local communities the knowledge and the competences they need it in situ. It is the wager of this article that our society needs to create alternative educational settings as a response for the increasing problem of exclusion faced by so-called minority populations. As long as schools are structured as credit systems (Vinner, 1997), only within non-scholarized settings can a genuine ethnomathematical approach be reached.
Ethnomathematics and schools
By reading the six guiding questions of the Topic Study Group for which we are submitting this paper[1], we easily notice how ethnomathematics is conceived in a strict relation with school. The spirit behind these questions in one that seeks to use research regarding mathematical thinking developed outside school to improve the understanding of mathematics and mathematics teaching and learning in school. This seems to be the most common approach to ethnomathematics within mathematics education research (Adam, Alangui & Barton, 2003): the use of students’ ethnomathematical knowledge to construct a bridge for the learning of school mathematics. However, researchers such as Knijnik (2004) clearly state that “it is not a matter of establishing connections between school mathematics and mathematics as it is used by social groups, with the purpose of achieving a better learning of school mathematics” (p. 228). Where some see as unproblematic the “making of the bridge” between local and school knowledge, others criticize this learning strategy, claiming a place for a more serious understanding of the role of school and how local knowledge is inserted into it. As explored by Pais (2011), the problem with the “bridge metaphor” is the reinforcement of the hegemony of school mathematics because the Other is valorised only as a way to achieve the true knowledge. Thus, it contradicts the critique that ethnomathematics makes to the hegemony of academic mathematics.
At stake here is what ethnomathematicians such as Knijnik (2004), Monteiro (2004), and Duarte (2004) have been referring to as the folkloric way in which ethnomathematical ideas appear in the curriculum. According to them, the use of local knowledge as a curiosity to start the learning of school mathematics could be the cause of social inequalities. However, to truly include ethnomathematical ideas in the curriculum is no less problematic. If we focus on a regular school and take into account its role in preparing students for a globalized market-orientated society, with all the pressure to learn the mathematics of the standard curriculum that will be essential to students’ approval in the high stakes tests, we can ask ourselves if there is a place for ethnomathematical knowledge (or other local, nonscholarly knowledge)? As explored in Pais (2011), after a review of the current research being done in ethnomathematics, the educational implications of ethnomathematics (in a regular school) end up being co-opted by a school that is worried with the uniformization/globalization of knowledge—and not so much with issues of diversity. Monteiro (2004), a Brazilian ethnomathematician, poses the crucial question: “Is it possible to develop ethnomathematical work in the current school model?” (p. 437, our translation from Portuguese).
What is at stake here is the very often disavowed role of schools as places of economical production and ideological reproduction (Pais, in press). One of the main features of ethnomathematics research consists in developing a critique of what is accepted as being mathematical knowledge, by the confrontation of knowledge from different cultures. The existence of different ways of dealing with quantity, space, and patterns are now well documented, and it is not possible to deny them. But, to pass from this acknowledgement to the aim of inserting it in a school setting in order to be disseminated through school education is problematic because schools are not open spaces of shared knowledge. On the contrary, curricular changes, especially when the subject is mathematics, are very strict. Whether we choose to use this different knowledge as a curiosity, an illustration or a “starter” to the formal mathematics of the curriculum, or to develop a curriculum where one of the topics is local knowledge per se, the result may not be students’ emancipation or the valorisation of different cultures. On the contrary, the process of bringing diversity and ethnomathematical ideas into the classroom may end up conveying practices opposed to the benevolent multicultural ideas these researchers want to enforce, by promoting a desubstantialized view of Other’s culture (Pais, 2011).
Urban Boundaries Project
This problem is connected with the educational aims of today’s world. Together with globalization, the concern with diversity is currently considered to be one of the two main educational functions (Izquierdo & Mínguez, 2003). While globalization refers to the social need to respond to market globalization, which imposes a convergent education by training individuals to perform a role in the global society, diversity demands an integration of different cultures in a model of divergent education, able to educate citizens in what has been called equity within diversity. To conciliate these two educational tasks could be a source of problems, as documented by recent research on the cultural dimension of education (e. g. Kincheloe & Steinberg, 2008); and as we previously addressed regarding the educational implications of ethnomathematics. This is especially the case in so-called developed countries where national cultural minorities and newer immigrant populations have been posing new challenges for education. In many cases, these populations rely more on non-formal educational sites, based in their everyday lives, than in the formal setting of school education, where they often experience problems of exclusion.
As a way to avoid the inconsistencies of school, a group of people from different backgrounds (among others, architects, biologists, physicists, teachers, and mathematics education researchers) decided to join efforts and built a project together with two communities, one based in a agricultural land and another dedicated to piscatoy activities, based in the outskirts of Lisbon. These communities are constituted by immigrant populations from other Portuguese-speaking countries, Gipsies, and Portuguese migrants. They have been experiencing throughout half a century diverse problems of inclusion—from the inexistence of piped water to the silencing of their voices in the political arena—, particularly concerning schooling. Through the development of a critical alphabetization, a multiple cartography and life-history portfolios we seek to address the educational needs of these populations in situ, that is, in the midst of their everyday lives where survival with dignity is often the first and foremost important daily struggle. Therefore, it is the everyday problems felted by these two communities that guide the organization of parameters that support a multicultural education curriculum based on the socio-cultural and economic reality of these communities. This way, we seek to address the tension between globalization and diversity by means of submitting these two educational aims to the needs of the communities, which have been systematically excluded both from globalization and from the social recognition of their differences.
It is our contention that this approach reduces the risk of desubstancialization, since we are working in the basis of communities’ local knowledge, and focusing on their communicative, analytic and material resources; and from the real problems they felt in their daily struggles in the midst of a society that doesn’t recognize them as citizen on their own right. In such an environment, ethnomathematics (as defined by D’Ambrosio (2002), who partly substantiates our approach to mathematics and education) acquires its full meaning: not some kind of pre-school mathematics ready to be used in the teaching and learning of school mathematics, but an all-encompassing societal program based on the idea that there are several ways, techniques, skills (tics) to explain, understand, deal with and live with (mathema) distinct natural and socioeconomic realities (ethnos). Against this background, ethnomathematics appears not so much as the study of “different mathematics”, but as a way to deal with different forms of “knowing” (Mesquita, Restivo & D’Ambrosio, 2011). In the Urban Boundaries Project ethnomathematics is not to be confused with a subfield of mathematics education, designed to improve school mathematics, but as a political space where new forms of emancipation can be thought and practiced.
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[1] Information about the group can be found in http://www.icme12.org/sub/tsg/tsgload.asp?tsgNo=36.