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Ubiratan D'Ambrosio (cited in Ernest, Greer, Sriraman, 2009, p. ix) asserts that "survival with dignity is the most universal problem facing mankind." In such an imperiled world, those who embrace their own humanity and that of others propose a myriad of places to begin countering such a formidable threat. One of those proposals falls under the protective aegis of education-or more precisely, under what is purported to be the shield of a "good" education. This "good" education ideally is one that first has merit qualitatively and second, is accessible to every student equally. Although this notion seems romanticized or nostalgic in some more fortunate communities, it is certainly worth pursuing-even insisting upon.
This type of rhetoric has found its way into discourses of mathematics education. Corporations offer initiatives to ensure mathematics for all. National organizations such as the National Council of Teachers of Mathematics (NCTM) embrace equity as one of its identified principles in the NCTM 2000 Principles and Standards for School Mathematics. The principle of equity demands that reasonable and appropriate accommodations be enacted to encourage the access and attainment for all students regardless of their backgrounds, cultures, or other characteristics.
Despite the best intentions and carefully considered initiatives, Anyon (cited in Moody, 2001) discovered that although students in five elementary schools experienced similar curricula and similar access, they endured quite different schooling experiences.
Additionally, often in classrooms with high concentrations of minority and lower social order students, the mathematics is taught through giving rules and procedures, whereas in classrooms of majority and higher social order, students are taught through engaging students in reasoning and problem solving. Certainly, the goal of extending equity in the presentation of mathematics for all is an illusive task.
Ethnomathematics studies how cultural groups use and explain mathematics (Garii & Silverman, 2009). The discipline investigates how communities "organize, articulate, and utilize mathematics and mathematical knowledge within their respective communities" (p. 335). In this paper, I will continue to explore the possibilities that ethnomathematics represents in the teaching of increasingly multicultural classrooms. I will give special attention to potential benefits for minority. I will primarily explore the use of ethnomathematics by considering aspects of its relationships with culture, power, and competence. I will conclude by considering some implications associated with attempts to implement such programs.
Complications of Culture
For D'Ambrosio, ethnomathematics applies to connections between mathematics and culture in every human group in all areas at all moments. Ethnomathematics posits that all mathematics is necessarily cultural. It becomes beneficial to define culture. However, that is an endeavor of underestimated challenge. More often culture is characterized, as it is as follows:
Cultures are neither coherent nor homogeneous nor univocal nor peaceful. They are inherently polyglot, conflictual, changeable, and open. Cultures invoke constant processes of reinscription and of transformation in which their diverse and often opposing repertoires are re-affirmed, transmuted, exported, challenged, resisted, and re-defined. (Fay, cited in Radford, 2008, p. 454)
Culture is not static. Neither is it monolithic. Even as we reflect on the idea of a group's
culture, it is not a rigid construction. So, although many members in minoritized communities share similar experiences, their responses to those similar experiences may indeed vary. At the same time, though, there are often salient "compatibilized" behaviors and shared knowledge. This accumulated knowledge shared by the group tends to make the behavior of the individuals compatible. When ethnomathematics examines mathematics through a cultural lens then, it must account for the possibility of other lenses. This is analogous to the declaration of ethnomathematics that there is a plurality of mathematics.
Whatever culture is and however it is defined, historically, culture was seen as an impediment to certain types of objective, logical thinking. The view was that culture is external to mathematics learning and teaching. It is a perspective that persists. Radford (2008) states that "true knowledge, in fact, was the reward for the individual's emancipation from his or her culture" (p. 439). This position is tenacious in its staying power. It leads to a discussion of power dynamics present in mathematics education.
Adherence to such rationalist epistemologies goes back to Plato and has been sustained to the present. Such a tradition privileges and fetishizes rational, logical thinking. It only finds it in [types of] particular systems. The strength of an ethnomathematical approach is that it has as one of its goals the presentation of other systems of mathematical reasoning. The audacity of this presentation is that it challenges the inherent bias embedded in the privileging of Western mathematical rationalization.
This type of asymmetrical power dynamic is also present in investigations of "street mathematics" and mathematical knowledge acquired and displayed in informal settings. The type of knowing demonstrated in these contexts might be labeled as hierarchically inferior.
Valero (cited in Ernest, Greer, & Sririman, 2009) thinks about "mathematics education as a field of practice covering the net-work of social practices carried out by different social actors and institutions located in different spheres and levels, which constitute and shape the way that mathematics is taught and learned in society, schools, and classrooms" (p. 240). Ethnomathematics introduces different actors to the stage of mathematics education. Through these actors different storylines may unfold. These
storylines are evocative of the narratives and discourses that surround mathematics and mathematics education. Within the story, different positioning of mathematics and doers of mathematics occur. Power is constantly shifting in these exchanges.
Wagner and Herbel-Eisenmann (2009) assert that "the stories or myths, told about mathematics powerfully format the way students approach mathematical problems and the way they use mathematics to address problems that are not necessarily mathematical" (p. 12). These authors insist that multicultural classrooms make it necessary to introduce multiple storylines in mathematics classrooms. Ethnomathematics not only draws attention to the narratives of the classroom, but it also invites those outside of the classroom. It is important to note that ethnomathematics is more than a feel-good program for minoritized students. It highlights mathematics, not simply "stories". However, it fails to ignore the stories, especially the histories of the people studying the discipline. By doing so, it lessens-even if by degrees-the power differential maintained by the tradition pedagogical and epistemological paradigms. Students are able, and perhaps more willing, to participate in the bounded ethnomathematical community of the classroom. Their participation challenges them to reconsider and reinvent notion of mathematical competence.
Constructions of Competence
Competence, like culture, is difficult to define. Gresalfi, Martin, Hand, and Greeno (2008) problematize the convention definition of competence. They expand the notion from a collection of skills or abilities attributed to a person apart from specific contexts to an attribute of a person participating in an activity system such as a classroom. Competence becomes, for the most part, "what students need to know or do in order to be considered successful by the teacher and other students in the classroom" (p. 50).
David and Watson (2008) refer to the concepts of affordances, constraints, and attunements. These concepts contribute to the discussion of competence. Affordances are "the possibilities for action and interaction offered in a classroom" (p. 32).
I contend that ethnomathematics broadens the affordances for students, particularly those who do not regularly see themselves or aspects of familiar culture that arise in the enactment of the curriculum. Constraints include "regularities of social practices and â€¦ interactions" (p. 32). Yackel and Cobb (1996) distinguish sociomathematical norms as those that are specific to the mathematical aspects of students' activity. They affirm that "what becomes mathematically normative in a classroom is constrained by the current goals, beliefs, suppositions, and assumptions of the classroom participants. Therefore, a program of ethnomathematics widens the bounds of sociomathematical norms by including references to mathematical systems not commonly recognized in formal classroom settings. Also ethnomathematics gives voice to more tacit forms of knowing by inviting different actors and actions to the discussion and engagement of mathematics. Ethnomathematics invites students to contribute to constructions of competence by it valuation of other patterns of mathematical behavior. At the individual level, students demonstrate attunements, that is, regular patterns of an individual's participation (David & Watson, 2008). The construction of competence made possible through programs of ethnomathematics may strengthen how marginalized students identify themselves and others with mathematics. In other words, the affective engagements possible through ethnomathematics may motivate minority students to reposition themselves in relation to mathematics and mathematics education. This repositioning helps students to author a more heightened sense of agency and a more robust concept of mathematics identity.
Conclusion and Implications
As mathematic continues to undergo a social turn, the investigation of the opportunities embedded in ethnomathematical instruction seems almost a natural progression. As the world and its classrooms grow increasingly multicultural, the approaches to mathematical instruction should also grow more diverse. Not only should other systems of mathematics be explored, but also other types of knowing should be acknowledged, valued, and
sanctioned. These efforts, which are integral components of ethnomathematics, highlight the roles of culture, interrogate notions of power, and broaden constructions of competence.
Attempts to incorporate programs of ethnomathematics understandably have concerns associated with them. One is that culture must not be perceived to be static, but dynamic and in flux. Ethnomathematics aggravates the largely uncontested paradigms of the Western, Eurocentric rationalistic epistemology and the singularity of its limited presentation. Therefore, ethnomathematics can not also limit itself in its definitions and presentation of culture. Also, de Abreu (2008) contends that "the reconceptualization of mathematics classrooms as situated communities of practice has been a first step, but as yet that have [sic] not offered a satisfactory account of the interplay between the individual and the sociocultural processes" (p. 377). Ethnomathematics must continue to interrogate the dynamics between these processes. The inquiries fueled by the discipline will address the need to examine how agency and opportunities are distributed. Also, ethnomathematics forces the essential considerations of who one is, who one is perceived to be, and who others are and are perceived to be, especially in relation to the discipline of mathematics. These are fundamental notions of identity that must be undertaken. They are imperative in the pursuit of the dignity that humans pursue. It is a pursuit that we advance in each other's company and one hardly achieved in the absence of other's aid.