DRAFT WORK IN PROGRESS

ETHNOMATHEMATICS AND THE TEACHING & LEARNING MATHEMATICS FROM A MULTICULTURAL PERSPECTIVE[i]

A basic tenant of ethnomathematics is the sincere belief that all peoples use mathematics in their daily life, not just academic mathematicians. Yet, globally speaking, all people do not have regular access to or do not attend school. Ethnomathematics as a program of study offers one possibility – allowing researchers to examine what and how we teach mathematics in context of the school, culture and society.

Um pressuposto básico da etnomatemática é a convicção sincera de que todos os povos utilizam a matemática em sua vida diária e que este fato não é um privilégio somente dos matemáticos. No entanto, globalmente falando, muitos destes mesmos povos não têm o acesso ou não freqüentam regularmente a escola. A etnometática atua como um programa de estudo que oferece uma possibilidade que permite aos pesquisadores examinarem o que ensinar e como ensinar no contexto da escola e da sociedade, ambientes nos quais estas mesmas informações emergem.

Un principio básico de etnomatemáticas es la sincera creencia de que toda la gente usa matemáticas en su vida diaria, no solo matemáticos académicos. Así, globalmente hablando, toda la gente no tiene acceso regular o no asiste a la escuela. Etnomatemáticas como un programa de estudio ofrece una posibilidad permitiendo a los investigadores examinar qué y como enseñamos matemáticas en el contexto de escuela, cultura y sociedad.

Modern 21^st century mathematics represents the grammar and language of a particular culture that originated when people began working with quantity, measure, and shape in the Mediterranean regions of the world. Like any culture, mathematics comes with a unique grammar and way of thinking and seeing the world, and this mathematics is now coming into contact with other ways of thinking and interpreting our increasingly interdependent world. However, the conquest of the planet by modern mathematics is not without its consequences. A subtle sense of entitlement and a scientific cultural hegemony has spread faster than it sought to understand or come to terms with the thousands of traditions and time honored forms of thinking, calculating, and solving problems. We are all attracted to mathematics for its fine scientific, cultural, and even artistic qualities, and 21^st century mathematics is allowing impressive marvels and scientific achievements. Yet at the same time, it has also enabled some the most horrific scientific and cultural disasters in the history of humanity.

The ethnomathematics community is now in position to move to the next step; that is to “walk the mystical way with practical feet”. In this paper we discuss concepts of multicultural education and multicultural mathematics that we have found useful in the interpretation of an ethnomathematics program for teacher professional development in our ongoing work in Brazil and the United States. We begin with an examination of multicultural education and ethnomathematics; and then we will outline both favorable and unfavorable arguments related to this paradigm.

Diverse concepts have emerged over the last few decades that have described the diverse programs and practices related to multiculturalism. We find the following definition useful. Multicultural education is…

Consequently, we may define multicultural education as a field of study designed to increase educational equity for all students that incorporates, for this purpose, content, concepts, principles, theories, and paradigms from history, the social and behavioral sciences, and particularly from ethnic studies and women studies (Banks & Banks, 1995, p. xii).

Multicultural mathematics is the application of mathematical ideas to problems that confronted people in the past and that are encountered in present contemporary culture. In attempting to create and integrate, multicultural mathematics materials related to different cultures and draw on students own experiences into the regular instructional mathematics curriculum, WG-10 on Multicultural/Multilingual classrooms at ICME-7, in 1992 pointed out aspects of multicultural mathematics:

An aspect of multicultural mathematics is the historical development of mathematics in different cultures (e.g. the Mayan numeration system). Another aspect could be prominent people in different cultures that use mathematics (e.g. an African-American biologist, an Asian-American athlete). Mathematical applications can be made in cultural contexts (e.g. using fractions in food recipes from different cultures). Social issues can be addressed via mathematics applications (e.g. use statistics to analyze demographic data (p.3-4).

The growing body of literature on multicultural education is stimulated by concerns for equity, equality, and excellence as part of a context of diversity. Teachers realize that students become motivated when they are involved in their own learning. This is especially true when dealing directly with issues of greatest concern to themselves (Freire, 1970). The challenge that many western societies face today is to determine how to shape a modernized, national culture that has integrated selected aspects of traditional cultures that coexist in an often delicate balance. This increased cultural, ethnic, and racial diversity provides both an opportunity and challenge to societies and institutions, with questions related to schooling forming an integral part of this question.

The inclusion of mathematical ideas from different cultures around the world, the acknowledgment of contributions that individuals from diverse cultures have made to mathematical understanding, the recognition and identification of diverse practices of a mathematical nature in varied cultural procedural contexts, and the link between academic mathematics and student experiences should become a central aspect to a complete study of mathematics. This is one of the most important objectives of an ethnomathematics perspective in mathematics curriculum development. Within this context, D’Ambrosio has defined ethnomathematics as,

The prefix ethno is today accepted as a very broad term that refers to the social-cultural context, and therefore includes language, jargon, and codes of behavior, myths, and symbols. The derivation of mathema is difficult, but tends to mean to explain, to know, to understand, and to do activities such as ciphering, measuring, classifying, ordering, inferring, and modeling. The suffix tics is derived from techne, and has the same root as art and technique” (D’Ambrosio, 1990, p.81).

In this case, ethno refers to groups that are identified by cultural traditions, codes, symbols, myths and specific ways to reason and to infer and mathematics is more than counting, measuring, classifying, inferring or modeling. Ethnomathematics forms the intersection set between cultural anthropology and institutional mathematics and utilizes mathematical modeling to solve real-world problems.

Essentially a critical analysis of the generation and production of mathematical knowledge and the intellectual processes of this production, the social mechanisms of institutionalization of knowledge (academics), and its transmission (education) are essential aspects of the program.

Multicultural education presents itself as a contemporary pedagogical trend in education. This approach allows a number of educators to deplore multicultural education and express numerous fears that this trend may represent a pulling away from certain cultural norms, even though some social realities underlie the need for many multicultural efforts to reform curricula.

The world’s economy is becoming increasingly globalized; yet, traditional curricula neglects contributions made by the world’s non-dominant cultures. Given these conditions, a multicultural approach may be seen as giving new, expanded, and often complicated definitions of a society’s unique experiences. Multicultural education can reshape our greater cultural identity in a positive way (Banks, 1999; D’Ambrosio, 1995; Zaslavsky, 1996) by requiring the inclusion of a diversity of ethnic, racial, gender, social classes, as well as the practices and problems of the student’s own community (D’Ambrosio, 1998; Zaslavsky, 1996). It helps students to understand the universality of mathematics, while revealing mathematical practices of day-to-day life, preliterate cultures, professional practitioners, workers, and academic or school mathematics. It can do this by taking into account historical evolution, and the recognition of the natural, social and cultural factors that shape human development (D’Ambrosio, 1995).

Multicultural education promotes the rights of all people, no matter their sexual orientation, gender, ethnicity, race, and socio-economic status. It does this in order to allow learners to enable students to understand issues and problems of our diverse society (D’Ambrosio, 1990, 1995; Croom, 1997; Fasheh 1982; Zaslavsky, 1991, 1996, 1998). Through increasingly sophisticated multicultural experiences, students learn to make contributions and learn to appreciate the achievements of other cultures (D’Ambrosio, 1990, Joseph, 1991, Zaslavsky, 1996).

Multicultural mathematics education / ethnomathematics deals with both content and the process of curriculum, classroom management, teacher expectations, professional development, and relationships among teachers, administrators, students, and the community (Borba, 1990; D’Ambrosio, 1985, 1990, 1995, 1998; Zaslavsky, 1998). This approach allows students to make connections with historical developments of mathematics and the contributions made by diverse groups and individuals.

Students need to be encouraged to develop skills in critical thinking and analysis that can be applied to all areas of life. These skills include vital issues involving health, environment, race, gender, and socioeconomic class (D’Ambrosio, 1990, 1998; Freire, 1970; Zaslavsky, 1998). Bassanezi (1990, 1994), Borba (1990), D’Ambrosio (1990, 1998), and Zaslavsky (1998) agree that ongoing contact of students with diverse ways of thinking and doing mathematics, will raise interest in learning required content, by having students apply mathematical concepts to future professional contexts and by facilitating student performance (Bassanezi, 1990, 1994; NCTM, 1989; Zaslavsky, 1990). In an ethnomathematics program students develop abilities, increased creativity, and a sound set of research habits. They will be able to develop a capacity to create a hypothesis (Bassanezi, 1990, 1994; D’Ambrosio, 1990, 1993; Biembengut, 1999; Hogson, 1995). Multicultural mathematics contributes to the development of student capacity by selecting data and subsequent adaptation to their needs (Biembengut, 1999, Croom, 1997; Hodgson, 1995), by encouraging contact with biology, chemistry, physics, geography, history, and language (Bassanezi, 1990, 1994; D’Ambrosio, 1995; Zaslavsky, 1991, 1993, 1996, 1998), and by developing work in groups, sharing tasks, learning how to take-in criticism and alternate opinions, respecting the decisions of others and the group, and by facilitating student interactions in a globalized society. Students share global and interactive visions necessary to develop successful mathematical content (D’Ambrosio, 1993; Bassanezi. 1990, 1994; Freire, 1970, Gerdes, 1988, 1988a; Zaslavsky, 1998).

Multiculturalism encourages further intellectual development of the teacher. It also encourages long-term learning through a diversity of experiences. Teachers are characterized as facilitators / advisers of the mathematics learning process (Bassanezi, 1990, 1994; Biembengut, 1999; Hogson, 1995). Biembengut (1999) and Hogson (1995) stated that teachers and students discovered a process of understanding mathematics together. This context allows students to learn mathematics content through varied experiences related to the cultural, historical, and scientific evolution of mathematics.

For several years it has been argued that traditional uses of the school curriculum do not foster genuine dispositions for realistic mathematics in students (Davis, 1989). Yet the same argument is used against attempts to make ethnomathematics useful to educators. Other concerns are related to the lack of enough time to develop content that enables teachers to execute pre-established pedagogical plans. It is difficult to mix multicultural education, ethnomathematics, benchmarks, standards and goals related to standardized testing that are based in traditional school mathematics (Burak, 1994; Pedroso, 1998). Concerns related to the application of ethnomathematics as pedagogical action include:

· Few, if any, textbooks and other materials about multicultural mathematics are in use in classrooms.

· A scarcity of university multicultural mathematics and ethnomathematics courses leave teachers and researchers unprepared to argue this issue.

· Few, if any, assessment instruments are appropriate to this new curriculum model.

· There is a danger of ethnomathematics being taught as folkloristic introductions to real mathematics.

· There exists great confusion between what is multicultural and ethnomathematics

· Much of the curricula represent a shallow, superficial learning with a sense of “multicultural” based upon “exposure to diversity”.

Many students have difficulty in group or cooperative learning. Many learners are unsure about how to work without the traditional classroom structure, and have difficulty assimilating several subjects simultaneously. Because of the traditional passive aspect of schooling, students often do not have the habit of formulating questions (Burak, 1994; Pedroso, 1998).

Often because of the lack of their own personal experience, many educators are reticent to try cross-cultural methods, and their academic training in mathematics. Many educators are timid, and are reticent to attempt de-emphasizing traditional authority in favor of group work (Burak, 1994; Cross & Moscardini, 1985; Pedroso, 1998). Other reasons relate to issues of time for planning lessons (Burak, 1994; Pedroso, 1998; Zaslavsky, 1998). Many educators are not familiar with the interface between mathematics and other subjects, and certainly the reverse is equally true. Many educators are not prepared to employ practices that will enable underserved and underrepresented groups to learn mathematics (Burak, 1994, Zaslavsky, 1994).

The inclusion of multicultural mathematics and ethnomathematics continues according to the history of research in this area simply because the growing migration, immigration and diversity of our populations demand it. However, it can be negative when it restricts ethnic groups to stereotypes and leaves us unprepared to participate in academic endeavors. It is equally negative when it waters down mathematics content in general. Multicultural education seeks to recognize the contributions, values, rights, and the equality of opportunities of all groups that compose a given society. Educators can begin to develop the ideal equality among students and build a foundation for promoting academic excellence for all students (Croom, 1997). In an earlier work, Orey stated,

A multicultural perspective on mathematical instruction should not become another isolated topic to add to the present curriculum content base. It should be a philosophical perspective that serves as both filter and magnifier. This filter/magnifier should ensure that all students, be they from minority or majority contexts will receive the best mathematics background possible. (Orey, 1989, p.7).

We recommend that the above questions continue to be debated in order to develop inclusive paths of further development of mathematics, our societies and the schools therein. As well, we hope that the Working group may come to some consensus in regards to the confusion between what is multicultural and ethnomathematics. Sociological questions about the relationships between institutionally dominant majority and minority cultures need be reflected by our increasingly globalized world.

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[i] Versions of this paper have been submitted for both ICME-10 Working Group on Ethnomathematics, Copenhagen, Denmark (August, 2004), the IV Festival Internacional de Matemática, San José Costa Rica (May, 2004), and the VII Encontro Nacional de Educação Matemática, Recife, Brasil (July, 2004).