Ethnomathematics: Why%3f

 

 

 

by
Wilma Godwin, K-5 Mathematics Facilitator, NC-PIMS
Sherman Sumpter , 6-12 Mathematics Facilitator, NC-PIMS

 

 

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Abstract | Paper | References

 


Ethnomathematics: Why%3f

Abstract:
            Ethnomathematics is the study of mathematics, which takes into consideration the culture in which mathematics arises. We all have some notions of what ethnomathematics is, but should it be influencing school mathematics%3f An important change in mathematical instruction needs to take place in order to accommodate the change in the demographics of students. Teachers and supervisors need to be instructed in gearing education more toward students of different cultures. This paper describes why and how ethnomathematics should influence mathematics. It emphasizes why ethnomathematics is important in mathematics education and focuses on the way that culture plays an important role in a child's life. The term "ethnomathematics" refers to mathematical concepts embedded in cultural practices.

 

Ethnomathematics: Why%3f

 

The term ethnomathematics was first used in the late 1960s by a Brazilian Mathematician, Ubiratan Dambrosio, to describe the mathematical practices of identifiable cultural groups.  Some see it as the study of mathematics in different cultures, others as a way of making mathematics more relevant to different cultural or ethnic groups, yet others as a way of understanding the differences between cultures.

As the twenty-first century opens, the demographics of our mathematics classrooms are changing, becoming increasingly diverse in cultures, ethnic groups, and languages. 

Without teaching to African Americans, Native Americans, and Hispanic populations, we are losing many students in early grades and this eliminates opportunities for African American, Native American and Hispanic students from advanced studies of mathematics. Teachers may not understand the need for addressing these issues or for addressing these issues throughout the year rather than one month a year. Teachers teach as they were taught. Pre-service education does not include pedagogy for use of multi-cultural activities.  There is a lack of in-service remediation to help teachers understand the needs of African American, Native American, and Hispanic Students. In the past and in most schools today, the African Americans, Hispanics, and Native Americans are not taught the contributions of their cultures in the field of mathematics. In educational terms, these comments are well-expressed:

Educating people mathematically consists of much more than just teaching them some mathematics.  It is much more difficult to do, and the problems and issues are much more challenging.  It requires a fundamental awareness of the values which underlie mathematics and recognition of the complexity of educating children about these values.  It is not enough merely to teach them mathematics; we need also to educate them about mathematics, to educate them through mathematics, and to educate them with mathematics (Bishop 1991b, p3).

Minorities comprise a larger portion of the country’s population, especially in the eastern part of North Carolina where the Hispanic population comprises as much as 60% of some of the schools’ populations. New innovated and comprehensive methods of teaching must become part of the traditional mathematics instruction to provide equitable access (Curriculum Standards, NCTM 1989) and Professional Standards for Teaching Mathematics (Teaching Standards, NCTM 1991) acknowledged this reality in the closing years of the previous century as they addressed the notion of connecting mathematics to other disciplines and cultures. 

An important change in mathematics instruction needs to take place in order to accommodate the change in population. Teachers and supervisors need to be instructed in gearing education more toward children of different cultures. The problem identified by many studies, is that a large number of minority students are not achieving, as necessary, for academic success. Concerns about equity in mathematics education have been coming to the forefront in many countries in the world (Keitel, Damerow, Bishop, & Gerdes).

At the same time that minority people are losing ground in college participation and completion, their share of the overall population is increasing. This growth is driven primarily by Hispanics, who have become the largest minority group in the United States. Accounting for 13 percent of this country’s population, Hispanics are moving into regions that have not seen large Hispanic populations before. Furthermore, it is projected that this group will grow much faster than the general population in years to come. Indications are that 93 percent of the additional school-age children in the United States in 2025 will be Hispanic.

Mathematics education originated when human beings began to quantify the phenomena in their lives.  Although the process of counting was the same for different groups of people around the world, the symbols by which they represented specific quantities varied according to particular cultural conventions. Thus, African, Aztec, Babylonian, Chinese, Mayan, and other cultural groups wrote numbers in many different ways.  Mathematical practices were developed as a result of every single culture, tribe, community, and individual trying to cope with everyday needs, problems, and challenges for their survival in direct relationship with the environment and fellow human beings.

Ethnomathematics refers to what some may call forms of mathematics that vary as a consequence of being embedded in cultural activities whose purpose is other than doing mathematics.  These include among other things, building houses, exchanging money, weighing products, and calculating proportions for a recipe which involve numbers, calculations, and precise geometrical patterns.

Many of us are interested in ethnomathematics, but how far are we willing to go%3f Are we content to dabble and to continue to get our academic papers from the cultures of others, sometimes with their consent but sometimes without even involving people of the culture%3f Are we committed to change and ready to give the power we have to the people of the cultures we work with%3f The belief is that we are approaching a time when our actions and decisions can influence the direction of mathematics education. One strategy is using ethnomathematics to provide a viable framework for curriculum development in mathematics, because of the potential for construction of mathematical ideas which are uniquely a student’s own. Another strategy is providing at least one course that deals with questions and issues concerning ethnomathematics, unless ethnomathematics is integrated into all courses.

In exemplar districts, educational leadership supports teachers and school personnels’ participation in mathematics and science professional development experiences designed to support the reexamination of beliefs, expectations, as well as cultural and linguistic diversity; to develop skills in teaching multi-cultural classrooms; and to improve practice in new curriculum instruction and assessment strategies.  In 2004, the Renaissance Group published Addressing the Issues of Underperforming Schools, which recommended the preparation of all teachers to accommodate diverse learners.

Ethnomathematics aims to draw from the cultural experiences and practices of the individual learners, the communities, and the society at large, in using them as vehicles to not only make mathematics learning more meaningful, but more importantly, to provide learners with the insights of mathematical knowledge as embedded in their social and cultural environment. With the growing Hispanic student population in North Carolina, the school curricula should reflect the intrinsic, cultural learning of Hispanic students and teachers should be prepared to address the cultural differences of Hispanic Americans.  Teaching Standards recommend that teachers emphasize connections between mathematics and other disciplines (p. 89). It advises teachers to consider students’ cultural backgrounds in designing and selecting mathematical tasks (p. 26, 115).

Students' beliefs and attitudes can be viewed as a product of their cultural heritage and, to a large extent, as an extension of parental beliefs and attitudes.  African American students generally learn in ways characterized by social and affective emphases, harmony with the community, holistic perspectives, field dependence, expressive creativity, and non-verbal communication (Barton, 1996).

 

A quasi-experimental research design was used to conduct a study. Data was collected from the unit examination taken by students who were enrolled in the researcher’s pre-algebra course at Torch Middle School. The mean test scores of Group A and Group B were then calculated and compared using a two-tail t-test, utilizing a level of significance at the 0.05 level.

The significance of statistical differences between the two groups demonstrated that the use of ethnomathematics software in combination with traditional teaching practices can increase student success in the area of coordinate planes and associated concepts. In concluding, it was found that there is distinct statistical evidence to suggest that teaching a coordinate planes unit integrating ethnomathematics software is an effective tool and tactic to increase student success in this area (Magallanes, 2003).

Another quasi-experimental design study was done. Quantitative and qualitative data were collected from the study. The quantitative data collected were analyzed using descriptive statistics. This study contributed to the fact that students’ achievement scores increased as they learned about African culture. This study also contributes to the field of mathematics education regarding culture in the mathematics classroom and African

American students' achievement.  Culture can be implemented in the mathematics classroom in various ways.  Geometry was the main mathematical concept that was used in this study. Research of this nature is crucial to reforming mathematics curriculum, influencing students’ mathematics achievement and perceptions.  The study can be beneficial to all students. 

The diversity of learners of today forces teachers to rethink how they teach, and what they teach, on a regular basis. Greater diversity is an advantage in the classroom where each student contributes important ideas and energies that promote diversity in each classroom. To honor the student diversity so that the entire society can benefit, socio-cultural and developmental differences of learners should receive equal attention regarding curriculum, instruction, and learning materials. Ensuring equity and excellence lays at the core of systemic reform efforts, especially in science and mathematics, the two academic areas that historically have not been widely open to females, ethnic minorities, or students from less affluent communities and families.  In the last 50 years, we have witnessed how education has battled issues of segregation resulting in the removal of some legal or policy barriers based on race and gender . We observed the 50th anniversary of the U.S. Supreme Court decision to outlaw segregation in public schools. But the time for celebration has not come yet. Not when the country is still plagued with issues of inequity.

NC-PIMS, the North Carolina Partnership for Improving Mathematics and Science, has embraced the NCTM Principles and Standards for School Mathematics.  Equity requires high expectations and worthwhile opportunities for all (NCTM, 2000, p. 12). Equity requires accommodating differences to help everyone learn mathematics. (NCTM, 2000, p.13). Equity requires resources and support for all. By "every child" we mean specifically:

"It is essential that schools and communities accept the goal of mathematics education for every child. However, this does not mean that every child will have the same interest or capabilities in mathematics."

 

Today, cultural minorities (African Americans, American Indians, and Hispanics) are severely underrepresented in mathematics-based careers. For example, even though these three groups collectively constitute 23 percent of the US  The National population. In 1993, only 12 percent of bachelors’ degrees in science and engineering were awarded to members of the three groups in that year (National Science Foundation 1996, p. 2-4).

The National Center for Education Statistics, NCES (2003a), reports that in 1999-2000, based on degrees conferred by degree-granting institutions, African Americans earned 10.7% of the associate degrees, 8.7% of the bachelor degrees, 7.8% of the master degrees, and 5% of the Ph.D. degrees. The gap between a White and Hispanic 13 year-old in NAEP mathematics score narrowed from 1973 to 1986 from 36 points to 19 points, it increased from 1986 to 1999 to 24 points. (NCTM Achievement Gap Task Force)

Culture should be included in the mathematics classroom because it improves students’ academic achievement, helps move classrooms towards an equitable learning environment, helps students have positive beliefs about mathematics, and integrates mathematics with other disciplines. (The Negro Educational Review, Vol 56, Nos 2&3, July, 2005).  Culture should also be addressed in the mathematics classroom to promote mathematical understanding. As students learn about the culture of other peoples, they can also learn about these peoples’ mathematics, since their mathematics is a part of their culture. Culture provides a means for students who usually do not fully participate in the mathematics class, to make connections to mathematical content.   When students feel that the mathematics in the class does not relate to them, or their culture, they may feel unconnected or even invisible (Davidson & Kramer, 1997).  In 2001, the North Carolina Commission on Raising Achievement and Closing Gaps issued a report detailing the reasons for the racial achievement gap and ways the state can close it.   One recommendation was to design and fund a required, but flexible, professional development initiative that will ensure that classroom teachers acquire the knowledge, skills, and dispositions needed to be successful in teaching a diverse population of students. (NC Issue Brief, May 2006)

Masingila and King (1997) stated, "ethnomathematics becomes a tool usable in the mathematics classroom to help students make connections and develop deeper mathematical understanding." They discussed how ethnomathematics, as a viable classroom tool, will help students learn about mathematical practices of other peoples as well as develop a deeper understanding of their own mathematical practices. This idea is shared or supported by several educators (Abdal-Haqq, 1998; Barta&Schaelling, 1998.)

Ron Eglash, an associate professor of science and technology studies at Rensselaer Polytechnic Institute, has uncovered mathematics embedded in the designs of various aspects of native and contemporary culture, from traditional beadwork and basket weaving to modern hairstyles and music. Using the discovery, he has developed a series of interactive, Web-based teaching tools that are capturing the interest and imagination of students in mathematics classes across the country.  “Making real-world connections-especially connections that tie in students heritage cultures-in math instruction has been recognized as increasingly important by educators. Culturally situated design tools provide a flexible space to do that, allowing students to reconfigure their relationship between cultures, mathematics, and technology,” said Ron Eglash.

At the Newark campus of Rutgers University, Arthur B. Powell leads his students in teacher education courses through river-crossing problems based on different cultures in their study of algebra.  And using a cultural analogy that’s close to home, Jim Barta teaches his elementary education students at Utah University a new way to think about the Cartesian coordinate system: street mapping in towns settled by Mormons is based on a system much like the one in which positive and negative numbers name intersections of lines.  “Every day, more and more pieces of the puzzle are coming together,” says Mr. Barta, an assistant professor who is treasurer of the North American chapter of the International Study Group on Ethnomathematics, a support group for people in the field.

"We're looking at multiple perspectives to help us better understand beings and relationships between being human and mathematics," he says (The Faculty, 10-6-2000).

Ethnomathematics can be used as a tool to motivate these disenfranchised students to pursue their study of mathematics. As teachers, we can provide such students with relevant mathematical experiences by integrating into the curriculum mathematical topics from their own cultures. Teaching Standards acknowledges the importance of using multi-cultural perspectives in achieving the important objectives of motivating students. Ethnomathematics is instrumental in implementing these standards. Ethnomathematics is also vital to implementing Curriculum Standards. The fourth standard for the three clusters of grades K-4, 5-8, and 9-12 recommends that connections be made among mathematics topics as well as among mathematics and other disciplines. Ethnomathematics can facilitate the achievement of two objectives in mathematics teaching.  It can establish a multi-cultural context for mathematics knowledge and skills, and it can help students in making connections among other cultures and disciplines. In so doing, we maximize the possibilities for improving their attitude towards mathematics as the same time that we are improving their mathematics skills.  Hence, ethnomathematics is a medium through which we can have a positive impact on the affective and cognitive domains of students who are underrepresented in mathematics.



Bibliography

Abdal-Haqq, I. (1994). Culturally responsive curriculum. ERIC Digest, 1-4

Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas.     
     Belmont, CA: Brooks/Cole Publishing Co.

Ascher, M. (1994) Ethanomathematics:  A Multicultural View of Mathematical Ideas.

Barta, J. & Schelling, D. (1998). Games we play: Connecting mathematics and culture in        
     The classroom. Teaching Children mathematics, 4(7), 388-393

Bishop, Alan J. (1988); Mathematical Enculturation: A Cultural Perspective on Mathematics Education. Dordrecht: Kluwer Academic Publishers

D’Ambrosio, U. (2001). “What is Ethnomathematics, and How Can It Help Children in
     Schools%3f” In: Teaching Children Mathematics, 7(6).  Reston, VA: National Council of
     Teachers of Mathematics.

Davidson, E., & Kamer, L. (1997).  Integrating with integrity: Curriculum, instruction,
     and culture in the mathematics classroom.  Reston, VA: The National Council of
     Teachers of  Mathematics.

Eglash, R. (1999). African Fractals: modern computing and Indigenous design.  New
     Brunswick: Rutgers University Press.

Faculty Form. Volume 12.  No.2, October 20, 2000

Keitel , C., Damerow, P., Bishop, A., & Gerdes, P. (1998). Mathematics, education, and
     Society (Document Series No.35). Paris: UNESCO, Science and Technology Ed.

Magallanes, A. (2003). Comparison of student test scores in a coordinate plane unit using
     Traditional classroom techniques versus traditional techniques coupled with
      Ethano-mathematics software at Touch Middle School.  National University.
                                           
Masingila, J. & King, K. (1997). Using ethnomathematics as a classroom tool.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation
     standards for school mathematics.  Reston, VA: NCTM

National Council of Teachers of Mathematics.  (2000). Principles and Standards for                 
     School mathematics.  Reston, VA: NCTM

National Center for Education Statistics: Digest of Education Statistics. (2003a). Degrees 
     Conferred by degree granting institutions race/ethnicity: 1999-2000. Washington,
      D. C.; US Government Printing Office.

The NCTM Achievement Gap Task Force.  Final Report. October 2004.

N. C. Issue Brief. May 2006.

The Renaissance Group. Addressing the Issue of Underperforming Schools. November
     2004
Snipes-Moses, Pamela. (2005). The Effect of African American Students’ Achievement
     On Selected Geometry Topics in the Elementary Classroom. The Negro Educational
      Review. Vol 56, Nos. 2& 3, July, 2005.

Web Pages

http:www.ccd.rpi.edu/Eglash/csdt/teaching/papers/indig_it.htm

National Center for Improving Education in Mathematics and Science
http://www.wcer.wise.edu/ncisla/research/index.html

The Chronicle of Higher Education. October 6, 2000.
http://chronicle.com/free/v47/i06/06a01601.htm

 


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