Article reproduced 2003 with permission of the ISGEm Newsletter editor for use in the Ethnomathematics Digital Library (www.ethnomath.org) developed by Pacific Resources for Education and Learning (www.prel.org).
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Originally
published in the International Study Group on Ethnomathematics (ISGEm)
Newsletter, Volume 5, Number 1, December 1989. Located at: http://web.nmsu.edu/~pscott/isgem51.htm. Article reproduced 2003 with permission of the ISGEm Newsletter editor for use in the Ethnomathematics Digital Library (www.ethnomath.org) developed by Pacific Resources for Education and Learning (www.prel.org). |
Daniel Orey
Sacramento State University
In the United States, the aftermath of the sixties has increased the visibility and participation by many minority group members in the mainstream of daily life. As well, a new understanding has developed; instead of a "melting pot," the United States had become an enormously diverse "salad bowl." I believe that the mathematics curriculum offers educators an excellent opportunity to give learning groups with diverse ethnicity the opportunity to experience success. The recent publication, Curriculum and Evaluation Standards for School Mathematics (Commission on Standards for School Mathematics, 1989) has caught the imagination of and been the topic for discussion by many mathematics educators. It is the purpose of this article to offer some ideas about implementing the Standards an ethnically diverse setting.
Those of us nurtured from within the Western cultural tradition tend to think of mathematics as a unique flowering of European culture, and insofar as the history of the subject is taught in schools in the United States, it may appear to be so. However, cultural evidence suggests that mathematics has flourished worldwide and that children benefit by learning how "mathematical practices arose out of the real needs and desires of all societies" (Zaslavsky, 1989). Students should learn that mathematical thinking is part of the basic human endowment. For as Anthropologist Edward T. Hall (1977) stated:
"Most cultures and the institutions they engender are the result of having to evolve highly specialized solutions to rather specific problems."
It is this very universality of mathematics that can become the most obvious contributor to a curriculum that seeks to address any challenges coming from diverse populations. Math developed by many non-European cultures can communicate a recognition and a valuing of the cultural heritage of ethnic minorities present in the classroom, whereas not doing so can communicate the opposite. This perspective can help minority students by increasing their knowledge of and respect for the cultures of their origins, at the same time informing students from the majority culture about the mathematical richness of the various cultures whose people now live alongside them. Additionally, students need to learn to identify, respect and value alternative solutions to problems, as well as the many unique and varied approaches to problem solving.
"Schools should prepare individuals to take part in the dynamic pluralistic society by teaching respect and value for different positions, by encouraging students to rely on the scientific method of problem solving, and by fostering a commitment to the general welfare of society (Appleton, 1983, p.93)."
An understanding of minority and learning styles can offer important insight for the development of experiences and problem solving tools relevant to the mathematics classroom. This awareness is important in order to build an understanding of why many minority students experience difficulty in certain contexts. An understanding of differences in learning styles allows the teacher to build upon a student's strength, instead of considering these differences as a deficit. A particular cognitive style, encompassing "the way one perceives and thinks about the world" including "thinking, perceiving, remembering and problem solving" is culturally determined (Appleton, 1983). Developing a cognitive style in learners that encourages diverse and creative methods, through cross cultural sharing and interchange, should become a vital attribute of any mathematics program.
Learning and Culture
Mental activity is part of the overall human endowment, yet at the same time, much of the way it is directed is culturally determined (Appleton, 1983). Cognitive style, or the way in which a person "encounters, orders and thinks about the world" (Appleton, 1983) influences how well a student performs in a given academic environment. Experience in multicultural learning environments, and specifically, experience in dealing with more than your own culture, exposes learners to alternative methods in perceiving the world around them. Hall (1977) has said:
"The natural act of thinking is greatly modified by culture; Western man uses only a small fraction of his mental capabilities; there are many different and legitimate ways of thinking; we in the West value one of these above all others--the one we call "logic", a linear system that has been with us since Socrates.
The "ability to solve problems, or create products, that are valued within one or more cultural settings" (Gardner, 1983) is a valuable asset for all societies. Finding ways to tap into the diverse strategies that exist within any given classroom should become a primary concern. While at the same time, a teacher can encourage those linear/logical methods that connect all students to the dominant culture. The recent call for a redirection in mathematics education (Commission on Standards fpr School Mathematics, 1989) as well as certain computer software activities offer an extraordinary opportunity for educators to accomplish this goal.
Table 1 outlines the following discussion, as gleaned from the literature on culturally determined differences in learning styles for school-aged children. It is understood by this author that not everyone falls into one or the other group. The literature has supported the idea that most children come to school stronger in one or the other style. Presently, the dominant culture stresses, indeed appears to have built its curriculum upon, the majority learning style. "Successful" students, as labeled by the dominant culture, tend to be better at the use of those items that are in the majority category.
Table 1: Learning Styles
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Minority |
Majority |
|
People-oriented |
Object-oriented |
|
Relational |
Analytical |
|
Field Dependent |
Field Independent |
|
Polychronic Time |
Monochronic Time |
|
(P-time) |
(M-time) |
While giving many students timed tests, dittos, rote memory work, or works that asks them to copy and answer (often meaningless) problems, is mind-numbing for many children, it is particularly alienating for many minority children who come from cultures where human interaction and cooperation are highly valued. Though there are times when these activities are necessary, it is imperative that teachers in multicultural environments understand that their students may have particular difficulty with these kinds of solo work activities. It is imperative that the teacher in an ethnically diverse environment, use cooperative strategies for problem solving because minority students come from cultures that place value upon interpersonal communication encouraging all students to work together in cooperative groups and gives opportunities to communicate mathematics information (Kantrowitz & Wingert, 1989). As well, learning to work successfully with other people, in a dynamic and complex environment, is vitally important in an information society (Peters, 1988).
The largest single reason employees can lose a job is because they cannot get along with their own fellow workers. Giving students opportunities to learn how to work cooperatively on problems (often with people they may prefer NOT to work with) is an important life skill. Minority students can become important role models for more competitive students in working together cooperatively.
Relational and Analytical Learning Styles
Some students will need to see the relationship of what is being newly introduced to what they already know. Many teachers have heard "but WHY do I have to learn this? (Jackson, 1989), and it is precisely this need, that the student may be trying to fulfill. Other students are just as easily overwhelmed by, or see no need to identify, the connections to the past and present, but need to know HOW it works. If we give information to students using only one of these modes, then we miss other students who do not learn well in that mode.
Experiencing concepts in a variety of contexts, or seeing a number of uses of the same skill, not only reinforce the skill in a number of areas, but allow students to make a variety of mental connections with which to remember the concept. A given concept must be taught using as many different styles of communication as is possible.
Using integrated lessons, realistic simulations or projects that show the relationship of mathematics to the real world, are essential for creating an environment for learning, because "a person discovers, or creates knowledge, in the course of some activity having a purpose" (Commission on Standards for School Mathematics, 1989). Learning when to focus energy towards a given type of data, as well as coming to an understanding of why others do not approach a given problem the same as you have is a vital experience in coming to understand our fellow human beings.
Field Dependent & Independent Learning Styles
Minority and majority groups have had different backgrounds and experiences that may classify them as either Field Dependent or Field Independent (Jackson, 1989; Appleton, 1983; Lowenfeld & Brittain, 1975; Witkin, 1962). For example, students from traditional Mexican-American backgrounds tend to be field dependent; they have come to rely on surrounding field or environmental cues or relations in perceiving and interpreting information (Appleton, 1983). Many Anglo students appear to be field independent; they have been trained to focus on specific stimuli or data without regard to the surrounding environment (Appleton, 1983). The distinction is similar to that of relational and analytical styles, yet it is more focused and applies to the ability to take in information. For example, some people are able to spot individuals in a crowd, yet others, seemingly overwhelmed see only the whole group. Some students need to have plenty of stimuli: music, crowds, noise, activity. Others operate at an optimum in a quiet room with orderly plans and activities and relatively little excitement. It is important that we recognize the relationship between environment and learning style.
Monochronic and Polychronic Time
Hall (1977) has observed that the world is dominated by at least two different frames of reference as regards usage of time: monochronic and polychronic. Monochronic (M-time) emphasizes schedules, segmentation and promptness. This view of time is found primarily in Anglo America and Western Europe. Polychronic (P-time) is characterized by several things happening at once and is less tangible than M-time. Many people using P-time come from Latin America and the Middle East. Understanding this vital frame of reference is crucial to creating connections for students of different cultural backgrounds.
Implications for the Mathematics Classroom
The recent publication, Curriculum and Evaluation Standards for School Mathematics, (Commission on Standards for School Mathematics, 1989) encourages the use of teaching strategies that can improve the learning of mathematics for minority students. In the Standards, the National Council of Teachers of Mathematics (NCTM) has created a vision of:
The very core of the Standards addresses equity. By emphasizing how mathematics is really something done to solve problems, communicate and reason; one is reminded how in reality mathematics is tools for communication and interpreting information, and therefore, so much more than the mere arithmetic that has so thoroughly dominated the curriculum. NCTM recommends that teachers develop curriculum that includes a broad range of content in a variety of contexts with deliberate connections. Teacher can use their own particular multi-ethnic classroom realities as a rich resource upon which to build. As well, NCTM calls for instruction to be based on real problems that students themselves create and solve, and whose solutions they discuss. The Standards emphasize that the primary function of evaluation should be as a means of improving instruction, learning and programs. Evaluation should not be used to track students. A consequence of tracking is often walls between culturally diverse groups of people.
In Conclusion
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. Every step a teacher makes in designing, planning and teaching mathematics should be fed through the filter and exposed to the magnifier. It is possible that the most interesting aspect of what NCTM has proposed not only is good for the majority student population, but empowers the minority learner as well.
For educators, these are indeed challenging and exciting times; the face of the classroom one will see tomorrow may well be quite different from that of today. Never before have we known so much about how human beings learn, how they develop and mature. Never before have we had the abundance of materials and ideas that are available in to assist teachers in this process. Never before have we had such a diversity of students in our classrooms. It is time to lend both our spiritual and material resources and rise to the challenge because the image of society in which few have the mathematical knowledge needed for the control of economic and scientific development is not consistent either with the values of a just democratic system or with its economics needs (Commission on Standards for School Mathematics, 1989).
Mathematics is a tool. Being proficient in the use of this tool is important for students if they are to have any input at all as to how their own society can change and evolve to include them.
References
Appleton, M. (193). Cultural Pluralism in Education: Theoretical Foundations, New York: Longman.
Burke, J. (1985). The Day the Universe Changed. London:British Broadcasting Corporation.
Committee on Economic Development (1985). Investing in our Children: Business and the Public Schools. New York: Committee for Economic Development.
Commission on Standards in School Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
Gardner, H. (1983). Frames of Mind: The Theory of Multiple Intelligences. New York: Basic Books.
Hall, E.T. (1977). Beyond Culture. New York: Anchor.
Jackson, 5. (1989, May 9). Presentation at the Excellence in Mathematics and Science Achievement Symposium. San Francisco: Southwest Center for Educational Equity.
Kantrowitz, B. & Wingert, P. (1989, April 17). Special report: How kids learn, Newsweek.
Kearns, D.T. (1988,February 17). School reform: Strengthening a weak system, The Sacramento Bee,. p. B-5.
Lowenfeld, V. & Britain, WI. (1975). Creative and Mental Growth. 6th ed.. New York: MacMillan.
Luria, A.R. (1978). Cognitive development: Its cultural and social foundation. Cambridge, MA: Harvard University Press.
Peters, T. (1989, June21). Learn, innovate, act--or lose the job, The Sacramento Bee, p. E-3.
Witkin, H.A. (1962). Psychological differentiation. New York: Wiley.
Zaslavsky, C. (1989), Integrating math with the study of cultural traditions, Newsletter International Student Group on Ethnomathematics, 4(2), p.6-9.