Volume 23 Number 2
January 1984

Helen Neely Cheek, Oklahoma State University

IN OUR INCREASINGLY technologically oriented society, mathematics has become the "critical filter" that often prevents females and minority members from attaining careers in high paying jobs. The amount of mathematics studied can serve as a predictor of future income (Sells, 1978). Native Americans are among the most impoverished in the nation (La Fromboise & Plake, 1983). They are also the most poorly represented among occupations in the natural sciences, the health sciences, and mathematics (Green, 1978a). The very small number of Native Americans in these mathematics-related fields may be related to the fact that Native American students have difficulty in traditional mathematics classes (Bradley, 1983; Brod, 1979 & 1981; Coombs, 1970; Green, 1978a & 1978b; Smith, 1981). The causes of this difficulty have not been documented. Possible solutions have been suggested. Few hypotheses have been tested empirically.

The average mathematical achievement levels of Native American students are extremely low in comparison with students of other ethnic groups. In New Mexico, a tenth grade computation proficiency examination found only 21% of Native students scoring 65% correct or higher while 27% of the black students, 41% of the Hispanics, and 72% of the white students scored at or above that level. In problem solving, the proportion of Native American students achieving 65% or higher was nearly equal to black students (57% and 58%, respectively); however, both were still much lower than Hispanics (79%) or white students (94%) (Southwest Resource Center for Science and Engineering, 1981, p. 7).

In the state of Washington the average mathematics score for Native American students attending public schools was the 33 percentile in 1980. Specific reservations scored as low as 24 (Brod & Brod, 1981).

The California Achievement Test average mathematics score of Choctaw students attending four Junior High schools in Mississippi were the 17.8 percentile in 1977, the 22.3 percentile in 1978, and the 26.3 percentile in 1979 (Brod, 1979). Although these scores indicate improvement, the average percentiles of Choctaw 12th graders during that time frame were 17.5 in 1977, 25.8 in 1978, and 18.1 in 1979 (Brod, 1979, p. 21).

The author is aware that longitudinal data is preferable in this research.

Brod’s (1979) Mississippi study confirmed a conclusion reached by the Senate Subcommittee on Indian Education (1969) ten years earlier: the American Indian child typically falls farther and farther behind national norms as he progresses through school. This phenomenon has been designated as "progressive retardation" (Combs, 1970). The third grade Choctaw students in Brod’s study scored at a 2.9 grade equivalency in mathematics in 1979. The "progressive retardation" apparent in his results shows sixth graders that year at 4.9 and twelfth graders at 8.1. The longer they were in school the farther they fell behind (Brod, 1979, p. 13).

Bradley (1983) in a paper on Native American Mathematics Education concludes:

Green suggests the problem of Native Americans lack of achievement in mathematics is one of emotional or psychological origin. She interviewed Indian college students, educators, counselors, teachers, program directors, and many non-Indian educators and advisors for the American Association for the Advancement of Science Project on Native Americans in Science (Green, 1978a). The purpose of her study was to find the barriers obstructing entry of Native American students in the natural sciences.

She found "of all the skill and attitudinally-related obstacles to success in both their general education and to a potential choice of a career in the sciences and technical fields, however, mathematics anxiety and math avoidance seemed to be the most pervasive and serious" (p.2). Mathematics anxiety and avoidance was not limited to Native students studying the humanities; it was expressed even by those who chose careers requiring mathematical competence. "Most expressed a distaste for math even when they were relatively competent in the skills required of them" (p. 2). This widespread loathing of mathematics was apparently based on a fear of failure, although few of them had actually ever failed. What occurred was that mathematics classes were dropped when the first indication of skill inadequacy appeared.

Smith (1981) described several studies which indicate that Native American students living on reservations in Arizona have a significantly different understanding of words used in mathematics than either white or Native American students from urban settings or urban children who speak only Spanish at home. He inferred that "Although the investigations are not conclusive, it does seem reasonable to suggest there are differences that exist, they are measurable, and they are culturally induced" (p. 7).

After working with one group of Native Americans, Moore (1981) reports that the basic concepts and objectives of the philosophy and religion underlying their culture are "entirely consistent with those views of the greatest contributors to the development of mathematics." Descartes, Kepler or Einstein "would have felt comfortable with the view of the [Navajo] Chanter . . . " he believes. Moore concluded that "any differences between the Indian and Anglo cultures which would impact upon the learning of mathematics would be incidental and superficial rather than fundamental and substantial" (1982, p. 2).

Numerous hypotheses suggesting the causes and possible solutions to the problem of mathematics underachievement by Native American students have been expressed. Some of the more promising areas of investigation are discussed below along with the hypotheses that need to be tested.

Participants attending the Conference on Mathematics in Indian Education in Albuquerque "felt the factor most important in keeping Indian students from obtaining a good mathematics education is the prevalent feeling among teachers, counselors and administrators that a more-than-rudimentary mathematics competence is beyond and/or irrelevant to Indian needs" (Green, Brown & Long, 1978, p. 2). Nash (1973 and 1976), for example, has demonstrated effects on children’s classroom and test performance resulting from teachers expectations. The influence of parental expectations can be so great that their belief in the child’s ability can predict course taking according to Ortiz-Franco (1981). Many Native American students report being "counseled out" of mathematics because it was perceived as too difficult for them or as unnecessary for their future (e.g., Green, 1978a).

The affective variable of causal attribution is also related to the students’ expectations of their ability to perform mathematics (Fennema, 1983). Thus, even students performing well in mathematics often attribute their success to such external forces as luck or chance which may or may not be repeated. These same students attribute their failures in mathematics to such stable, internal forces as lack of ability, however. The students’ locus of control is often different for success and failure.

Empirical data are now needed to demonstrate successful techniques for convincing Native American students, their parents, teachers and counselors that mathematics is important to these students’ future and that they do have the ability to perform successfully. Projects such as the following could provide the necessary data. One and two report successful programs designed to increase the mathematics participation of females while the third is the effort of a single classroom teacher.

1. Two videotaped programs provide protocols on which future Native Americans projects could be patterned. MULTIPLYING OPTIONS AND SUBTRACTING BIAS is a total program aimed at convincing females and those who influence them that mathematics is important. The program is composed of four workshops aimed at a particular group: students, parents, teachers, and counselors. The tapes use a variety of formats, candid interviews, dramatic vignettes, and expert testimony to describe the problem of mathematics avoidance. The tapes and workshop activities provide awareness of existing stereotyping, differential treatment of females as learners of mathematics, and the need of all people for mathematical competency. Extensive evaluation (Fennema, Wolleat, Pegro, & Becker, 1981) has shown the program to be successful in changing attitudes and increasing female mathematics participation.

The second set of video tapes is distributed by the Mathematical Association of America (MAA). Entitled MATHEMATICS AT WORK IN SOCIETY, the series interviews persons in various career fields who discuss the use of mathematics in their occupations. The interviewees include black and whites of both sexes. Neither videotape series was intended for Native American audiences. The message of the tapes, however, is the importance of mathematics for all students. This message should be clear to any English speaking audience.

2. Another program that has proven effective in increasing female expectations related to mathematical achievement is presented in the Math/Science Network conferences supported by the Women’s Educational Equity Act (Perl & Cronkite, 1979). One-day conferences bring junior and senior high school girls together for a panel or speaker, hands-on science/math workshops in which the girls interact with female role-models working in mathematic related fields. Over two thousand participants reported plans to take more than two years of high school mathematics as a result of the conferences.

This program can be used in Native American communities in conjunction with role model from professional organizations such as the American Indian Science and Engineering Society, the Council of Native American Architects and Engineers, and the American Indian Physicians Association.

3. Green (1978a) found none of the math anxious Native students in her sample had heard of Mayan or other Indian mathematical system. "They had either no knowledge or a negative impression of the mathematical and scientific capabilities of Native peoples" (p. 3). Vera Callahan-Preston has recently begun teaching mathematics at a predominantly Native American school in Oklahoma. She is hoping to increase the expectations of her Native American students by involving them in study of Native mathematical systems which formed the basis of her graduate thesis, Mathematics in the Mayan, Aztec, and Inca Cultures (Callahan, 1969).

Participants at the Conference on Mathematics in American Indian Education considered culturally-based education to be especially appropriate for pre-collegiate math and science (Green, et al., 1978). Johnson (1975) recommends introducing mathematics concepts via materials and examples from both the dominant culture and the specific ethnic culture of the students within the classroom. He advocates encouraging students to interpret abstractions in the form of story situations which they contrive; using foods, occupations, places and events from the learners’ environment. Green, et al., (1978) recommend looking at how the culture uses mathematical concepts (e.g., astronomy, cooking, crafts) and including these in the curriculum. The Ohoyo Resource Center has published a bibliography of culturally-based curriculum materials available for teachers of Native Americans (Nelson & Walton, 1982). Although relatively few of the materials are for mathematics, the bibliography will prove extremely valuable to those attempting to prepare culturally-based programs.

One of the difficulties plaguing research in this area is the lack of generalizability of successful programs. There is no single "Native American culture" upon which to base a mathematics curriculum. Rather, there are over 400 Native American tribes, each with to some degree a different culture (see, for example, Keshena, 1980). Since culturally-based materials developed for one tribe may not be appropriate for use by students from other tribes, curriculum developers in this area may need to look primarily at those universally (or widely) accepted activities that are culturally appropriate for numerous tribes. Activities prepared to teach mathematics through such activities can be made tribal specific by the classroom teacher. For example, games of chance are played by members of most tribes. A unit on probability could be developed using several examples of these games while encouraging the teacher to include the games played by the specific tribe or tribes represented in the classroom.

Another issue to be considered in culturally-based curricula concerns the role of teachers with no experience in the culture. Should they attempt to teach the culture to children who do experience it? This problem may be manifest by spending too much class time on superficial cultural aspects such as traditions, songs, and games but very little time on skills. Dr. Thier (1976) suggests that the school develop an appropriate curriculum with the advice and cooperation of community members. He further suggests an experience-based curriculum which incorporates school, home, and other life experiences.

Researchers in this area need to test the process of developing a culturally-based mathematics curriculum. Approaches which have proven successful when tribe and school have worked together on similar projects in other disciplines must be identified. Questions such as the following need to be considered: How much formal mathematics education do community members need in order to work with the school? Must teachers also be tribal members? Must teachers speak the language of the tribe? What background factors in the school and in the community are most important?

Green’s (1978a) conclusions are bleak:

Her concerns were echoed by participants of the Conference on Mathematics in American Indian Education. "All concurred that a basic mathematics education, as it is customarily taught may be inappropriate for the needs of most people, and most certainly for Indians on reservations" (Green, et al., 1978, p. 4). The Ford Foundation (1981) also agreed that the way mathematics is taught to all students requires radical reform and results of the second National Assessment of Educational Progress (NAEP) in mathematics tend to support the same conclusions. Only 39 per cent of nine-year-olds sampled believed they usually understood "what we are talking about in mathematics" (Carpenter, Corbitt, Kepner, Lindquist, & Reys, 1980).

One often recommended approach for improving mathematics learning is the activity-based approach (e.g., Biggs & MacLean, 1969; Copeland, 1974; or Souviney, et al., 1978). Suydam and Higgins (1977) outlined the research needed in this area five years ago. A follow-up study by Engelhardt (1981) indicated that few empirical studies following Suydam and Higgins’ outline have been published.

Scott (1982) looked at the differences in performance in mathematics between Pueblo Indian and white students entering a teacher training program. The subjects of this survey were matched on over-all math scores. The white students in this sample scored higher in arithmetic while Pueblos scored higher in measurement. Scott noted that the arithmetic items were all highly symbolic and could be done with rote manipulation devoid of any real world context while the measurement items were application problems that related to "real world experience." Scott suggests that this may provide a useful pedagogical hint in providing basic mathematics instruction to Pueblo groups; namely, that computational skill development be related to real world situations such as those involving measurement.

Another possibility for improved pedagogy lies in computer-assisted instruction (CAI). The staff of the All Indian Pueblos’ CAI Project

The microcomputer revolution which has occurred since Green’s report was published, makes this a possible teaching resource for even the smallest, most remote schools. Curriculum developers must seek high quality mathematics software programs for microcomputer use with Native American students.

Another research need requires longitudinal studies. We need to see, for example, whether Native American students learn to understand mathematics over a period of 2 or 3 years through a LOGO environment (Bradley, 1976; Howe, O’Shea & Plane, 1980; Papert, 1980). The availability of the LOGO computer language on several microcomputers and the tendency of some reservation schools to have stable populations over long time periods help make it a timely program for investigation.

Increasing the number of Native American students who study advanced mathematics is important for the economic improvement of all Native Americans (Bradley, 1983; Green, 1978a). Increasing the amount of mathematics studied by individual Native American students will broaden the career choices and income opportunities of those students (Sells, 1978). Educators, researchers, and tribal members must cooperate in efforts to increase the mathematical achievement of these students. Some promising areas of investigation have been suggested in this paper. Any research findings in this area should be widely disseminated. Successful intervention programs should be widely publicized. We must provide the Native American student of mathematics every opportunity to succeed.

Biggs, Edith E. & MacLean, James R. Freedom to learn: An active learning approach to mathematics. Ontario, Canada: Addison Wesley, 1969.

Bradley, Claudette. Native American loom beadwork can teach mathematics (Logo Working Paper #49). Cambridge, Mass.: Artificial Intelligence Laboratory, Massachusetts Institute of Technology, March 1, 1976.

Bradley, Claudette. The state of the art of Native American mathematics education. In H. N. Cheek (Ed.), Handbook for conducting equity activities in mathematics education. Reston, VA: National Council of Teachers of Mathematics, 1983.

Brod, Rodney L. Choctaw education. LPS & Associates, Rocky Boy’s Route, Box Elder, MT 59521, December, 1979.

Brod, Rodney L., & Brod, Mary Jean. Educational needs of Colville Confederated Tribes. LPS & Associates, Rocky Boy’s Route, Box Elder, MT 59521, August, 1981.

Callahan, Vera Alma. Mathematics in the Mayan, Aztec, and Inca cultures. Unpublished Master’s Thesis, The Graduate School, University of Maine, Orono, Maine, January, 1969.

Carpenter, T.P., Corbitt, M.K., Kepner, H., Lindquist, M.M. and Reys, R.E. Students effective responses to mathematics: Results and implications from national assessment. Arithmetic Teacher, 1980, 28 (2), 34-37, 52-53. (October, 1980).

Coombs, L. Madison. The educational disadvantage of the American Indian student. Las Cruces, New Mexico: New Mexico State University, 1970.

Copeland, Richard W. How children learn mathematics (2nd ed.). New York: Macmillan, 1974.

Engelhardt, Jon M. Manipulative materials and mathematics instruction—A literature review. Unpublished, 1980. Available from author, Arizona State University, Tempe, AZ 85287.

Fennema, Elizabeth. Girls and mathematics: The state of the art. In H.N. Cheek (Ed.), Handbook for conducting equity activities. Reston, VA: National Council of Teachers of Mathematics, 1983.

Fennema, Elizabeth, Wolleat, P.L., Pegro, J.D., & Becker, A.D. Increasing women’s participation in mathematics: An intervention study. Journal for Research in Mathematical Education, 1981, 12 (V), 3-14.

Ford Foundation Staff Paper. Minorities and mathematics. New York: Ford Foundation, 1981. Available from the Ford Foundation, 320 E. 43rd St., New York, NY 10017.

Green, Rayna. Math avoidance: A barrier to American Indian science education and science careers. BIA Educational Research Bulletin, 6, 3, September, 1978a, pp. 1-8. (ERIC Document #ED 170-084).

Green, Rayna, AAAS News: Math called key to Indian self-determination. Science, 201, August 4, 1978b.

Green, Rayna, with Janet Walsh Brown & Roger Long. Report and recommendations: Conference on mathematics in American Indian education. Washington, D.C.: Educational Foundation of America and American Association for the Advancement of Science, February, 1978.

Howe, J.A.M., O’Shea, T., & Plane, F. "Teaching mathematics through Logo programming: An evaluation study." In R. Lewis and E.D. Tagg (Eds.), Computer assisted learning. New York: North-Holland Publishing Co., 1980.

Johnson, Willis N. Teaching mathematics in a multicultural setting: Some considerations when teachers and students are of differing cultural backgrounds. Murray, KY: Murray State University, 1975. (ERIC Document #ED 183 414).

Keshena, Rita. Relevancy of tribal interests and tribal diversity in determining the educational needs of American Indians. In the National Institute of Education’s Program on Teaching and Learning, Report of the Conference on Educational and Occupational Needs of American Indian Women, October, 1980.

Moore, Charles G. A preliminary report on an investigation of elements of the Navajo culture that may impact upon the learning of mathematics. Paper presented April 24, 1981, at the NCTM 59th Annual Meeting, St. Louis, Missouri. Copy available from author at Northern Arizona University, Flagstaff, AZ 8 1011.

Nash, R. Classrooms observed: The teacher’s perception and the pupil’s performance. Boston: Routledge & Kegan Paul, 1973.

Nash, R. Teacher expectations and pupil learning. Boston: Routledge & Kegan Paul, 1976.

Nelson, M.F. & Walton, M.F. OHOYO IKHANA: A bibliography, of American-Indian-Alaska Native curriculum materials. Wichita Falls, Texas: Ohoyo Resource Center, 1982.

Ortiz-Franco, Luis. Suggestions for increasing the participation of minorities in scientific research. Washington, D.C.: National Institute of Education, April, 1981.

Papert, Seymour. Mindstorms. New York: Basic Books, 1980.

Perl, T. H., & Cronkite, R. Evaluating the impact of an intervention program: Math-science career conference for young women. Unpublished manuscript, 1979. Available from Dr. Teri Hoch Perl, 3332 Britten #17, San Carlos, CA.

Scott, Patrick B. Mathematics achievement test score comparison of American Indian and Anglo students entering an elementary teacher training program. Journal of American Indian Education, 1983 22(3), 17-19.

Sells, Lucy W. High School mathematics enrollment by race and sex. In The mathematics filter: A new look at an old problem, 1978. (Available from Overcoming Math Anxiety, c/o S. Hamer Associates, 15 Lewis Street, Hartford, Conn.)

Smith, Lehi. Mathematics education in an American Indian culture. Unpublished manuscript. Copy available from author, Mathematics Dept., Arizona State University, Tempe, AZ 85287.

Southwest Resource Center for Science and Engineering. A planning grant proposal for a comprehensive mathematics program in Northern New Mexico. Albuquerque, New Mexico: Southwest Resource Center for Science and Engineering, 1981.

Souviney, Randall, with Tamara Keyser & Alan Sarver. Mathmatters. Santa Monica, Cal.: Goodyear Publishing Co., 1978.

Suydam, M.N., & Higgins, J.L. Activity-based learning in elementary school mathematics: Recommendations from research. Columbus, Ohio: ERIC Information Analysis Center for Science, Mathematics, and Environmental Education, 1977.

Thier, Herbert D. Some thoughts in educational experiences and Pueblo Indian children. The Education Profile (Newsletter of the Southern Pueblo Education Agency, Albuquerque), 1976, 6, (3), 9-11.

United States Senate, Special Subcommittee on Indian Education. Indian education: A national tragedy—a national challenge. Washington, D.C. U.S. Government Printing Office, 1969.

Helen Neely Cheek received the Ph.D. from Arizona State University. She is presently an Assistant Professor at Oklahoma State University in the Reading/Math Center and Dr. Cheek can be reached c/o Route 1, Box 60, Perkins, OK 74059.