Volume 36 Number 2
Winter 1997

In today's technological society a good mathematics and science background is becoming more and more important. Are we providing minority students with the necessary tools to survive and prosper in today's society? Statistics indicate we are not. For example, while African Americans, Hispanics, and American Indians collectively make up approximately eighteen percent of the total U.S. work force, they make up less than six percent of all employed scientists and engineers, 2.6 percent, 1.8 percent, and less than I percent respectively (Clemens Anderson, & Thorpe, 1992). While many factors may impact this under representation of non-Asian minorities in the fields of mathematics and science, one primary factor worth investigating is mathematics education.

While many studies, such as the National Assessment of Educational Progress (Dossey, Mullis, Lindquist, & Chambers, 1988), fail to include information on American Indian students, those studies which identify American Indian students show a marked underachievement in mathematics, with 80% of American Indian students failing to demonstrate mastery of simple arithmetic (Hafner, Ingles, Schneider, Stevenson, & Owings, 1990). Statistics also show 44% of American Indian eighth graders score below grade level in mathematics Ornstein & Levine, 1993); only 4.8% of American Indian eighth graders score at an advanced level, compared to 22.4% of white students (Peng & Hill, 1995) and, while non-Hispanic White students scored 491 on the mathematics component of the 1992 SAT, American Indian students scored 442 (K. Simmons, Scholastic Aptitude Test representative, personal communication, August 15, 1994). The latter could be influenced by the fact that American Indian students take fewer mathematics courses in grades nine through twelve. Twenty eight percent of American Indian students took eight or more semesters of high school mathematics, compared to 44% of White students, but 24% of American Indian students took three or fewer semesters of mathematics compared to only 12% of white students (Peng & Hill, 1995).

When the 25% dropout rate of American Indian students is taken into account (M. Frase, National Center for Educational Statistics representative, personal communication, July 17, 1995), the aforementioned statistics can be hypothesized to be an underestimation of the true scope of the problem (Oakes, 1988). These facts led the author to conduct a research study involving both qualitative and quantitative elements. The study was designed to investigate the perceptions of American Indian, African American, Hispanic, and White fifth and sixth graders in relation to mathematics, mathematics ability, mathematical and educational role models, treatment in the mathematics classroom, and teaching practices in the mathematics classroom. The study provided a comparison of American Indian elementary student perceptions with those of African American, Hispanic, and White elementary students.

Procedure
The research study was conducted during the Spring of 1994, after the survey instrument had been field tested with 85 fifth and sixth graders in classroom situations, as well as with individual students. Authorization was obtained from the administration of all schools according to their school policies. An anonymous, confidential questionnaire requiring responses to both multiple choice and openended questions dealing with the designated perceptions was administered to 61 different classes in 15 schools to a total of 1,015 students. Ethnicity and/or race, grade, and age were self reported on the questionnaire. Data were also obtained through interviews of randomly selected students, teachers, and classroom observations in three school districts.

Administration of the questionnaire took approximately thirty minutes per class. 'Me questionnaire was read orally to each class by the researcher in English and/or Spanish as was appropriate. Each student was provided a copy of the questionnaire, in either English or Spanish, to follow if they wished. Students marked their responses on a separate answer sheet and were allowed to skip any question with which they felt uncomfortable.

Due to individual school policies, teachers or other certified school personnel were often present during the survey. In these instances they were separated from the students, located where they could not see responses, and were busy with other work. In many classes, however, the survey was conducted with no school personnel in attendance.

Interviews with individual students and teachers, as well as classroom observations, were used to corroborate survey findings. Field notes were taken during interviews and observations, and after informal conversations.

Participants
Participants in the study were fifth and sixth graders in publicly supported schools in a southern Plains state. The schools had varying percentages of minority students ranging from less than ten percent to over ninety percent. The schools also varied from rural to urban settings. The schools included English speaking, limited English speaking, non-English speaking, and bilingual students. Whenever possible all fifth and sixth grade classes in each school participated in the study. When it was not practical for all classes to take the survey, efforts were made to assure the classes participating were representative of the wide range of abilities in any school.

The students varied in type of class attended. Some students were from totally self-contained classes but most were from departmentalized classes or a self-contained class with a designated teacher coming in for mathematics instruction. Of the 1,015 students involved 181 were American Indian, predominantly Plains Indians; 216 were African American; 155 were Hispanic; and 426 were White. Thirty-seven students did not fall into a single designated group. Data from these 37 students were not used in any of the comparison tests.

Questionnaire
The questionnaire was modeled after several attitudinal survey instruments, including the Fennema-Sherman Mathematics Attitudes Scales (Fennema & Sherman, 1976), Math Anxiety Questionnaire (Wigfield & Meece, 1988), Gourgey's Mathematical Self-Concept Scale and Attitudes Toward Mathematics Interview Instrument (Gourgey, 1982). The questionnaire was analyzed using a Chi-Square test on each multiple choice question with a single response. Comparisons were made between African American responses and American Indian responses, Hispanic responses and American Indian responses, and White responses and American Indian responses. Multiple response and open ended questions were analyzed for patterns using frequency tallies. Field notes from interviews, observations, and conversations were used in combination with the questionnaires to triangulate.

Findings
The responses from the questionnaire, substantiated in interviews and observations, revealed fifth and sixth grade American Indian respondents perceived mathematics as both important and not too hard to learn. These findings were in roughly the same percentages as African American, Hispanic and White respondents. Thus this perception of mathematics appeared to be unrelated to the race/ethnicity of the student.

Of particular interest in this area were the responses to the set of questions inquiring which class a student would most like to miss and least like to miss in order to attend an assembly. American Indian, African American and Hispanic students, indicated they would "least like" to miss mathematics, and "most like" to miss language arts/reading. These responses differed significantly from those of White students who reported they would "least like" to miss science class and ,'most like" to miss mathematics.

Multiple responses were allowed on a question asking to what object(s) a student would most liken mathematics, followed by an open-ended response explaining their answer. Table I shows a comparison of some of the most common answers. After reviewing the open ended responses, interviewing students, and doing observations, it appeared that students, regardless of race or ethnicity, had fairly negative perceptions of the way mathematics was taught in the classrooms. Seventy percent of American Indian students likened it to a maze, and 53.6% likened it to a prison.

In terms of mathematics capabilities, for example, learning new things in math or finishing class assignments, American Indian students perceived their abilities to be essentially the same as did Hispanic and White students. Only 12% of American Indian students described themselves as "very good in math" compared to 24% of African American students and 19% of White students. On the other hand, more American Indian students described themselves as "awful in math" (17%) compared to African American Hispanic or White students (9%, 11% and 10% respectively).

Responses relating to perceptions of role models were mixed (Table 2). The largest percentage of American Indian students, and students in general, thought most teenagers they knew believed that math was not too hard to learn, and was important to learn. However, more American Indian students than students of other groups believed most teenagers they knew thought mathematics was useless. In addition, a relatively high percentage of American Indian students responded that most of the 13 - 18 year olds they knew were not doing well in school and similarly that most of the 19 - 21 year olds they knew were dropouts. When looking at role models on T`V or in the movies, 36% of American Indian students responded they "never saw" any teenagers like themselves, with 13% responding that those they saw were either dropouts or not doing well in school. For role models in books, there was an even higher response rate indicating they never read about any teenagers like themselves. However, fewer of the role models in books were dropouts or not doing well in school when compared to those in TV or movie. In terms of more intimate role models, 13% of American Indian students responded they had no one to ask for help if they had mathematics homework, twice the rate for either African American or White students. A discouraging statistic showed that of all groups 16 - 32% had never heard of any famous mathematicians or scientists. Of those who had, only 36% of American Indian students had heard of any famous mathematicians or scientists of their same racial/ethnic background, compared to 65% of White students.

In terms of teacher treatment, responses indicated American Indian students believed their teachers generally thought they would go to college and were comparable to their classmates in their ability to learn mathematics, in how often the teacher called on them, and in how much time their teacher spent with them. These all appeared to be generic findings as they were consistent regardless of the race or ethnicity of the student.

While there were only limited differences in classroom teaching practices, their similarities spoke volumes (Table 3). The majority of students, regardless of their ethnicity or race, reported that they never or almost never used computers, worked in groups, played mathematics games, or worked with manipulatives (hands-on materials) in mathematics class, but that they used worksheets quite regularly, at least once a week. While these findings were not what was expected considering the recent reform trends in mathematics education, both interviews and observations corroborated these perceptions of classroom practices.

When looking at educational and career goals of students, most American Indian students appeared to believe they positively or probably would graduate from high school. The most popular career for American Indians students was teacher. In fact, teaching was vastly more popular with American Indian students than with African American, Hispanic, or White students. In comparing responses, it was seen that American Indian students were less likely to want to be a scientist, doctor, or veterinarian than White students; less likely to want to be a doctor, athlete, or scientist than African American students; and were less likely to want to be an athlete, policeman, secretary, or engineer than Hispanic students.

Limitations
While the study was done with a relatively large number of students, it was restricted to a single southern Plains state. It might be beneficial to replicate the study in another state(s) to see if the findings are consistent across the United States, or if they are localized. It would also be interesting to get additional information on role models such as "What famous mathematicians and/or scientists have you heard of-" and "If you have heard of any American Indian mathematicians and/or scientists, where or from whom did you learn about them?" (Through interviews it was revealed that some of the minority students who had heard of minority mathematicians and scientists had heard of them at home, not at school). Thus, while many questions were answered, many more were raised.

Some areas of potential concern, however, involve the findings dealing with role models and classroom practices. It appears that American Indian students (1) have significantly fewer positive role models, either educational or mathematic/scientific role models, than other racial/ethnic groups, and (2) have few opportunities to learn mathematics through group work, the use of manipulatives, the use of games, or the use of computers. This does not conform to research which has shown repeatedly that minority students benefit from the use of those particular teaching strategies (Ascher, 1983; Beane, 1988; Bradley, 1984; Cajete, 1988; Cheek, 1984; Davison, 1992; & Garza, 1992), and to the recommendations of the National Council of Teachers of Mathematics (1989).

It would seem, considering the small numbers of American Indian mathematicians and scientists, that even though American Indian students seem to appreciate the importance of mathematics and believe in their ability to learn math, there are other factors contributing to their low achievement in mathematics and ultimately to their under representation in the fields of mathematics and science. American Indian students appear to differentiate the ability to learn math, from performance in math class; and liking math and thinking it is important, from liking math class. What could the findings of this study imply for educators?

1. The perception of classroom practices shows the need to actively implement the recommendations of the National Council of Teachers of Mathematics, including the expanded use of technology, cooperative learning, active learning, student centered learning, modeling, games, relevance, connections, and manipulatives; with decreased use of worksheets and rote drills. These approaches should complement the learning styles of many American Indian students which tend to include global/holistic learning, use of imagery when learning, and visual/perceptual/spatial learning (More, 1989; Swisher & Deyhle, 1989).
2. The high dropout rate and under representation of American Indians in public school teaching and in mathematics or science related fields shows the need to nurture and encourage students to go to college, to enter fields of mathematics or science, and to become teachers.
3. Role model responses reveal a need to expose students to media which reflect more positive American Indian representation in books, movies, and on television. In particular, multicultural education should be actively incorporated into the curriculum, making all students aware of famous or successful mathematicians and scientists of all cultural backgrounds, especially American Indian.
4. The lack of help with mathematics at home suggests that educators should be more aware that many students do not have someone who could help them with mathematics homework, and that alternatives such as a tutoring, a homework buddy, mentors, or a homework help line may be necessary.
5. Student descriptions of a good math teacher reveal the need to identify and utilize mathematics teachers who are knowledgeable, enthusiastic, patient, caring, creative, flexible, who possess a sense of humor and believe that all students should, can, and will learn mathematics.

There are no acceptable reasons why American Indians should regularly score below grade level, nor be so under represented in the fields of mathematics and science. This inequity reflects both social and educational problems. These problems can and must be addressed to enable American Indian students to succeed.