Ethnomathematics and aboriginal student anxiety.

Abstract

Mathematics anxiety has been identified as a barrier to aboriginal learners who wish to enroll in post secondary education and training in Canada. We examined student beliefs about mathematics anxiety and their perceptions about how increased culturally-relevant mathematical content could enhance their feelings of efficacy in mathematics. We found higher levels of anxiety among aboriginal students; and identified differences between aboriginal and non-aboriginal students' views of how mathematics anxiety can be reduced.

Introduction

Mathematics anxiety is present in many learners, regardless of age, level of mathematical knowledge, gender or ability (Ashcraft, 2002). Mathematics anxiety is defined as a "feeling of tension, apprehension, or fear that interferes with math performance" (p. 181). Its most concerning consequence is the mathematics avoidance behaviour that results from high levels of fear. Fear of mathematics is a significant barrier to college student success. Perry (2004) suggested as many as 85% of students in an introductory mathematics course feel at least some degree of anxiety. Woodward (2004) suggested that mathematics anxiety is particularly prevalent among developmental mathematics college students. Anxiety levels among college students can differ on the basis of gender (Woodward, 2004: Zettle & Raines, 2000; Ashcraft, 2002) or among nontraditional, older students (Royce & Rompf, 1992). Bernstein's (1992) study of adults in a non traditional career programs found that men of African-American, Hispanic, Asian and Native American descent exhibited high levels of mathematics anxiety, as did women of Hispanic and Asian descent.

Aboriginal student enrolment in post secondary institutions is of particular concern to government agencies and educational institutions in Canada as participation rates among aboriginal students, particularly in mathematics and sciences are significantly lower than the rate for other Canadians (The Millennium Scholarship Foundation, 2004). In Canada, "aboriginal" is the term used to describe all persons of indigenous ancestry (Indian and Northern Affairs Canada, 2004). About 20% of aboriginal people between the ages of 15-24 participate in post secondary training compared to 43% of non-aboriginal people. As a result, provincial authorities have given regional colleges a mandate to improve aboriginal enrolment in post secondary and career training programs. One such college that has responded created bridging programs and developmental courses, including several in mathematics. As mathematics anxiety was seen by administrators as a barrier to aboriginal student enrolment, curriculum in one developmental mathematics course was modified to include aboriginal content. In our evaluation, we explored student beliefs about mathematics anxiety, and, in particular, how increasing socio-cultural mathematics content might affect mathematics anxiety.

Socio cultural Learning Theory and Mathematics Anxiety

A decade of research in mathematics education has demonstrated the benefits of adopting a socio-cultural perspective to mathematics education (FitzSimons, 2002). A socio-cultural perspective offers a different lens through which to view student success, curricular content, historical contributions and educational practices by recognizing that mathematics is not free of social, political, economic or cultural context. The adoption of an alternative epistemology that questions a dominant western discourse of mathematics as culturally neutral is recommended. D' Ambrosio (1999) is credited with the first use of the term "ethnomathematics'. Ethnomathematics "tak[es] into account the cultural differences that have determined the cultural evolution of humankind and the political dimension of mathematics" (p. 150). Ethnomathematics scholars that have focused on particular indigenous groups, include Knijnick's (2002a) work with the Brazilian Landless movement, Meaney (2002) and Robinson & Nichol's (1998) work with indigenous Australians, and Ezeife's (2003) work with aboriginal Africans. Ethnomathematics also promotes a pedagogical stance that connects mathematics instruction to problems of everyday life (Vithal & Skovsmose, 1997).

Other research specifically documenting indigenous learners and mathematics education suggests that the inclusion of indigenous examples within the curriculum increases aboriginal students sense of cultural pride, enhances understanding of the contributions that aboriginal peoples have made to mathematics and science, improves ability to apply mathematical knowledge to contextually relevant examples of mathematics in real life, and enhances interest and motivation in mathematical learning Student performance will improve and there will be reduced levels of mathematics anxiety, increased comfort and interest in mathematics learning (Robinson & Nichol, 1998; Meaney, 2002; Adam, Alangui & Barton, 2003). An assumed benefit of ethnomathematical approaches is that improved student motivation and interest will enhance conceptual understanding. Percival's (2004) study of elementary school experiences with cultural mathematics includes teacher reports of increased student motivation and deeper conceptual understanding (p. 123). Grugnetti and Rogers (2000) reported that an emphasis on studying the diverse cultural history of mathematics helped students make enhanced cross curricular connections. Little scholarship however, has been focused on the possible links between mathematics anxiety and socio-cultural approaches to learning mathematics in college settings. This study illustrates the potential such approaches may offer.

Methods

Efforts to re-conceptualize the mathematics curriculum were accomplished by amending the student textbook to include culturally relevant mathematics problems in a variety of units of instruction (geometry, measurement, area and perimeter, number operations, data analysis, graphing, ratio and percentages). We identified 24 examples of newly introduced aboriginal content. In addition, three group projects that required collaborative problem solving were added, including, tessellations in aboriginal art and beadwork; the construction of a traditional moose-caller; and a multicultural cookbook. The projects were graded and used as a replacement for unit tests (McGregor & MacMillan, 2004). The teacher maintained her usual teaching practices of presentation, modeling of algorithms, responding to student questions and providing time for individual assistance and independent practice. The socio-cultural projects required a format where students worked in small groups of up to four students.

Population.

The sample consisted of all members of the Mathematics 030 class of 2004. Its targeted clientele included students who have not completed a mathematics course at the Grade 10 level. Mathematics 030 is designed to offer an equivalent designation for adult students who may not have completed secondary school and are upgrading in order to receive their Grade 12 equivalency, or alternately for students who need to take a mathematics course in order to qualify for admission into a university program, trades or technology career. As this altered version of the course was not advertised as ethnomathematics nor was it described as altered to the students in the class, selection bias in terms of students opting to take it or not or to dropping out of it should not be a factor. In the Winter 2004 class there were 17 members, none refused to participate in the study. Of the 17 members, 11 were female and six were male. Of the females four identified themselves as being Aboriginal while one of the males self-identified as such. Student ages ranged from 20 to 49. The aboriginal students tended to be older than the other students, reporting their ages as between 30-49. Overall the class was relatively homogeneous when classified by age and relatively equally split by gender. The vast majority of students (95%) reported only "some high school" or "high school graduation" for their educational status.

Instruments

The questionnaire consisted of 81 dichotomous choice (True/False or Agree/Disagree) items related to broad topics of "Beliefs about Math Learning" and "Barriers to Learning Math". In addition there were two mathematics anxiety items, a 0--no anxiety to 7--very anxious scale. It concluded with an invitation to make additional comments. Fourteen students (82%) completed this questionnaire; three students were absent that day. The focus group guide consisted of a preamble about the nature of our intended investigation followed by 8 main questions, some with several sub-questions that dealt with fear of mathematics, useful ways of learning, and recollection of word-problems or projects that had an aboriginal locus. All 17 students participated to varying degrees. Students were later given the opportunity to participate in a follow-up interview. There was a $25 stipend that was designed to defray cost and provide a small incentive to the students. Eight students (42%) of the class, four aboriginal and four non-aboriginal took part in the interviews. The first two authors interviewed students but only one person interviewed any one student. Using an interview guide, questions centered on fears about mathematics, effective methods for learning mathematics, plus additional questions about comfort and safety issues for the aboriginal students. Interviews took place in an open setting at the college.

Results

Students expressed a variety of beliefs about why they experienced mathematics anxiety including: math's complexity and level of difficulty; lack of success in high school mathematics; mathematics avoidance behaviour; not putting adequate effort into their previous attempts; fear of failure; lack of confidence; and fear of looking 'stupid' in front of others. Fear was also linked with a concern for the unknown, particularly for students who had been out of school for some time. These results confirm previous scholarship notably Ashcraft, (2002), Perry (2004), and Norwood (1994). The response of aboriginal students showed some important differences from non-aboriginal students. While there were common sentiments (as above) other concerns were linked to unfamiliarity with an urban, college environment, and a lack of traditional family or cultural support. Two aboriginal women who participated in individual interviews revealed they had only recently moved to the urban environment, having spent most of their lives in smaller, remote aboriginal communities. Both expressed anxiety with unfamiliar settings and expectations; this was exacerbated by the stress of enrolment in a subject that was difficult and complex and unfamiliar given their traditional family roles. Socio-cultural projects were described as a possible bridge between traditional life and school life. Mary (pseudonym), while discussing the value of a class project that studied patterning in aboriginal clothing suggested "for...other[s]... who have anxiety about going back to school and they can see that there are some native things going on in school ... [and say] Hey, I belong here!"

Differences also arose in the degree to which the pace and specd through which mathematical concepts were introduced and then abandoned contributed to mathematics anxiety. Both aboriginal women interviewed identified concerns with balancing homework, family responsibilities and full time classes. "I sometimes stayed up until 3:00 or 4:00 am most days just to get the homework done. I am still doing so much homework". This response indicates how gender roles may be a factor in aboriginal anxiety. Similar proportions of aboriginal and non-aboriginal students expressed high levels of continuing anxiety in the rating scale items within the student surveys. Twenty percent of non-aboriginal students surveyed indicated that their anxiety level had continued to remain high, while 25% of aboriginal students indicated anxiety remained high. However, the emotive descriptors used by aboriginal students help illustrate how this anxiety might differ in intensity: "I don't think I can do this ... I remember for the first three weeks my heart was racing, my hands were shaking, I was like [often] crying, and I sat at the back, and couldn't wait to get home." Non-aboriginal students descriptors were more likely to be oriented towards early anxiety that faded as familiarity with routines and confidence increased. Robbie's (pseudonym) comments were typical: "It's like just getting started, the anxiety will go down after you get used to a course ... it is really about fear of the unknown."

Aboriginal students expressed a higher degree of preference for mathematics problems and projects that included indigenous perspectives. This belief was reiterated in both personal interviews and in the written surveys. Transcripts show all aboriginal students expressed considerable enthusiasm for the culturally focused projects, and in particular expressed a desire to learn more about the cultural contributions aboriginal peoples had made. Considerable pride was expressed in the tone and descriptions that these aboriginal students used in their personal interviews. Projects also required students to work collaboratively together, an alternative to the usual individual question/answer cycle, which was also identified as a source of anxiety.

In contrast, non-aboriginal students generally expressed the view that socio cultural examples were unnecessary for learning mathematics: evidence from the survey and interviews illustrated that non-aboriginal students believed mathematics was culturally neutral and required only sufficient effort and practice. Darryl's (pseudonym) comments were typical of those views shared during the focus group or interviews: "Using examples from native culture in math on [Aboriginal] reserves, that does work. But when it comes into [the college], in my class, I don't see how it makes any difference, because the natives in my class are regular people, most of them pay taxes, and they aren't receiving any special benefits. I don't think [ethnically focused] examples would help them learn it more. I think encouraging them, help them maybe, that would be good. But there are lots of people who don't know math, not just aboriginal people".

However, many non-aboriginal students expressed interest in problems that required the application of mathematical ideas to everyday situations; for example, 75 % or more of non-aboriginal students supported the usefulness of examples including grocery shopping, determining gas mileage or buying supplies for a home renovation project. In every case where cultural interests might be reflected such as basket construction, weaving, or beading however, support dropped to about 20%.

Discussion

Mathematics educators are highly motivated to find ways to augment their practice to support and enhance student learning. We have identified ethnomathematics as pedagogical practice that may assist in reducing mathematics anxiety among aboriginal adult students. In reporting on student beliefs, we draw upon the work of other scholars who have illustrated the crucial links between personal efficacy, motivation and learning. We have documented how personal and cultural worth are important foundations to build student understanding of mathematics for aboriginal learners. We also sought to understand what factors contributed to mathematics anxiety among aboriginal students.

At the same time, our work reveals the beliefs and views of students who form part of the dominant white, middle class culture of this college. By using a sociological perspective we have helped illustrate how "power lie at the heart of ethnomathematics ... 'other' mathematical knowledge ... impregnated by practice, tends to be devalued by the dominant groups, since it has closer ties to the local world where it is produced than to universal narratives" (Knijnik, 2002b, p. 14). In documenting the conflicting beliefs and perceptions of aboriginal and non-aboriginal students, we see an opportunity to differentially address student needs. Our data suggests a need to include culturally sensitive materials to meet the needs of Aboriginal mathematics students, while also suggesting that the curriculum and teacher practice should more explicitly explore the contributions other civilizations, races and cultures have made to mathematics.

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Catherine McGregor, University of Northern BC

Peter MacMillan, University of Northern BC

Barbara Old, College of New Caledonia

Catherine McGregor and Peter MacMillan are professors in the Education Program at UNBC. Barbara Old is the Associate Director of Continuing Education at CNC.