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This paper summarizes the literature and research on the relationships between culture and mathematics. Ethnomathematics examines the ways that different cultural groups use mathematics. Various definitions of ethnomathematics are presented, along with a framework covering areas of mathematics and mathematics education included in the term. Summaries and sample writings are offered for each of these areas: the cultural nature of mathematics, mathematical thought in different cultures, cultural history of mathematics, politics of mathematics, mathematics learning in different cultures, situated cognition including language and bilingualism, societal effects of mathematics education, and relationships between ethnomathematics and mathematics education. In addition, research is cited on the effects of culture on mathematics achievement, focusing on the transmission of cultural influences via popular media, parents, teachers, and students' own beliefs and attitudes. Examples of cultural influences on mathematics achievement are offered for Asian American, African American, Native American, and Hispanic students, as well as students from some foreign cultures. A research agenda for culture and mathematics is outlined that is relevant to understanding how mathematics is situated in a rural setting. (Contains 119 references.) (SV)

In the United States, African Americans, Latinos, and Native Americans have lower success rates and higher drop-out rates in mathematics than other racial or ethnic groups. Given that quantitative competency serves increasingly as a vehicle for economic enfranchisement, these differential success rates make mathematics achievement a civil rights issue. Failure and dropouts starts early; moreover, "algebra" is becoming a major stumbling block: many states require students to pass algebra tests in order to graduate high school. This social/mathematical problem is becoming increasingly urgent. This paper describes the American context and suggests its relevance world- wide. It then explores the following issues: (1) is mathematics culture-free and what are the implications for instruction?; (2) the institutional support necessary for high quality instruction; (3) the differential treatment of student groups; (4) pedagogical practices that enfranchise a wide range of students; (5) the roles of language and discourse in learning and classroom communities; (6) individual agency; and (7) what it means to engage meaningfully with mathematics. The challenge is to conduct classroom research that helps to explain, at a level of mechanism, how classroom interactions can be structured to help students who vary widely in terms of cultural backgrounds and prior mathematical success to all learn some very solid mathematics. (Contains 49 references.) (Author/KHR)

Development assistance was started for the sake of reconstruction of Europe shattered by World War II, and turned its attention to north- south problems starting at the Development Decade by the United Nations in 1960. In spite of all the efforts the international community has made, the situation for poor countries seems to have worsened and many insurmountable problems still lie ahead. "World Declaration on Education for All" (UNESCO, 1990) has changed the course of international cooperation and intends to address this global issue with attention to education as human rights and the potentiality of local culture. Verb- based curriculum in this paper is meant to activate the potentiality contained in ethnomathematical activities based upon the idea of universal activities, and substantiates the basic learning needs described in the declaration. (Contains 21 references.) (Author/MM)

The authors are in the process of interweaving mathematical ideas and the cultural contributions of the indigenous peoples of the Americas into what they teach. They are interested in how mathematics can be viewed culturally through the teaching of Indian Studies and Cross Cultural Education classes, how cultural components can be included in mathematics methods classes at the elementary level and in how specific examples of local cultures can be integrated into the teaching and learning of mathematics. Advancements in technology have made it possible for them to disseminate their ideas to preservice and inservice teachers through a Web resource called Math Central http://MathCentral.uregina.ca, the creation of an indigenous mathematics resource Web site http://education.uregina.ca/arnasonk, and an online mathematics course together with in-house published textbooks. This paper provides a context for the authors' work, describes a collaborative Transdisciplinary Project, and uses individual narratives to outline their explorations into the interweaving of mathematics and culture. (Author)

This paper presents an exposition of the mathematics of native peoples of North America related to the Western mathematics traditionally studied at the elementary through college level. This ethnomathematical review is made not only to allow instructors of Native American students to include in the school curriculum relevant mathematics developed by Indian people, but also to offer all students a fuller understanding of the universal nature and power of mathematics. Primary and secondary sources of Indian and Western mathematics were surveyed, summarized, analyzed, and synthesized. Sources of curriculum materials for inclusion of Native American approaches to various mathematical topics are offered throughout. The review concludes with a discussion of the implications for teaching and learning mathematics. (Contains 28 references.) (Author/ASK)

This paper examines how Ciulistet, a group of Yup'ik Eskimo elders, teachers, aides, and university collaborators, has slowly begun transforming education in southwest Alaska. Specifically, this paper shows how this indigenous group has produced, interpreted, and applied ancient Yup'ik wisdom to the modern context of schooling. Formally established in 1987, Ciulistet meets three or four times a year for a week or weekend. An example describes how elders have led discussions of Yup'ik numeration, exercises in grouping and place value, and explorations of connections to other mathematical and scientific concepts of time and place. Based on the body, the Yup'ik base-20 and subbase-5 system offers at least four concrete and conceptually different ways of teaching numeration and lead to considerations of the mathematics embedded in the Yup'ik linguistic system and of cultural differences in number patterns, grouping, and addition. As in the number system, Yup'ik ways of measuring also involve the body. Ciulistet meetings provide support to teachers attempting to develop, refine, and implement Yup'ik mathematics in the elementary curriculum of their schools. Implications for teacher education are discussed, particularly in minority and ethnic linguistic communities concerned with representing themselves in the processes and products of schooling. (Contains 32 references.) (SV)

This paper compares and analyzes preschool mathematics education in Singapore and India in terms of strategies, learning activities, teacher expectations, and parental involvement. The paper describes the mathematics curriculum of one school in Erode, India, including teaching methods, and in Singapore. The results of a parent survey in each country are presented, highlighting different parental attitudes toward mathematics education, math achievement for boys and girls, parental involvement in math education, and classroom instruction. (JPB)

This paper presents a case study of the Puerto Rico Statewide Systemic Initiative (PR-SSI) based on the analysis of data gathered from semi-structured interviews with key officials, field notes from site visits, progress and evaluation reports, and documents used in dissemination workshops for teachers. Although substantial data on student achievement are not available at this time, the qualitative analysis conducted here indicates that the PR-SSI is implementing an innovative reform program that deserves close attention. The path toward more effective schools was laid out by the PR-SSI as the direct result of simultaneously developing and implementing a variety of strategies to tackle all elements involved in making education reform systemic, i.e., policy, curriculum, student assessment, professional development, project evaluation, monitoring, and administrative support. Also, the PR-SSI articulated a form of conceptual systemic clarity throughout the initiative that became the cohesive theoretical and ideological force driving the reform effort forward. (Author/KHR)

An ongoing research project that investigates how mathematics educators can prepare prospective and practicing teachers to cope with cultural diversity is presented. The first component of this project is investigation of the ways that students can use their cultural identities and practices in constructing mathematical ideas that belong uniquely to them through a graduate course called "Ethnomathematics." The second is the investigation of ways teachers can facilitate students' construction of such uniquely personal cultural mathematics ideas in a high school classroom. The third component is the development of a grounded theoretical framework in which to situate the two previous components using semiosic chaining. The semiotic framework developed is being applied to the work from the graduate course and to the high school project, which took place in the 1995-96 school year. Data from the graduate project consisted of student journal entries, field notes, and more than 170 student project reports collected since 1993, some of which are described. The high school project involved seven students from differing ethnic backgrounds. Evidence from these students makes a strong case that traditional mathematics teaching does not facilitate a view of mathematics that encourages students to see the potential of mathematics outside the classroom. Although their own reports indicated that students were involved in many life activities with mathematical aspects, they continued to see mathematics as an isolated subject without much relevance to their lives. Semiosic processes may be used to illustrate connections as symbol systems are constructed in a bridge between cultures. Symbolism provides possible connections between mathematical ideas frozen in academic mathematics and practices, and different symbolism would facilitate the construction of different mathematics structures and concepts with increased relevance to students from different cultures. (Contains 33 references.) (SLD)

With the increasing recognition that connections are an important component in the pedagogy of school mathematics (National Council of Teachers of Mathematics, 1989), there is a need for a theoretical framework that addresses the ways in which the real experiences and cultural practices of students may be connected with mathematics classroom pedagogy. In this paper, the objective is to construct such a theoretical framework, drawing on literature from semiotics and ethnomathematics. Examples and evidence that suggest the efficacy of this framework in connecting school mathematics and mathematical ideas constructed from cultural practice are drawn from the literature and from data collected in a research project in a multicultural high school mathematics class. Seven high school students from African American, Caucasian, Asian American, and Hispanic American cultural backgrounds described their lives and cultural heritages as bases for the development of culturally responsive mathematics curricula. (Contains 1 figure and 12 references.) (SLD)

The purpose of this report is to document changes in U.S. mathematics achievement by reviewing national trend studies, college admissions examinations, and advanced placement tests. This report examined this quantitative research literature to determine trends in mathematics achievement of various social groups defined along lines of race, class, gender, ethnicity, and language proficiency. The findings of this review indicate that over the last 15 years all demographic groups have improved in mathematics achievement. Moreover, the mathematics achievement gap is slowly closing between white students and students of color. Males tended to outperform females on standardized measures; however, gender differences were small and generally not significant. Consistent with past reviews of mathematics achievement, coursetaking was a powerful variable, often resulting in similar achievement gains across diverse groups. This finding has serious implications for equity-related policy. (Author)

Mathematical performance of young Chinese children in Taiwan as compared to American children beginning as early as first grade has been well-documented. A similar study by Huntsinger, et al, 1995, demonstrated the same phenomenon in comparisons of Chinese-American young children with Euro-American children. Parents influence young children's developing competence by the experiences they provide and the activities they choose for their children, and cultural belief systems influence parents' ideas concerning the relative importance of activities. This study is a longitudinal comparison of 36 second-generation Chinese-American children and 40 Euro-American young children (from well-educated families in the suburban Chicago are) in their family environments, providing a synopsis of the data collected in 1995 when the children were in first and second grades. The data were collected in order to: (1) investigate whether the Chinese-American early mathematics advantage is maintained after children are exposed to formal mathematics teaching in first grade; (2) further identify differences in the early socialization practices of parents in the two cultural groups; and (3) examine relationships between mathematics achievement, parental socialization practices, and perceptions of children's competence. A total of 36 second-generation Chinese-Americans from Chicago suburbs participated in this second phase of data collection, including 95 percent from the first phase (1993). Each child was given the Sequential Assessment of Mathematics Inventories (SAMI) and other assessments. According to the results, Chinese-American children continued to demonstrate higher mathematics performance in Phase 2. Parents provided different experiences for their young children, who reflected different parental values and appeared to foster different competencies. Contains 7 tables of data and 14 references. (BGC)

Despite suggestions for incorporating students' experiences into school math lessons, mathematics education seems to be the last bastion of formalism. This paper reports on a sociocultural study of the use of students' personal experiences in early childhood elementary mathematics lessons. This study documents the use of students' personal out-of-school experiences in classroom math and other subjects and investigates barriers that may prevent such linking. The following questions are addressed: (1) To what extent do teachers currently link school math and students' personal out-of-school experiences? and (2) What influences the use of such linking? The study included observations of lessons in mathematics, language arts, and social studies in public, private, and homeschool settings. Despite recommendations in the literature, results showed that teachers rarely link students' personal experiences to math concepts. Linking is more common in language arts and social studies than in mathematics lessons. This study found that the gap between school math and the life experiences of students is established early in elementary school. It is therefore suggested that any reforms need to be implemented in the early grades as well as higher grades. (PVD)

This paper is based on efforts to bring change to school mathematics by trying to develop mathematics classroom communities in predominantly minority classrooms. In these communities, students work towards doing mathematics by working on open-ended, investigative situations; sharing ideas and strategies; and jointly negotiating meanings. Students also need to develop mathematics from their backgrounds and experiences with everyday mathematics. This paper explores the tensions and compromises resulting from the different conceptions of program participants (school and university teacher-researchers, students, and parents) of what mathematics is and of what mathematics children should learn. The work discussed focuses on geometry in a fifth-grade class. An appendix contains written work by students on finding angles on pattern blocks. Contains 38 references. (Author/MKR)

This study was designed to address two related issues: (1) Why are Blacks, Hispanics, and American Indians underrepresented in science and mathematics-related fields, and (2) Why do students of these minority groups have lower achievement test scores in science and mathematics than other students? Data on a number of home, school, and student variables were collected from the 1988 eighth-grade cohort of the National Education Longitudinal Study. Major findings include: (1) At early ages, all students have equally positive attitudes toward science and mathematics learning in school and have similar aspirations for science and mathematics-related careers, but as they get older, more minority students become unprepared to enter these fields as they fall behind in mathematics and science learning; (2) a larger percentage of minority students come from families in poverty which have fewer learning materials at home such as books and computers, and their parents are more likely than others to have low educational levels and to be unemployed and are less likely to provide adequate mentoring or role models for mathematics and science learning; and (3) these minority students are more likely to attend disadvantaged schools where the overall academic and supporting environments are less conducive to learning, suffer from the lack of persistent effort and active involvement in school, and are in low-track achievement groups. Appendices include data tables; National Center for Education Statistics (NCES) Databases for Studies of Science and Mathematics in Education; Specification of Variables Used in the Study; and a table of Correlation Coefficients for Contextual and Process Variables. (Contains 44 references.) (MKR)

This study compared Chinese-American and Caucasian-American children and families in order to better understand which cultural and family characteristics, parent beliefs, and parent practices operate at the early childhood level to produce the more uniform high level of math achievement among Asian-American children. Forty second-generation Chinese-American and 40 Caucasian-American preschoolers and kindergartners from well-educated, 2-parent families were given math, name writing, visual discrimination, spatial relation, and vocabulary measures. Parents completed questionnaires, interviews, and a social behaviors checklist. The study found that Chinese-American children outperformed Caucasian-American children on measures of mathematics, spatial relations, visual discrimination, numeral formation, and name writing. Caucasian-American children had higher scores on receptive English vocabulary. Chinese-American parents indicated a stronger belief in the role of hard work and early skill development in academic achievement, gave more direct math instruction, structured their children's time to a greater degree, and reported more encouragement for math-related activities than did Caucasian-American parents. Ethnicity, parents' child-specific attitudes, and directive teaching techniques were the strongest predictors of child math performance, numeral formation, and motor coordination. Six tables showing study data are included. A description of Chinese-American and Caucasian-American parent characteristics is appended. Contains 29 references. (MDM)

Educators can learn to use the unique cultural aspects of their students to create a learning environment that fosters the acquisition of mathematics concepts and principles. When teaching students in a multicultural setting, it is important to build on the student's intuition of the subject matter, to base instruction on situational story telling, and to establish within the student a strong number sense. When possible, everyday fun-type problems should be incorporated into teaching strategies. Studying the history of mathematics can sometimes help explain why things are done, and presenting the chronological as well as logical reasons for a mathematics idea can help achieve teaching for understanding. The following strategies are particularly useful in teaching students from culturally diverse backgrounds: (1) use cooperative-learning groups; (2) use modern techniques and technology; (3) use supervised practice and time with individual students; (4) learn the special cultural needs of each student; (5) respect the sources of difference and adapt teaching strategies; and (6) discuss the history of mathematics and the contributions of diverse mathematicians. (Contains 18 references.) (SLD)

Chinese-American girls perform as well as Chinese-American boys at higher levels of mathematics. Caucasian-American girls perform significantly less well than Caucasian-American boys. This study, designed to examine factors involved in this differential, contrasts 25 first generation Chinese-American mother-father pairs and 27 Caucasian-American mother-father pairs guiding their fifth- and sixth-grade daughters in solving math-related computer problems. Caucasian-American parents used more verbal mediation, displayed more emotion, relied more on questioning, used more encouraging and discouraging comments, and focused on the computer monitor less than did Chinese-American parents. Daughters' mathematics achievement test scores and mathematics grades were negatively related to mothers' verbal partipation for Chinese-Americans and to fathers' verbal participation for Caucasian-Americans. (Contains 20 references.) (Author)

Classifies ethnomathematics in relation to the teaching of formal, academic mathematics. Investigates whether ethnomathematics should replace academic mathematics, be a supplement to the mathematics curriculum, be used as a springboard for academic mathematics, or be taken into consideration when preparing learning situations. Suggests that only formal, academic mathematics is sensitive to the real value of mathematics inherent in cultures and societies. (Author/KHR)