Reference List

Ethnomathematics Reference List

By Irene Duranczyk

1. Ethnomathematical origins of algebra. (1986). Mathematics Teaching, 115, 19-21.
Abstract: A collage of the remnants of ethnomathematical history from which algebra sprung.

2. Abraham, J., & Bibby, N. (1988). Mathematics and society: Ethnomathematics and a public educator curriculum. For the Learning of Mathematics, 8(2), 2-11.
Abstract: The aim of this article is to provide a conceptual picture of a "Mathematics and Society" curriculum. Examples of such curricula are described, along with discussion of ethnomathematics and self-generated mathematics, the social institution of mathematics, critical thinking and conscientization, and policy issues. (MNS)

3. Adam, M. (2002). Helping students "Shine like never before" UMDNJ's special commitment to diversity. The Hispanic Outlook in Higher Education, 12(7 ), 20.
Abstract: This article showcases the efforts of the Hispanic Center of Excellence, a federally funded program which is part of the University of Medicine and Dentistry of New Jersey. The Center's goal is to increase the number of Latinos in the health professions. The center, which opened in 1991, offers programs for children as young as 3rd grade who have an interest in the health sciences. Among the resources they offer are an MCAT preparatory program, Gifted and Talented Elementary School Program, and also mentoring and guidance. A major goal of this program is to help "unnoticed" students with modest academic achievement to accomplish their goals, to offer them the right kind of support and encouragement so that they may "shine like never before."

4. Anderson, J. A. (1988). Cognitive styles and multicultural populations. Journal of Teacher Education, 39( 1), 2-9.
Abstract: Social scientists generally agree that different cultures have different cognitive styles. New educational models which operate within a multicultural framework are necessary. As a result, traditional approaches to training educators must be adjusted if minority groups are to enter teacher education programs. (JL)

5. Anderson, M. (2001). Integrating multiple perspectives into curricula and teaching: Resources for getting started. The Hispanic Outlook in Higher Education, 11(10), 29.
Abstract: In this article, the author points out the growing diversity of America's college population. Embracing these differences and using them to expand knowledge, she argues, will contribute to the inclusion of all people in different aspects of our society. She suggests that, by curriculum reform, college faculty can contribute to this inclusion. She suggests a variety of literary resources that college faculty can use to aid them in curriculum reform.

6. Arcavi, A., Kessel, C., Meira, L., & Smith, J. P. I. (1998). Teaching mathematical problem solving: An analysis of an emergent classroom community. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), CBMS Issues in Mathematics Education. Volume 7: Research in collegiate mathematics education. (pp. 1-70). Providence, RI: American Mathematical Society.

7. Arismendi-Pardi, E. J. (1999). What is ethnomathematics and why should we teach it? Crossing cultures: Communicating through the curriculum. Paper presented to the National Conference of the Center for the Study of Diversity in Teaching and Learning in Higher Education .
Abstract: This paper defines ethnomathematics and reviews the methods used to incorporate this philosophy into the current teaching of mathematics. Ethnomathematics rejects inequity, arrogance, and bigotry while challenging the Eurocentric bias that denies the mathematical contributions and rigor of other cultures. A review of the literature shows that the teaching of ethnomathematics will bring awareness to students that Europe is not now nor was it ever the center of civilization. Ultimately, this method will present an accurate history of mathematics, use a variety of examples to solve problems from a variety of cultures, and recognize that learning mathematics is a unique process for every individual. (CCM)

8. Armstrong, W. B. (2000). The Association Among Student Success in COurses, Placement Test Scores, Student Background Data, and Instructor Grading Practices. Community College Journal of Research and Practice, 24(8), 681-696.

9. Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas. Pacific Grove, CA: Brooks/Cole Publishing Company.
Abstract: Ethnomathematics" refers to the study of mathematical ideas of traditional peoples who have generally been excluded from discussions of mathematics. This college-level text discusses mathematical ideas as they are expressed and embedded in cultures including the Inuit, Inca, Maori, and Bushoong. It also looks at the scope and implications of ethnomathematics and how it relates to other areas.

10. Ascher, M. (1988). Graphs in cultures: A study in ethnomathematics. Historia Mathematica, 15(3), 201-227.
Abstract: As the author observes, the philosopher Wittgenstein pointed to the problem of tracing graphs or figures as one that everyone can recognize as mathematical. Related problems have occurred in a variety of cultures. In western Europe, problems of tracing graphs or figures have occurred in Danish folk puzzles, where they were used as an alternative to dancing. Two patterns that are traced out are said to be similar to those on an artifact from Viking times, and are said to have mystical significance; and two others are said to be useful in witchcraft. Similar problems occur in other cultures as well. The article focuses on the context of the puzzles and the methods used to solve them in New Ireland and the Republic of Vanuatu, especially on the island of Malekula. A number of designs from Vanuatu have mythic significance. There is a tradition that one must complete a certain diagram to enter the Land of the Dead; failure results in being eaten. The methods used to draw the diagrams are also very interesting. In many cases, Ascher shows how individual drawing elements are transformed by processes such as reflection and rotation and are combined in systematic ways to draw the figure. Other types of mathematical ideas from Malekula include a drum signaling system with rhythms for each clan, rank, grade of pig, and special phrases, and a six-class marriage system which the elders explained with diagrams in the sand.

11. Ascher, M. (1995). Models and maps from the Marshall Islands: A case in ethnomathematics. Historia Mathematica, 22(4), 347-370.
Abstract: Stick charts are a significant part of the Marshallese navigation tradition. Here we focus on the mathematical ideas of modeling and mapping embodied in these charts as well as on the ideas about wave dynamics that they incorporate. These planar representations were used to teach prospective navigators the principles and specifics of the unique Marshallese system of "wave piloting."

12. Ascher, M., & D'Ambrosio, U. (1994). Ethnomathematics: A dialogue. For the Learning of Mathematics, 14(2), 36-43.
Abstract: Presents a dialogue about ethnomathematics that includes discussions of: quipus (knotted cords) as a form of language, difficulty in defining mathematics, culturally embedded mathematical ideas, philosophy and mathematics, quantification without giving meaning to numbers, and evolution in mathematical thinking. (MKR)

13. Ascher, M., & Robert Ascher. (1981). Code of the quipu: A study in media, mathematics, and culture. Ann Arbor, MI: The University of Michigan Press.
Abstract: Extensive and readable discussion of the quipu, a system of knotted cords used by the Incas to store massive amounts of information important to their culture and civilization. Includes much information about the Inca culture, as well as an analysis and comparison of how data is stored and managed with a quipu with the way data is handled with computers.

14. Atweh, B., Forgasz, H., & Nebres, B. (editors). (2001). Sociocultural research on mathematics education: An international perspective. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
Abstract: This book, based on research on sociocultural aspects of mathematics education, presents contemporary and international perspectives on social justice and equity issues that impact mathematics education. In particular, it highlights the importance of three interacting and powerful factors--gender, social, and cultural dimensions. The book is research based and presents recommendations for practice and policy and identifying areas for further research. It addresses all aspects of formal and informal mathematics education and applications and all levels of formal schooling. The book is especially intended for researchers, graduate students, and policymakers in the field of mathematics education.

15. Baba, T., & Iwasaki, H. (2000). The development of mathematics education based on ethnomathematics (2): Analysis of universal activities in terms of verbs. Paper presented at the 24th Conference of the International Group for the Psychology of Mathematics Education .
Abstract: In the development of new curriculum whose focus is mathematical activity as signifie, the verb as its signifian should be a center of consideration. This is why the proposed curriculum is named verb-based. In mathematics education, an activity deepens itself in a recursive manner through symbolization of activity. Bishop (1991) widened this concept of activity and claimed each culture has developed its own mathematics through six universal activities.
All the verbs at the primary level in the Japanese course of study were collected and analyzed in this paper. As a result this research showed the structure of activities on mathematical recognition through the verbs under the theory of internalization.

16. Ball, D. L. (1997). What do students know? Facing challenges of distance, context, and desire in trying to hear children. In B. J. Biddle, T. L. Good, & I. F. Goodson (Eds.), International handbook of teachers and teaching (pp. 769-818). Dordrecht, The Netherlands: Kluwer Academic.

17. Ball, D. L. (1991). What's all this talk about "discourse"? Arithmetic Teacher, 39(3), 44-48.
Abstract: Explores possible outcomes of using the "Professional Teaching Standards" as a set of tools to construct productive conversations about teaching. Presents a discussion taking place in the author's third grade classroom illustrating discourse in the classroom, accompanied by the author's commentary on the lesson. (MDH)

18. Barkley, C. A., & Cruz, S. (2001). Geometry through beadwork designs. Teaching Children Mathematics, 7(6), 362-367.
Abstract: Part of a special issue on mathematics and culture. A geometry lesson for fourth-grade students that focused on the beadwork designs of the Ute Native American people is described. This lesson invited students to integrate their knowledge of mathematics and the art of the Ute into the knowledge they acquired from social studies. This integration helped students to bridge the gap between school mathematics and real-world mathematics.

19. Barta, J., Abeyta, A., Gould, D., Galindo, E., Matt, G., Seamann, D., & Voggessor, G. (2001). The mathematical ecology of the Shoshoni and implications for elementary mathematics education and the young learner. Journal of American Indian Education, 40(2 ), 1-25.
Abstract: The Shoshoni are an indigenous people who traditionally inhabited parts of what is now northern Utah, central and southern Idaho, and western Wyoming for the past 14,000 years. While many facets of their historical and recent culture have been analyzed, little investigation has taken place to date concerning their use of mathematics in culturally specific ways. This manuscript is the report of a two-year study involving semi-structured interviews of Shoshoni representatives to describe the culturally specific use of mathematics in Shoshoni traditional living practices. Qualitative research methods were selected in order to gain a rich understanding of the mathematical insight and uses of mathematics for the Shoshoni. The inquiry methods and related interview questions may serve as a model to structure research investigating mathematical practices of other American Indian cultures, thus allowing for a broader understanding of indigenous people and the culturally-specific mathematical practices of each tribe. Insight gained from this research prepares the way for American Indian educators to create culturally specific mathematics curricula reflecting the local culture of those they teach. Reprinted by permission of the publisher.

20. Barton, B. (1999). Ethnomathematics: A political plaything. For the Learning of Mathematics, 19(1), 32-35.
Abstract: Describes the meanings given to the word "ethnomathematics." Discusses three important publications on ethnomathematics, the new inspiration provided by the First International Conference on Ethnomathematics, and examines the critical mathematical direction represented by Powell and Frankenstein's collection. Contains 14 references. (ASK)

21. Barton, B. (1999). Ethnomathematics and philosophy. ZDM: Zentralblatt Fur Didaktik Der Mathematik, 31(2), 54-58.
Abstract: Any concept of ethnomathematics must eventually meet philosophical debates about the nautre of mathematics. In particular neo-realist positions are anathema to the idea that mathematics is culturally based, but even modern quasi-empiricist philosophies are challenged by the fundamental relativity implied in ethnomathematical writing.
A new way of interpreting mathematical history which may allow for a truly relativist mathematics is described, and some evidence is presented to support this view. The kind of studies which would arise from this perspective on mathematics are outlined.

22. Bassanezi, R. C. (1994). Modelling as a teaching-learning strategy. For the Learning of Mathematics, 14( 2), 31-35.
Abstract: Presents examples of the use of mathematical modeling in mathematics courses in order to not lose sight of the essence of the mathematical attitude; encourage students' concern with problems that surround them; appreciate human resources; and associate mathematics with other sciences. (MKR)

23. Baturo, A. R., & Cooper, T. J. (2000). Year 6 students' idiosyncratic notions of unitising, reunitising, and regrouping decimal number places. Research report presented at the 24th Conference of the International Group for the Psychology of Mathematics Education .
Abstract: Having flexible notions of the unit (e.g., 26 ones can be thought of at 2.6 tens, 1 ten 15 ones, 260 tenths, etc.) should be a major focus of elementary mathematics education. However, often these powerful notions are relegated to computations where the major emphasis is on "getting the right answer" thus procedural knowledge rather than conceptual knowledge becomes the primary focus. This paper reports on 22 high-performing students' reunitising processes ascertained from individual interviews on tasks requiring unitising, reunitising and regrouping; errors were categorised to depict particular thinking strategies. The results show that, even for high-performing students, regrouping is a cognitively complex task. This paper analyses this complexity and draws inferences for teaching.

24. Belkhir, J. A., Jack, L. Jr., & Smith, D. B. (2000). Introduction to race, gender and class in education. Race, Gender & Class, 7(3), 6.
Abstract: This is an appeal to the readers of this journal to more closely examine intersections of race, gender and power in your writing because such materials are needed to teach future teachers and educators in general (Carl Grant et al., 2000).

25. Benezet, L. P. (1935). The Teaching of Arithmetic 1: The Story of an Experiment. Journal of the National Education Association, 24(8), 241-244.

26. Bishop, A. J. (1994). Cultural conflicts in mathematics education: Developing a research agenda. For the Learning of Mathematics, 14(2), 15-18.
Abstract: Discusses research issues deriving from different interpretations and responses to cultural conflicts in mathematics education and presents a possible research agenda. (25 references) (MKR)

27. Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht, Netherlands: Kluwer Academic Publishers.
Abstract: This book breaks new ground in Mathematics Education by taking as its focus the idea of Mathematics as a cultural product and analyzing the educational consequences of this cultural perspective. Drawing on a wide variety of sources and references, the book integrates the literature into a new conceptual schema that demonstrates and substantiates the meaning of Mathematics as cultural product. A new curriculum structure integrating enculturation into the mathematics education curriculum is introduced, as well as exploring the mathematical enculturation process. Finally, there are several important implications for mathematics teacher preparation and for the whole process of teacher education made in the final chapter. Following a preface by the author, the seven chapters include: (1) "Towards a Way of Knowing"; (2) "Environmental Activities and Mathematical Culture"; (3) "The Values of Mathematical Culture"; (4) "Mathematical Culture and the Child"; (5) "Mathematical Enculturation: The Curriculum"; (6) "Mathematical Enculturation: The Process"; and (7) "The Mathematical Enculturators." An extensive bibliography contains over 200 references. (MDH)

28. Bishop, A. J. (1990). Western mathematics: The secret weapon of cultural imperialism. Race & Class, 32( 2), 51-65.
Abstract: Mathematics, like many other school subjects, was imposed on indigenous pupils in the colonial schools. According to Bishop, mathematics continues to have the status of a culture-free phenomenon in the otherwise turbulent waters of education and imperialism. Bishop identified three levels of response to the cultural imperialism of Western mathematics: 1) increasing interest in the study of ethnomathematics, 2) creating a greater awareness of one's own culture, 3) re-examining the whole history of Western mathematics itself. Bishop concluded his article claiming the resistance to Western mathematics is growing, critical debate is informing theoretical development, and research is increasing, in particular in those situations in which cultural conflict is recognized.

29. Boaler, J. (1993). Encouraging the transfer of 'school' mathematics to the 'real world' through the integration of process and content, context and culture. Educational Studies in Mathematics, 25, 341-373.
Abstract: Considered transfer of students' (n=100) mathematical understanding across different task contexts in an integrated process-content approach using open-ended activities and a typical English content-based approach. The integrated approach facilitated transfer. (Contains 26 references.) (MKR/Author)

30. Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics more "real"? For the Learning of Mathematics, 13(2), 12-17.
Abstract: Suggests that contexts may be useful in mathematics instruction in relation to learning transfer and that the factors that determine whether a context is useful are complex. Discusses the context effect, learning in context, how well students identify with tasks taken out of an adult world, and the effects of ethnomathematics. (MDH)

31. Bockarie, A. (1993). Mathematics in the Mende culture: Its general implication for mathematics teaching. School Science and Mathematics, 93(4), 208-211.
Abstract: Mathematics that exists in the Mende culture, an African tribe in Sierra Leone, includes counting, computation, ratios, fractions, forecasting games, and mathematical applications. Presents The Mende representations of these concepts and discusses implications of their integration into mathematics teaching. (MDH)

32. Boekaerts, M. (1998). Do Culturally Rooted Self-Construals Affect Students' Conceptualization of Control Over LEarning? Educationl Psychologist, 33(2/3), 87-108.

33. Borba, M. C. (1990). Ethnomathematics and education. For the Learning of Mathematics, 10(1 ), 39-43.
Abstract: Discussed is the notion of ethnomathematics as an epistemological approach to mathematics. The relationship between ethnomathematics and mathematics education is described. Suggestions regarding mathematical pedagogy are provided. (CW)

34. Breidenbach, D., Dubinsky, E., Hawks, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23, 247-285.
Abstract: Our goal in this paper is to make two points. First, college students, even those who have taken a fair number of mathematics courses, do not have much of an understanding of the fundtion concept; and second, an epistemological theory we have been developing points to an instructional treatment, using computers, that results in substantial improvements for many students. They seem to develop a process conception of function and are able to use it to do mathematics. After an introductory section we outline, in Section 2, our theoretical epistemology in general and indicate how it applies to the function concept in particular. In Sections 3, 4, and 5 we provide specific details on this study and describe the development of the function concept that appeared to take place in the students that we are considering. In Section 6 we interpret the results and draw some conclusions.

35. Byrnes, J. P. (2003). Factors Predictive of Mathematics Achivement in White, BLack and Hispanic 12th Graders. Journal of Educational Psychology, 95(2), 316-326.

36. Carraher, D. , & Schliemann, A. D. (2002). The transfer dilemma. The Journal of the Learning Sciences, 11(1), 1-24.
Abstract: In this article we provide an overview of research on transfer, highlighting its main tenets. Then we look at interviews of two 5th-grade students learning about mathematical concepts regarding operations on positive and negative quantities. We attempt to focus on how their learning is influenced by their prior knowledge and experience. We take the position that transfer is a theory of learning and we attempt to show that it cannot provide a solid foundation for explaining such examples of learning.

37. Caston, J. J. (1994). The learning experience: Impact on measures of institutional effectiveness. Paper presented at the Sixteenth Annual Leadership 2000 Conference .
Abstract: In spring 1994, a study was conducted to compare student outcomes for instructors use of a mixed teaching repertoire (i.e., lecture, student-centered discussion, cooperative learning, and computer-assisted instruction) and those using lectures alone in social science, science/math, humanities, and business classes at Cosumnes River College, in California. Based on surveys of instructors and students and class observations, 22 matched pairs of courses were determined based on instructor technique. In addition, the ethnicity, gender, age, and English-as-a-Second-Language (ESL) status of the 812 students in the lecture-only and the 603 in the mixed-repertoire courses were analyzed to determine group outcomes. Study findings included the following: (1) attendance was generally better in lecture-based than in mixed-repertoire classes especially among 25 or older, native English speaking, white, and female groups; (2) while, students over 25, native English speakers, Asian/Pacific Islanders, Whites, and females earned higher grades in lecture-based courses, students under 25, ESL students, African-Americans, Hispanics, and males earned higher grades in classes using a mixed repertoire; (3) with respect to course completion rates, students in social science mixed-repertoire courses were significantly more likely to successfully complete than in lecture courses; and (4) while students felt they had opportunity to succeed regardless of methodology, they felt they had a greater opportunity to succeed in the lecture group. (Contains 16 references.) (KP)

38. Civil, M. (1995). Everyday mathematics, "mathematicians' mathematics," and school mathematics: Can we (should we) bring these two cultures together? Symposium: "Communities of Practice in Mathematics Classrooms: Reconciling Everyday and Mathematicians' Mathematics?" at the Annual Meeting of the American Educational Research Association Washington, D.C.: Office of Educational Research and Improvement.
Abstract: 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)

39. Cobb, P., & McClain, K. (2001). An approach for supporting teachers' learning in social context. In F. Lin, & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 207-231). the Netherlands: Kluwer Academic Publishers.
Abstract: Our purpose in this chapter is to outline a general approach to collaborating with teachers in order to support the establishment of a professional teaching community. As will become apparent, our goal is to help teachers develop instructional practices in which they induct their students into the ways of reasoning of the discipline by building systematically on their current mathematical activity. We develop the rationale for the aproach we propose by describing how our thinking about in-service teacher development has evolved over the last thirteen years or so. To this end, we first revisit work conducted in collaboration with Erna Yackel and Terry Wood between 1986 and 1992 in which we supported the development of American second- and third-grade teachers. In doing so, we tease out aspects of the approach we took that still appear viable and discuss two major lessons that we learned. In the next section of the chapter, we draw on a series of teaching experiments we have conducted over the past seven years in American elementary and middle-school classrooms both to critique our prior work and to develop three further aspects of the approach we propose. We conclude by highlighting broad features of the approach and by locating them in institutional context.

40. Cobb, P. (1996). Accounting for mathematical learning in the social context of the classroom. Proceedings of the Eighth International Congress on Mathematical Education .
Abstract: This paper focuses on the issue of accounting for students' mathematical learning as it occurs in the social context of the classroom. In the opening section of the paper, I first clarify why this is a significant issue for myself and my colleagues and develop criteria for classroom analyses that are relevant to our purposes. In the second part of the paper, I outline the interpretive framework that we currently use by presenting a sample analysis. In the final section, I reflect on this analysis to address four more general issues. These concern the contributions of the type illustrated by the sample analysis, the relationship between instructional design and classroom-based research, the role of symbols and other tools in mathematical learning, and the relation between individual students' mathematical activity and communal classroom processes.

41. Cobb, P. (1986). Contexts, goals, beliefs, and learning mathematics. For the Learning of Mathematics, 6(2), 2-9.
Abstract: Advanced is the hypothesis that students organize their beliefs about mathematics to resolve problems that are primarily social rather than mathematical in origin. The contextuality of cognition, meaning-making, and learning in interactive situations are each discussed. (MNS)

42. Cobb, P., & McClain, K. (2001). An Approach for Supporting Teachers' Learning in Social Contexts. F. L. Lin, & T. J. Cooney Making Sense of Mathematics Teacher Education (pp. 207-231). The Netherlands: Kluwer Academic.

43. Collins, B. (1992). Staff development for multicultural education in mathematics. 7th International Congress on Mathematics Education .
Abstract: A fertile area for the improvement of mathematics achievement in the United States is in staff development for multicultural education. Multicultural mathematics is best defined by what it is not; it is not ethnomathematics, nor simply Afrocentrism or Eurocentrism. Multicultural mathematics furthers the multicultural goals of the school system because it shows minority students that all social groups have contributed to the body of knowledge they learn in mathematics class. Preservice education for teachers is the best opportunity to introduce a multicultural perspective on mathematics. Multicultural mathematics education should be taught in inservice programs as well. Regardless of the depth of instruction necessary to acquaint teachers with multicultural mathematics, the important ingredient is a commitment to inclusion. Problem solving in mathematics provides an opportunity to pose problems from many cultures that highlight many social groups. National standards efforts do not always address multicultural approaches directly, but they do encourage the inclusion of all cultures. Inservice education offerings must also be locally relevant, with emphasis on the cultural groups served. (SLD)

44. Colomeda, L. (1998). A literature guide: Resources for teaching math and science to American Indian students. Tribal College Journal of American Indian Higher Education, 10(1), 18.
Abstract: Descriptions of organizations that provide resources for teaching math and science to American Indian students. Also includes a list of websites providing these resources.

45. Connoly, P., & Vilardi, T. (1989). Writing to learn mathematics and science. New York: Teachers College Press.
Abstract: The emphasis on writing in the teaching of mathematics and science can empower teachers to reach all sectors of the pupil population. The use of ordinary language can help break the cultural barriers that have prevented minorities and women from achieving well in proportionate numbers in these fields. This volume focuses on pedagogical issues of using ordinary language to teach science and mathematics. Topics addressed by the 23 collected papers include: (1) general issues; (2) writing as problem solving; (3) applications in the classroom; (4) program policies; (5) learning in context; and (6) some responses to this method. (CW)

46. Cooney, M. P., Dewar, J. M., Kenschaft, P. C., Krains, V., Latka, B., & LiSanti, B. (1990). Recruitment and Retention of Students in Undergraduate Mathematics. The College Mathematics Journal, 21(4), 294-301.

47. Cooper, J. L. (1995). Cooperative Learning and Critical Thinking. Teaching of Psychology, 22(17-9).

48. Crotty, T., & Allyn, D. (2001). Evaluating student reflections. River Falls, WI: University of Wisconsin.
Abstract: This paper traces the development of guidelines to help education instructors effectively evaluate and provide guided practice for student teachers as they reflect on their professional work. The University of Wisconsin River Falls requires student teachers to videotape their teaching experiences, then reflect on how, why, and where they meet Wisconsin learning outcomes and standards with the videotaped assignments. Students must reflect on how to change and improve their instruction and establish goals for professional development. Instructor feedback on students' reflections is an important part of the effort. Researchers reviewed and ranked five preservice teachers' videotaped teaching and reflections. This led to levels of reflection rubric, which divided reflections into high, medium, and low levels. Three students were then assisted with their reflections as they viewed their videotapes, and they engaged in a dialogue about their teaching. New insights gained by the three guided practice sessions included the need to provide instruction on videotaping, guidelines for editing and reflecting, and instructors' need to provide developmentally appropriate reflective assessments and accompanying assessments. A three-stage developmental model for reflective practitioners emerged which applies the six levels of Bloom's Taxonomy and includes the Ten Wisconsin Teaching Standards. Videotape Reflection Feedback Form (rubric for enhancing peer dialogues or faculty assessments of reflective practice) and the same rubric reduced to reflect this assignment are appended. (Contains 20 references.) (SM)

49. Cuoco, A. A. , Goldenberg, E. P., & Mark, J. (1995). Connecting geometry with the rest of mathematics. P. A. House, & A. F. Coxford (Editors), Connecting mathematics across the curriculum: NCTM 1995 yearbook (pp. 183-197). Reston, VA: NCTM.
Abstract: This article discusses how different experimental tools can be used to help high school student to understand geometry and to make connections with other areas of mathematics. Among these tools is a new breed of geometry software that allows students to visualize geometric concepts. These tools, along with a curriculum that supports a spirit of mathematical research, will allow students to increase their achievements in their mathematics classes.

50. D'Ambrosio, U. (1999). Ethnomathematics and its first international congress. ZDM: Zentralblatt Fur Didaktik Der Mathematik , 31(2), 50-53.
Abstract: The First International Congress of Ethnomathematics took place in Granada, Spain, from 2 to 5 September 1998, hosted by the University of Granada, with the support of several organizations. In this paper I make some considerations on the why's and when of ethnomathematics as an academic research field and report on the ISGEm/International Study Group on Ethnomathematics and its first international congress.

51. D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 44-48.
Abstract: Some basic issues which may lay the groundwork for a historical approach to teaching mathematics by developing the concept of ethnomathematics are presented. A historical review and relationships between history and pedagogy are discussed in detail. (MNS)

52. D'Ambrosio, U. (1996). Ethnomathematics: Where does it come from? And where does it go? Proceedings of the Eighth International Congress on Mathematical Education .
Abstract: The history and geography of human behavior allows for us to have a new look into the emergence of mathematical ideas in different cultural environments. With this background, we can develop a conceptual framework for ethnomathematics. Scenarios of the future can lead to considerations about the next steps of the ethnomathematics movement.

53. D'Ambrosio, U. (1999). In focus...mathematics, history, ethnomathematics and education: A comprehensive program. The Mathematics Educator, 9(2), 34-36.
Abstract: Discusses the nature of mathematics, the goals of education, and the political dimension of mathematics. Considers ethnomathematics, the history of mathematics, and advances in ethnomathematics. Proposes a new conception of curriculum. (ASK)

54. D'Ambrosio, U. (2001). What is ethnomathematics, and how can it help children in schools? Teaching Children Mathematics, 7(6), 308-310.
Abstract: Part of a special issue on mathematics and culture. Information on ethnomathematics and how it can assist children in schools is provided. The information relates to the definition of ethnomathematics, goals of multicultural mathematics, current mathematics curricula, and consequences of acultural mathematical perspectives.

55. Dahlberg, C. (1989). Alternative course of mathematics. The ALM project. (Report No. ED 305 242). Stockholm, Sweden: National Swedish Board of Education.
Abstract: School mathematics is governed by a powerful tradition as regards both content and methods. In the first stage of the Alternative Course of Mathematics (ALM) project, an analysis is being made of the mathematics used in the everyday life of the community. By interviewing adults and children outside school, an analysis is also being made of the way in which people handle this mathematics, which methods they employ and how, for example, they use modern aids such as the pocket calculator. Both analyses can be related to the concept of "Ethnomathematics" in the broad sense. The main concern of the ALM project is to inquire whether any of this mathematics can be introduced as an alternative in school mathematics and whether any of the methods which people use in their everyday lives or in their working lives can also be presented as a method in school mathematics. Under the ALM project, therefore, parallel to research activities, an experimental scheme is being conducted in various grades to test new methods. (Author/YP)

56. Davison, D. M., & Miller, K. W. (1998). An ethnoscience approach to curriculum issues for American Indian students. School Science and Mathematics, 98(5), 260-265.
Abstract: A course offered to teachers of Native American students focused on the development of culturally relevant activities as part of the science and math curricula. These activities were embedded in a holistic approach to the curriculum, and the informal math and science of the culture were linked with traditional school science and math.

57. Dias, A. (1999). Ethnomathematics vs. epistemological hegemony. For the Learning of Mathematics, 19(3), 23-26.
Abstract: Investigates the mathematical practices used by a home designer and builder. Points out the existence not only of diverse forms of mathematics, or ethnomathematics, but also of diverse ways of doing mathematics. Argues that these idiosyncratic ways of mathematizing, whether pertaining to individuals or to entire cultural groups, should be recognized and legitimized in mathematics classrooms. (ASK)

58. Drew, D. E. (1998). America's wasted talent: A Karplus lecture. Journal of Science Education and Technology, 7(4), 287-295.
Abstract: Millions of young people who could achieve in mathematics and science are being discouraged or prevented from studying these subjects. Access to jobs, status and power in a high-tech, information economy depends upon mastery of these fields, but erroneous beliefs about aptitude are limiting the options for young women, students of color and students from poverty. Curriculum reform efforts are exciting, much-needed improvements, but the single most important change we need is a national consciousness raising. We should hold high expectations for all students and expect virtually all of them to achieve. Outdated and false notions about which groups possess the aptitude for technical subjects should not be used as barriers to access.

59. (1999). New Brunswick, NJ: Rutgers University Press.
Abstract: Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences.
Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structure--circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems.
Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative technologies, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.

60. Eglash, R. (1998). Geometry in Mangbetu design. The Mathematics Teacher, 91(5), 376-381.
Abstract: Introduces a few examples of Mangbetu designs and examines their underlying structure. Describes Mangbetu design and analyzes its geometric features. (ASK)

61. Eglash, R.Multicultural mathematics: An ethnomathematics critique.
Abstract: This article consists mostly of excerpts from the author's article, "When math worlds collide: intention and invention in ethnomathematics." The author first defines ethnomathematics, then describes five subfields in ethnomathematics: non-western mathematics, mathematical anthropology, sociology of mathematics, vernacular mathematics, and indigenous mathematics. Eglash addresses the dangers of using ethnomathematics as part of the curriculum, as this may unintentionally perpetuate stereotypes by assigning a certain "romantic" or "primitive" meaning to these cultures. Also, the author emphasizes the importance of incorporating the cultural concepts held by students themselves--rather than broad, essentialist concepts--to the curriculum.

62. Ensign, J. (1997). Linking life experiences to classroom math. Paper presented at the Annual Meeting of the American Educational Research Association .
Abstract: 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)

63. Ernest, P. (1996). Social constructivism as a philosophy of mathematics. Proceedings of the Eighth International Congress on Mathematical Education .
Abstract: Social constructivism as a philosophy of mathematics is concerned with the genesis and warranting of mathematical knowledge. These processes take place both in the contexts of research mathematics and in the contexts of schooling, where they concern learning and assessment. A theoretical account of these processes situated in human practices will be given, based on the work of Lakatos and Wittgenstein. The resulting theory might be termed a post-modernist philosophy of mathematics, since it dethrones logic as the foundation of mathematical knowledge in favour of decentred human practices and context-bound warranting conversations. Attention will also be devoted to the relations between the philosophy of mathematics and mathematics education. The fact that developments in the philosophy of mathematics and corresponding informal conceptions have important outcomes for mathematics education is widely noted. What is less remarked is that issues of learning and assessment have significant implications, for the discipline of mathematics and for its philosophy, at least from social constructivist and fallibilist perspectives. This will be discussed, together with other relevant issues.

64. Everson, H. T. Do Metacognitive Skills and Learning Strategies Transfer Across Domains? Annual Meeting of the American Educational Research Association .

65. Everson, H. T., Tobias, S., & Laitusis, V. (1997). Do metacognitive skills and learning strategies transfer across domains? Paper presented at the Annual Meeting of the American Educational Research Association New York, NY: College Entrance Examination Board.
Abstract: Current theories of metacognition suggest that effective control of learning by either metacognitive or self-regulatory processes cannot occur without accurate monitoring of learning. Given this theoretical framework, there are questions of whether knowledge monitoring and self-regulated learning abilities are domain-specific or whether metacognitive processes, in particular knowledge monitoring ability, generalize across academic domains. This study examines that issue by exploring the correlations among measures of metacognitive knowledge, learning, and study strategies, and academic achievement across the domains of verbal ability and mathematics. Using parallel measures of knowledge monitoring in both the verbal and mathematical domains, 120 undergraduates estimated their metacognitive knowledge, reported their confidence in the accuracy of those estimates, and completed a self-report measure of learning and study strategies. Results suggest that metacognitive knowledge is generalizable across both the verbal and mathematical domains. The correlations between the two knowledge monitoring measures and students' confidence estimates were also in the expected directions. Moreover, both knowledge monitoring measures correlated with students' grade point averages. Correlations with subscales of the Learning and Study Strategies Inventory were not significant. Findings are discussed in the framework of current theory in metacognition and conceptions of strategic learning. An appendix shows multiple regression results. (Contains 1 table and 47 references.) (Author/SLD)

66. Fasheh, M. (1982). Mathematics, culture, and authority . For the Learning of Mathematics, 3(2), 2-8.
Abstract: This article deals with the interaction between mathematics instruction on the one hand and established cultural patterns of belief, thinking and behaviour on the other hand, especially in Third World countries. The article points to the importance of culture in influencing the way people see things and understand concepts, and to the importance of using cultural and societal sources and personal experiences in making the teaching of mathematics more effective and more meaningful, as well as to the ways in which mathematics can be used to deal with some drawbacks in one's own culture and society. In addition, the article points out the conflict that usually arises between existing authorities and the teaching of mathematics when the latter is taught in such a way as to enhance critical thinking, self-expression, and cultural and social awareness. The region under consideration is the West Bank of Jordan (Eastern Palestine) where I spent my school years and over fifteen years as a mathematics teacher and educator.

67. Federici, S. (Ed.). (1995). Enduring western civilization: The construction of the concept of western civilization and its "others". Westport, Connecticut: Praeger.
Abstract: What do we mean by "Western Civilization"? When did the expression originate and why? At a time when there is a widespread perception that "Western Civilization" is undergoing a historic crisis, and when postmodernism, feminist theory, afrocentrism, deconstruction, and other current philosophical schools define themselves as alternatives to, or critiques of, "Western Civilization," this book seeks to trace the development of the concept of Western Civilization and to examine the reasons for its endurance.

68. Frankenstein, M. (1989). Relearning mathematics: A different third R--radical maths. London: Free Association Books.
Abstract: Frankenstein's mathematics textbook differs a great deal from traditional mathematics texts since it includes not only mathematical content but also approaches to learning mathematics, a social and political context for learning mathematics, and numerous historical insights. The style of the book provides strong support for the idea that mathematics is a human endeavor and mathematics can be a powerful tool for all people. The mathematical topics included integers, rational numbers, numerical operations, and variables. The author "situates the teaching of mathemaics within a rationale that links schooling to the wider considerations of citizenship and social responsability."

69. Frankenstein, M., & Powell, A. B. (1994). Toward liberatory mathematics: Paulo Freire's epistemology and ethnomathematics. In P. McLaren, & C. Lankshear (Eds.), Politics of liberation: Paths from Freire . New York: Routledge.
Abstract: This chapter discusses Paulo Freire's theories about the nature of knowledge and the range of intellectual traditions that underlie the concept of ethnomathematics. The authors then argue that Freire's epistemology informs the theoretical basis of ethnomathematics. They proceed to categorize and elaborate on areas central to ethnomathematics, and conclude by indicating implications for further investigations of mathematical knowledge and its connections to cultural and political action.

70. Freire, P. (1973). Education for critical consciousness. New York: Seabury Press.
Abstract: Here for the first time in English are two major studies on Education as the Practice of Freedom and Extension or Communication, by the author of Pedagogy of the Oppressed. Education as the Practice of Freedom grows out of Freire's creative efforts in adult literacy throughout Brazil prior to the military coup of April 1, 1964, which eventually resulted in his exile. It describes the basic components of Freire's literacy method. Education in the Freire mode is the practice of liberty because it frees the educator no less than the educatees from the twin thraldom of silence and monologue. Both partners are liberated as they begin to learn, the one to know self as a being of worth and the other as capable of dialogue in spite of the strait jacket imposed by the role of educator as one who knows. Extension or Communication, written in Chile in 1968, applies the lessons of "conscientizaçăo" to rural extension. In recent years rural extension based on the U.S. model has spread through Latin America, bringing advanced techniques and products developed in agricultural schools and land-grant colleges to farmers. Freire analyzes the terms "extension" and "communication," and argues that there is a basic contradiction between the two. Genuine dialogue with peasants, he holds, is incompatible with "extending" to them technical expertise or agricultural know-hoe. Not merely a specialized tract of interest only to rural people, Extension or Communication has general significance precisely because it demystifies all "aid" or "helping' relationships. What the authors says of extension agents he might also say of social workers, city planners, welfare administrators, community organizers, political militants, and a host of others who allegedly render "services" to the poor or the powerless

71. Funkhouser, C. P., Porter, A. D., Ipina, L., & Hirstein, J. J. (2000). Indian mathematics: An ethnomathematical review. (Report No. ED 438 170).
Abstract: 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)

72. Furr, G. C. I. (2003). From "Paperless classroom" to "Deep reading": Five stages in internet pedagogy. The Michigan Virtual University.

73. Galbraith, P. (1996). Issues in assessment: A never ending story . Proceedings of the Eighth International Congress on Mathematical Education .
Abstract: This talk does not concern itself with aspects such as instrument design, or with how to make techniques or systems work better. Rather it identifies and elaborates points of debate at technical, practical and political levels that make assessment in mathematics at once an important, a stimulating, and a controversial subject.

74. Garegae-Garekwe, K. G. (1998). Bringing ethnomathematics into the classroom in a meaningful way. Paper presented at the 22nd Annual Meeting of the Canadian Mathematics Education Study Group = Groupe Canadien d'etude en didactique des mathematiques.
Abstract: This working group discussed some aspects of ethnomathematics that can be brought into the classroom, as well as the reasoning for doing so. Specific mathematical curriculum concepts that can be explored using ethnomathematics and the history of mathematics are discussed. This working group discussed whether the label of "ethnomathematics" is problematic, and what kind of ethical considerations are pertinent in bringing ethnomathematics into the classroom. There was a general concensus that there is a need to understand what is meant by ethnomathematics, and also that the way mathematics is taught in the 21st century should be different from the way it has been taught in the past.

75. Gerdes, P. (1996). On culture and mathematics education in (southern) Africa. Proceedings of the Eighth International Congress on Mathematical Education .
Abstract: This article presents evidence that supports the idea that incorporating cultural factors into mathematics education in Africa will improve math achievement in education and contribute to Africa's development in general. Examples are presented of well-known African politicians, historians, scientists, and educators who have lately stressed the importance of cultural factors in education. A short overview of the research done in Africa on culture and mathematics education, or ethnomathematics, is given.

76. Gerdes, P. (1990). On mathematical elements in the Tchokwe "Sona" tradition. For the Learning of Mathematics, 10(1), 31-34.
Abstract: This article discusses the mathematical relevance of the drawing tradition of the Tchokwe people of Angola. The study of the Tchokwe drawing tradition is interesting for historical and educational reasons. Several mathematical concepts, such as symmetry, monolinearity, and geometric algorithms, are discussed, as well as possibilities for incorporating them into educational practice. It is believed that the incorporation of this sona tradition in the curriculum, both in Africa and in other parts of the world, will contribute to the revival and valuing of the old practice of the "akwa kuta sona", and it may contribute towards the development of a more productive and more creative mathematics education. Also, an analysis of Tchokwe sona stimulates the development of new mathematical research areas.

77. Gerdes, P. (1994). Reflections on ethnomathematics. For the Learning of Mathematics, 14(2 ), 19-22.
Abstract: Discusses the ethnomathematics movement, the emergence of concepts related to ethnomathematics, ethnomathematics as a field of research that studies mathematics in its relationship to the whole of cultural and social life, and the beginning of ethnomathematical research in Mozambique. (41 references) (MKR)

78. Gerdes, P. (1998). Women, art, and geometry. Trenton, NJ: Africa World Press, Inc.
Abstract: This volume is another in the author's continuing investigation of the mathematics underlying artistic decorations that occur among the peoples of southern Africa. The specific forms are woven handbags (sipatsi) from Inhambane Province, Mozambique, spiral basketwork (titja) from Swaziland, mat weaving by Venda women from the extreme north of South Africa, string figures (buhlolo) from the Thonga in the eastern Transvaal, decorated pottery (oku-taleka) from Southwest Angola, straw broom (mafielo) among Basotho women, tattoos and body painting (nembo) among Mozambiquan people, pearl ornaments (ovilame) among the Ovimbundu women of Angola, and wall decorations produced by Sotho men and Ndebele women in South Africa. Like the earlier books, this one is very much a catalogue of illustrations, with remarkable symmetries in complicated designs. The author asks how people learn to produce the symmetric designs, how they keep the symmetries accurate, and whether they serve any purpose other than decoration. He concludes with a discussion of the Pythagorean theorem as shown in basket weaving among Ovimbundu women.

79. Gilmer, G. F. (1998). Ethnomathematics: An African American perspective on developing women in mathematics. Paper presented at The First Mathematics Education and Society Conference Centre for the Study of Mathematics Education.
Abstract: This paper was written for the NCTM publication - Changing the Faces of Mathematics: Perspective on Gender. Hence, the paper is at the intersection of research and practice. The paper also speaks directly to issues of equality, inclusivity and accountability. The author borrows from gender, ethnomathematics and social context research to guide practice in mathematics teaching and learning. Specifically, the paper focuses on three principles of feminist pedagogy useful for developing mathematical power in all students but especially women students. In addition, the paper presents strategies found to be effective for discerning mathematical ideas in ones own surroundings. Many strategies presented stem from research methodologies of ethnomathematicians. These methods expand and extend ones vision of what mathematics is , who creates it and in what kind of environment mathematical thinking flourishes for women in general and African American women in particular.

80. Gordon, M. (1978). Conflict and liberation: Personal aspects of the mathematics experience. Curriculum Inquiry, 8(3), 251-271.
Abstract: For the mathematics experience to be liberating, the curriculum must share how and why mathematical knowledge is developed, with special emphasis on its grounding in belief, intuition and subjectivity, and facilitate our understanding of the world in which we live and create and the beliefs we act upon. (Author)

81. Greene, E. (2000). Good-bye Pythagoras? The Chronicle of Higher Education, A16-A18.
Abstract: Some college classes and degree programs for future teachers are using a new method of mathematics instruction called ethnomathematics. This method employs a cultural perspective and embraces non-European mathematical methods. The history of the ethnomathematics movement, ethnomathematics instruction, and critics' fears about the use of this method of mathematics instruction are discussed.

82. Grow-Maienza, J., Hahn, D.-D., & Joo, C.-A. (2001). Mathematics instruction in Korean primary schools: Structures, processes, and a linguistic analysis of questioning. Journal of Educational Psychology, 93(2), 363-375.
Abstract: Reports results of a collaborative study of mathematics instruction in 1st and 5th grade students in Korea. Lessons consisted of sequences of highly organized, systematic patterns of instruction dominated by teacher questions that included higher level procedural and conceptual questions. Observations have implications for educators interested in why Asian students perform so well on mathematical tests. (BF)

83. Hadden, C. (2000). The Ironies of Madatory Placement. Community College Journal of Research and Practice, 24( 10), 823-839.

84. Henderson, R. W., & Landesman, E. M. (1992). Mathematics and middle school students of Mexican descent: The effects of thematically integrated instruction. Santa Cruz, CA and Washington, D.C.: National Center for Research on Cultural Diversity and Second Language Learning.
Abstract: This paper reports the effects of thematically integrated mathematics instruction on achievement, attitudes, and motivation in mathematics among middle school students of Mexican descent. A school-university collaborative effort led to the development and testing of a thematic approach undertaken as a means of contextualizing instruction for students considered to be at risk for school failure. Instruction relied heavily on small collaborative learning groups and on hands-on activities designed to help students make real-world sense of mathematical concepts. As hypothesized, experimental and control students made equivalent gains in computational skills, but experimental students (who received thematic instruction) surpassed controls in achievement on mathematical concepts and applications. The two programs did not have a differential effect on students' attitudes toward mathematics or self-perceptions of motivation in mathematics, but motivational variables did predict achievement outcomes for both groups. Issues related to the opportunity to learn the full range of mathematics content of the curriculum within a thematic approach are examined. (Contains over 50 references.) (Author)

85. Hershkowitz, R., & Schwarz, B. B. (1999). The emergent perspective in rich environment: Some roles of tools and activities in the construction of sociomathematical norms. Educational Studies in Mathematics, 39(1-3), 149-166.
Abstract: The emergent perspective (Yackel and Cobb, 1996) is a powerful theory for describing cognitive development within classrooms. Yackel and Cobb have shown that the formation of social and sociomathematical norms, and opportunities for learning are intertwined. The present study is an attempt to extend the range of application of the emergent perspective to middle high school classrooms. The learning environments we consider are rich in the sense that (i) th tasks in which students are engaged are open-ended problem-situations (ii) the activities around the tasks are multiphased, consisting of small group collaboration on problem solving, reporting and reflection in a classroom forum with the teacher (iii) the tools used are multi-representational software. We identify here some practices rooted in such rich environments from which several sociomathematical norms stemmed. The present study shows that socio-mathematical norms do not rise from verbal interactions only, but also from computer manipulations as communicative non-verbal actions.

86. Hill, S. (1964). Cultural differences in mathematical concept learning. American Anthropologist Special Issue: Transcultural Studies in Cognition, 201-223.
Abstract: This article examined the acquisition of two mathematical concepts, identity of sets and identity of ordered sets, by young children in two different cultures. Data from a concept formation experiment performed with children in California was compared to data from a similar experiment in Ghana. The learning model used was an all-or-nothing conditioning model. Results support the hypothesis of differing "natural" concepts, or concepts preferred at the outset of the experiment. Although some cultural differences were apparent, results showed that this learning model seemed to be a good approximation to actual response behavior from children in both cultures.

87. House, P. A. , & Coxford, A. E. (1995). Connecting mathematics across the curriculum. Reston, VA: The National Council of Teachers of Mathematics, Inc.
Abstract: Connecting disciplines within mathematics to other subjects of the curriculum, and to the everyday world is an important goal of the NCTM Standards. This yearbook illustrates these connections and is designed to help classroom teachers, teacher educators, supervisors, and curriculum developers. The 26 papers in the collection are organized into five parts. Part One examines general issues and various perspectives as they relate to the development and use of mathematics connections. Part Two focuses on connections within mathematics itself. Parts Three, Four and Five show how to connect mathematics across the curriculum of the elementary, middle, and high school years, respectively.

88. Huang, G., Taddese, N., Walter, E., & Peng, S. S. (2000). (Report No. NCES 2000-601). Washington, DC: National Center for Education Statistics.

89. Ironsmith, M., Marva, J., Harju, B., & Eppler, M. (2000). Motivation and Performance in College Students Enrolled in Self-Paces Versus Lecture-Format Remedial Mathematics Courses. Journal of Instructional Psychology, 30(4), 276-284.

90. Iseke-Barnes, J. M. (2000). Ethnomathematics and language in decolonizing mathematics. Race, Gender & Class, 7(3), 133-149.
Abstract: Examines mathematics and mathematics education drawing on antiracist and critical race theorizing to discuss ethnomathematics, languages, and mathematics. Focuses attention on mathematics as dominant and privileged discourses that are entwined with colonialism. Discusses decolonizing mathematics through ethnomathematics. (SLD)

91. Joseph, G. G. (1991). The crest of the peacock: Non-European roots of mathematics. London : Penguin Books.
Abstract: From the Ishango Bone of central Africa and the Inca quipu of South America to the dawn of modern mathematics, The Crest of the Peacock makes it clear that human beings everywhere have been capable of advanced and innovative mathematical thinking. George Gheverghese Joseph takes us on a breathtaking multicultural tour of the roots and shoots of non-European mathematics. He shows us the deep influence the Egyptians and Babylonians had on the Greeks; the Arabs' major creative contributions; and the astounding range of successes of the great civilizations of India and China. This challenging and erudite book questions familiar assumptions and enlarges our sense of what we mean by mathematics.

92. Joseph, G. G. (1987). Foundations of Eurocentrism in mathematics. Race & Class, 28(3 ), 13-28.
Abstract: In this article, Joseph suggests that "there exists a widespread Eurocentric bias in the production, dissemination and evaluation of scientific knowledge." He claims that this Eurocentric approach served as a "comforting rationale for an imperialist/racist ideology of dominance" and has remained strong despite evidence that there was significant mathematical development in Mesopotamia, Egypt, China, pre-Columbian America, India, Arabia, and many other countries. Joseph urges the "countering of Eurocentrism in the classroom." His concluding paragraph appears to be a strong statement of support for Ethnomathematics in the classroom.

93. Joseph, G. G. (1995). Mathematics and Eurocentrism . In S. Federici (Ed.), Enduring western civilization: The construction of the concept of western civilization and its "others". Westport, Connecticut: Praeger.
Abstract: This article discusses the ethnocentric bias that exists in the British education system. Although there is wide agreement among many professionals that this is a problem, the efforts to create a more culturally balanced curriculum has been met with some resistance. Some politicians and academics believe that an important goal of the education system is to instill a greater awareness of British culture and history. It is feared that this focus on one cultural tradition may "disempower" students of different ethnic backgrounds. The racism inherent in mathematical theory is discussed; other cultures have contributed to the mathematics of today without receiving due credit. The article concludes by outlining the objectives of multicultural/antiracist mathematics.

94. Juhler, S. M. (1998). The effect of optional retesting on college students' achievement in an individualized algebra course. The Journal of Experimental Education, 66(2), 125-137.

95. Katz, V. J. (1994). Ethnomathematics in the classroom. For the Learning of Mathematics, 14(2), 26-30.
Abstract: Discusses important mathematical ideas taken from combinatorics, arithmetic, and geometry which are considered in the context of their development in various societies around the globe, including Hebrew, Islamic, Italian, Mayan, German, and Anasazi work. (11 references) (MKR)

96. Kawagley, O. (1990). Yup'ik ways of knowing. Canadian Journal of Native Education, 17(2 ), 5-17.
Abstract: Explores traditional Yupik means of gaining knowledge through a blending of pragmatic, inductive, and spiritual methods. Proposes teaching mathematics and science to Native youth in a synergistic manner by capitalizing on Native knowledge, skills, and spiritual relationship to nature, then relating these to the Western perspective. Contains 14 references. (SV)

97. Kensinger, K. M. (1991). A body of knowledge, or, the body knows. Expedition, 33(3), 37-45.
Abstract: In this article, the author discusses the beliefs of the Cashinahua people of Eastern Peru in regard to the origin of knowledge. The Cashinahua believe that knowledge is contained in the body. Knowledge is gained through bodily experiences and expresses itself through bodily activity.

98. Kerka, S. (1995). Not just a number: Critical numeracy for adults. (Report No. EDO-CE-95-163). Columbus, Ohio: ERIC Clearinghouse on Adult, Career, and Vocational Education.
Abstract: Emerging perspectives on numeracy and their social, cultural, and political implications provide a context for new ways of thinking about adult numeracy instruction. Beyond daily living skills, numeracy is now being defined as knowledge that empowers citizens for life in their particular society. Thus, numeracy has economic, social, and political consequences for individuals, organizations, and society. Despite the myths surrounding math and numeracy, the realities are as follows: numeracy is culturally based and socially constructed; math reflects a particular way of thinking; numeracy reflects cultural values; numeracy is not just about numbers; math evolves and changes; numeracy is about procedural, practical knowledge; and numeracy involves different ways of solving problems. This perspective of numeracy and math suggests that numeracy instruction should be based on the belief that everyone can do math and everyone uses numeracy practices that may go unrecognized. Literacy and numeracy should be linked and contextualized. Familiar contexts may make math more accessible for those who have been alienated from it. Contextualized math can help learners recognize the math characteristics of everyday situations and can help learners with different ways of thinking. Teaching from the perspective of adult education as a tool for social justice, instructors can change the system in which math serves as a barrier and equip people with knowledge and tools to examine and criticize the economic, political, and social realities of their lives. (Contains 11 references.) (YLB)