Applying ethnomodelling to explore glocal mathematical knowledge systems
Tipo de documento
Autores
Lista de autores
Rosa, Milton y Orey, Daniel Clark
Resumen
Background: ethnomodelling methods examine how members of distinct cultural groups have come to develop local mathematical knowledge. However, what may indeed be less evident is how mathematical thinking can be part of the way in which researchers and educators attempt to make sense of the underlying cultural frameworks within which mathematical ideas, procedures, and practices are embedded. Objectives: the main objective of this theoretical article is to present arguments that link mathematics and culture in order to develop an effective understanding of the development of dialogical mathematical knowledge. Design: the theoretical and methodological concepts of this qualitative study are supported by the assumptions of ethnomodelling that adds an important cultural perspective to the modelling process through the development of an extensive literature review on this topic. Results: we present arguments to show that the linking of mathematics and culture is appropriate and necessary for an effective understanding of the development of dialogical mathematical knowledge, which aims at providing a holistic understanding of human knowledge. This means that cognition is a process that is not only embodied and situated, as well as distributed because the members of distinct cultural groups create, process, accumulate, and diffuse mathematical information conjointly. Conclusions: we discuss the role of ethnomodelling in order to develop an understanding the connection between ethnomathematics and modelling. In this context, we present concepts related to the use of both local (emic), global (etic) approaches by applying the glocal (dialogical) approach found in ethnomodelling research.
Fecha
2021
Tipo de fecha
Estado publicación
Términos clave
Etnomatemática | Modelización | Práctica del profesor | Teórica
Enfoque
Nivel educativo
Educación primaria, escuela elemental (6 a 12 años) | Educación secundaria básica (12 a 16 años)
Idioma
Revisado por pares
Formato del archivo
Volumen
23
Número
1
Rango páginas (artículo)
199-232
ISSN
21787727
Referencias
Adolph, K. E., & Berger, S. E. (2006). Motor development. In: D. Kuhn, R. S. Siegler, W. Damon, & R. M. Lerner (Eds.). Handbook of child psychology: cognition, perception, and language (pp. 161–213). John Wiley & Sons. Agar, M. (2005). Agents in living color: Towards emic agent-based models. Journal of Artificial Societies and Social Simulation, 8(1). http://jasss.soc.surrey.ac.uk/8/1/4.html. Anderson, M. L. (2003). Embodied cognition: a field guide. Artificial Intelligence, 149, 91-130. Ascher, M. (2002). Mathematics elsewhere: an exploration of ideas across cultures. Princeton University Press. Babbitt, B., Lyles, D., & Eglash, R. (2012). From ethnomathematics to ethnocomputing: Indigenous algorithms in traditional context and contemporary simulation. In S. Mukhopadhyay & W. M. Roth (Eds.), Alternative forms of knowing in mathematics: Celebrations of diversity of mathematical practices (pp. 205-220). Sense Publishers. Berry, J. W. (1969). On cross-cultural comparability. International Journal of Psychology, 4, 119-128. Berry, J. W. (1999). Emics and etics: a symbiotic conception. Culture & Psychology, 5, 165-171. Bishop, A. (1988). Mathematics education in its cultural context. Educational Studies in Mathematics, 19, 179-191. Bishop, A. (1991). Mathematical enculturation: a cultural perspective on mathematics education. Kluwer. Bishop, A. I.; Hart, K.; Lerman, S., & Nume, T. (1993). Significant influences on children’s learning of mathematics: influences from society, science and technology education. UNESCO Document series, 47, 125. Brown, S. I., Cooney, T. J., & Jones, D. (1990). Mathematics teacher education. In W. R. Houston (Ed.), Handbook of research on teacher education (pp. 639-656). Macmillan. Cortes, D. P. O., & Orey D. C. (2020). Connecting ethnomathematics and modelling: a mixed methods study to understand the dialogic approach of ethnomodelling. REVEMOP, 2(1), 1-25. Craig, E. (1998). Routledge encyclopedia of philosophy: questions to sociobiology. Volume 8. Routledge. Cresswell, J. W., & Plano Clark, V. L. (2007). Designing and conducting mixed-methods research. Sage. D’Ambrosio, U. (1985). Ethnomathematics and its place in history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 4448. D’Ambrosio. U. (2006). The program ethnomathematics and the challenges of globalization. Circumscribere: International Journal for the History of Science, 1, 74-82. D’Ambrosio, U. (2011). Nonkilling mathematics. In: PIM, J. E. (Eds.), Engineering nonkilling: scientific responsibility and the advancement of killing-free societies (pp. 121-148). Center for Global Nonkilling. Dossey, J. A. (1992). The nature of mathematics: its role and its influence. In D.A Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning. Macmillan. Eglash, R. (1997). When math worlds collide: intention and invention in ethnomathematics. Science, Technology and Human Values, 22(1), 79-97. Eglash, R., Bennett, A., O’Donnell, C., Jennings, S., & Cintorino, M. (2006). Culturally situated designed tools: ethnocomputing from field site to classroom. American Anthropologist, 108(2), 347-362. Ernest, P. (1998). Social constructivism as a philosophy of mathematics. State University of New York Press. Gallagher, S. (2007). Simulation trouble. Social Neuroscience, 2, 1-13. Geertz, C. (1973). Thick description: toward an interpretative theory of culture. In C. Geertz (Ed.), The Interpretation of culture: Selected essays (pp. 3-30). Basic Books. Gibbs Jr., R. W. (2006). Embodiment and cognitive science. Cambridge University Press. Goldman, A. (1988). Strong and weak justification. Philosophical Perspectives, 2, 51-69. Greene, J. C., & Caracelli. (2003). Making paradigmatic sense of mixed methods practice. In: Tashakkori, A., & C. Teddlie (Eds.). Handbook of mixed methods in social and behavioral research. Sage. Gudykunst, W. B. (1997). Cultural variability in communication. Communication Research, 24(4), 327-348. Headland, T. N., Pike, K. L., & Marvin Harris (1990). Emics and etics: the insider/outsider debate. Sage. Helfrich, H. (1999). Beyond the dilemma of cross-cultural psychology: resolving the tension between etic and emic approaches. Culture & Psychology, 5(2), 131–153. Hofstede, G. (1997). Cultures and organizations: software of the mind. McGraw Hill. Johnson, M. (1992). Lore: capturing traditional environmental knowledge. Dene Cultural Institute and International Development Research Center. Joseph, G. G. (2000). The crest of the peacock: Non-European roots of mathematics. Penguin, 2000. Kline, M. (1953). Mathematics in Western culture. Oxford University Press. Lett, J. (1990). Emics and etics: notes on the epistemology of anthropology. In: Headland, T. N., & Pike, K. L. (Eds.). Emics and etics: the insider/outsider debate. Frontiers of anthropology. Volume 7. Sage. Lett, J. (1996). Emic-etic distinctions. In: Levinson, D.; Ember, M. (Eds.). Encyclopedia of cultural anthropology (pp. 383-383). Henry Holt. Li, J., & Karakowsky, L. (2002). Cultural malleability in an East Asian context- an illustration of the relationship between government policy, national culture, and firm behavior. Administration and Society, 34(2), 176-201. Lindblom, J. (2007). Minding the body: interacting socially through embodied action. Doctorate dissertation. Department of Computer and Information Science. Institute of Technology. Linköping University, Sweden. Lonner, W. L., & Berry, J. W. (1986). Field methods in cross-cultural research. Sage. Lovelace, G. (1984). Cultural beliefs and the management of agroecosystems. In Rambo, T., & Sajise, P. E. (Eds.). An introduction to human ecology research on agricultural systems in South East Asia (pp. 194-205). East–West Centre. Luna, D. (2001). An integrative framework for cross-cultural consumer behavior. International Marketing Review, 18(1), 45-69. McCracken, G. (1988). Culture and consumption: new approaches to the symbolic character of consumer goods and activities. Indiana University Press. Matarić, M. J. (2001) Learning in behaviour-based multi-robot systems: policies, models, and other agents. Cognitive Systems Research, 2, 8193. McNeil, J. D. (1983). Curriculum: comprehensive introduction. Little, Brown. Morris, M. W., Leung, K., Ames, D., & Lickel, B. (1999). Views from inside and outside: integrating emic and etic insights about culture and justice judgment. Academy of Management Review, 24(4), 781-796. Nasir, N. S., & Cobb, P. (2007). Equity in students’ access to significant mathematical ideas. Teachers College Press. Orey, D. C. (2000). The ethnomathematics of the Sioux tipi and cone. In Selin, H. (Ed.). Mathematics across culture: the history of nonwestern mathematics (pp. 239-252). Kluwer. Pike, K. L. (1954). Emic and etic standpoints for the description of behavior. Summer Institute of Linguistics. Pollak, R., & Watkins, S. (1993). Cultural and economic approaches to fertility: proper marriage or mésalliance? Population and Development Review, 19, p. 467-496. Read, D. W. (2004). Mathematical modelling issues in analytical representations of human societies. Cybernetics and Systems: An International Journal, 35(2-3), 163-172. Rosa, M. (2010). A mixed-methods study to understand the perceptions of high school leader about English language learners (ELL): the case of mathematics. Doctorate dissertation. College of Education. Sacramento, CA: California State University, Sacramento. Rosa, M., & Orey, D. C. (2007). Cultural assertions and challenges towards pedagogical action of an ethnomathematics program. For the Learning of Mathematics, 27(1), 10-16. Rosa, M., & Orey, D. C. (2008). Ethnomathematics and cultural representations: teaching in highly diverse contexts. Acta Scientia, 10(1), 27-46. Rosa, M., & Orey, D. C. (2010). Ethnomodelling: an ethnomathematical holistic tool. Academic Exchange Quarterly, 3, 14-23. Rosa, M., & Orey, D. C. (2011). Ethnomathematics: the cultural aspects of mathematics. Revista Latinoamericana de Etnomatemática, 4(2), 3254. Rosa, M., & Orey, D. C. (2012). An ethnomathematical study of the symmetrical freedom quilts. Symmetry Culture and Science, 23, 1, 191-220. Rosa, M., & Orey, D. C. (2013a). Ethnomodelling as a research lens on ethnomathematics and modelling. In: G. A. Stillman; J. Brown. (Orgs.). Teaching mathematical modelling: Connecting to research and practice - International perspectives on the teaching and learning of mathematical modelling (pp. 117-127). Springer Science+Business Media. Rosa, M., & Orey, D. C. (2013b). Ethnomodelling as a methodology for ethnomathematics. In: G. A. Stillman; J. Brown (Orgs.). Teaching mathematical modelling: Connecting to research and practice - International perspectives on the teaching and learning of mathematical modelling (pp. 77-88). Springer Science+Business Media. Rosa, M., & Orey, D.C. (2015). A trivium curriculum for mathematics based on literacy, matheracy, and technoracy: an ethnomathematics perspective. ZDM Mathematics Education, 47(4), 587-598. Rosa, M., & Orey, D. C. (2016). Humanizing mathematics through ethnomodelling. Journal of Humanistic Mathematics, 6(3), 3-22. Rosa, M., & Orey, D. C. (2017). Ethnomodelling as the mathematization of cultural practices. In: Stillman, G. A., Blum, W.; Kaiser, G. (Eds.). Mathematical modelling and applications: crossing and researching boundaries in mathematics education (pp. 153-162). Springer Nature. Rosa, M., & Orey, D. C. (2018). Reflecting on glocalization in the contexts of local and global approaches through ethnomodelling. Educação Matemática Pesquisa, 20(2), 171-201 Rosa, M., & Orey, D. C. (2019). Ethnomodelling as the translation of diverse cultural mathematical practices. In: B. Sriraman, B. (Ed.), Handbook of the Mathematics of the Arts and Sciences (pp. 1-29). Springer Nature. Shuell, T. J. (2001). Teaching and Learning in the Classroom. International Encyclopedia of the Social & Behavioral Sciences, 15468-15472. Sue, D. W., & Sue, D. (2003). Counseling the culturally diverse: theory and practice. John Wiley & Sons. Ting-Toomey, S., & Chung, L. C. (2005). Understanding intercultural communication. Roxbury. Wilson, M. (2002). Six views on embodied cognition. Psychonomic Bulletin & Review, 9(4), 625-636.