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Alaska Native Indigenous knowledge: opportunities for learning mathematics

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Notes

  1. Dora Andrew-Ihrke is an adjunct faculty/consultant to the Math in Cultural Context program at the University of Alaska Fairbanks, and a retired teacher and bilingual co-ordinator.

  2. For a full account of the underpinnings of the present work, see Transforming the Culture of Schools: Yup’ik Eskimo Examples (Lipka et al. 1998).

  3. Subsistence activities used in MCC supplemental curriculum include picking berries, egging (gathering bird eggs), building a fish rack and smokehouse, kayak design and making border patterns for parka hoods and hemlines. Details of these models and a description of mathematical concepts incorporated can be found at http://www.uaf.edu/mcc/modules/.

  4. For an in-depth description see Lipka et al. (2011).

References

  • Andrich, D. (1988). Rasch models for measurement. Newbury Park: Sage Publications.

    Google Scholar 

  • Beaulieu, D. L. (2000). Comprehensive reform and American Indian education. Journal of American Indian Education 39 (Special Issue 3).

  • Bond, T. G., & Fox, C. M. (2007). Applying the Rasch model: Fundamental measurement in the human sciences (2nd ed.). Mahwah: Erlbaum.

    Google Scholar 

  • Brayboy, B. M. J., & Castagno, A. (2008). How might Native science inform “informal science learning”? Cultural Studies of Science Education, 3, 731–750.

    Article  Google Scholar 

  • Brenner, M. E. (1998). Adding cognition to the formula for culturally relevant instruction in mathematics. Anthropology and Education Quarterly, 29, 214–244.

    Article  Google Scholar 

  • Callingham, R., & Watson, J. (2004). A developmental scale of mental computation with part-whole numbers. Mathematics Education Research Journal, 16, 69–86.

    Article  Google Scholar 

  • Cole, M., & Scribner, S. (1974). Culture and thought; A psychological introduction. New York: Wiley and Sons.

    Google Scholar 

  • Cole, M., Gay, J., Glick, J., & Sharp, D. W. (1971). The cultural context of learning and thinking: An exploration in experimental anthropology. New York: Basic Books.

    Google Scholar 

  • Confrey, J., Maloney, A., Nguyen, K., Mojica, G., & Myers, M. (2009). Equipartitioning/splitting as a foundation of rational number reasoning using learning trajectories. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceeding of the 33rd annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 345–352). Thessaloniki: PME.

    Google Scholar 

  • Dalton, S. S., & Tharp, R. G. (2002). Standards for pedagogy: Research, theory and practice. In G. Wells & G. Claxton (Eds.), Learning for life in the 21st century: Sociocultural perspectives on the future of education (pp. 181–194). Oxford: Blackwell.

    Chapter  Google Scholar 

  • Demmert, W. G., & Towner, J. C. (2003). A review of the research literature on the influences of culturally based education on the academic performance of native american students. Portland: Northwest Regional Educational Laboratory.

    Google Scholar 

  • Executive Order No. 13336, 69FR 25297. (May 5, 2004). Retrieved 01 March 2011, from http://www.archives.gov/federal-register/executive-orders/2004.html

  • Gonzalez, N., Andrade, R., Civil, M., & Moll, L. (2001). Bridging funds of distributed knowledge: creating zones of practices in mathematics. Journal of Education for Students Placed at Risk, 6, 115–132.

    Article  Google Scholar 

  • Greenfield, P. M. (1997). You can’t take it with you: Why ability assessments don’t cross cultures. [Special issue: intelligence and lifelong learning]. American Psychologist, 52, 1115–1124.

    Article  Google Scholar 

  • Grigorenko, E. L., Meier, E., Lipka, J., Mohatt, G. V., Yanez, E., & Sternberg, R. (2004). The relationship between academic and practical intelligence: a case study of the tacit knowledge of native American Yup’ik people in Alaska. Academic and Practical Intelligence, 14, 183–207.

    Google Scholar 

  • Heath, S. B. (1983). Ways with words: Language, life and work in communities and classrooms. Cambridge: Cambridge University Press.

    Google Scholar 

  • Kisker, E., Lipka, J., Adams, B. L., Rickard, A., Andrew-Ihrke, D., Yanez, E. E., et al. (2012). The potential of a culturally-based supplemental math curriculum to reduce the math performance gap between Alaska Native and other students. Journal for Research in Mathematics Education, 43, 75–113.

    Article  Google Scholar 

  • Lipka, J., & Adams, B. (2004). Culturally based math education as a way to improve Alaska Native students' math performance (working paper no. 20). Athens: Appalachian Center for Learning, Assessment, and Instruction in Mathematics.

  • Lipka, J., Mohatt, G., & the Ciulistet Group. (1998). Transforming the Culture of Schools: Yup’ik Eskimo Examples. Mahway: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lipka, J., Yanez, E., Andrew-Ihrke, D., & Adam, S. (2009). A two-way process for developing effective culturally based math: Examples from math in a cultural context. In B. Greer, S. Mukhopadhyay, A. B. Powell, & S. Nelson-Barber (Eds.), Culturally responsive mathematics education (pp. 257–280). New York: Routledge.

    Google Scholar 

  • Lipka, J., Andrew-Ihrke, D., & Yanez, E. E. (2011). Yup’ik Cosmology to school mathematics: the power of symmetry and proportional measuring. Interchange, 42, 157–183.

    Article  Google Scholar 

  • Meriam, L., Brown, R. A., Cloud, H. R., & Dale, E. E. (1928). The problem of Indian administration. Baltimore: Johns Hopkins.

    Google Scholar 

  • Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. The Journal of Mathematical Behavior, 22, 335–368.

    Article  Google Scholar 

  • Moje, E. B., Ciechanowski, K., Kramer, K., Ellis, L., Carrillo, R., & Collazo, T. (2004). Working toward third space in content area literacy: an examination of everyday funds of knowledge and discourse. Reading Research Quarterly, 39, 38–70.

    Article  Google Scholar 

  • Nasir, N. S., Hand, V., & Taylor, E. (2008). Culture and mathematics in school: boundaries between “ cultural” and “domain” knowledge. Review of Research in Education, 32, 187–240.

    Article  Google Scholar 

  • No Child Left Behind (NCLB) Act of 2001, Pub. L. No. 107-110, § 115, stat. 1425. (2002).

  • Pendergrast, S., Lipka, J., Watt, D. L., Gilliland, K., & Sharp, N. (2007). Patterns and parkas: Investigating geometric principles, shapes, patterns, and measurement. Calgary: Detselig Enterprises Ltd.

    Google Scholar 

  • Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests. Chicago: The University of Chicago Press.

    Google Scholar 

  • RUMM Laboratory. (2004). Interpreting RUMM2020: Part 1 dichotomous data [software manual].

  • Siemon, D., Izard, J., Breed, M., & Virgona, J. (2006). The derivation of a learning assessment framework for multiplicative thinking. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceeding of the 30th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 113–120). Prague: PME.

    Google Scholar 

  • Sternberg, R. J. (2004). Culture and intelligence. American Psychologist, 59, 325–338.

    Article  Google Scholar 

  • Sternberg, R. J., & Grigorenko, E. L. (2008). Ability testing across cultures. In L. A. Suzuki & J. G. Ponterotto (Eds.), Handbook of multicultural assessment: Clinical, psychological, and educational applications (3rd ed., pp. 449–470). San Francisco: Wiley.

    Google Scholar 

  • Sternberg, R. J., Lipka, J., Newman, T., Wildfeuer, S., & Grigorenko, E. L. (2006). Triarchically-based instruction and assessment of sixth-grade mathematics in a Yup’ik cultural setting in Alaska. Gifted and Talented International, 21, 6–19.

    Article  Google Scholar 

  • Wong, M. (2009). Assessing students’ knowledge and conceptual understanding of fraction equivalence. Unpublished doctoral thesis, University of Sydney, NSW.

  • Wong, M. (2010). Equivalent fractions: Developing a pathway of students’ acquisition of knowledge and understanding. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education. Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia (pp. 673–680). Fremantle: MERGA.

    Google Scholar 

  • Wright, B. D., & Stone, M. H. (1979). Best test design. Chcago: MESA Press.

    Google Scholar 

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Acknowledgments

This research was conducted, in part, with the financial support provided by the University of Sydney, Faculty of Education and Social Work, Alexander Mackie Travel Fellowship. In addition, this article was partially supported by a grant from the National Science Foundation Award#ARC-1048301, Indigenous Ways of Doing, Knowing, and the Underlying Mathematics: Exploratory Workshop and from the U.S. Department of Education, Institute of Education Sciences, Award #R305A070218, Determining the Potential Efficacy of 6th Grade Math Modules. However, any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or the U.S. Department of Education.

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Lipka, J., Wong, M. & Andrew-Ihrke, D. Alaska Native Indigenous knowledge: opportunities for learning mathematics. Math Ed Res J 25, 129–150 (2013). https://doi.org/10.1007/s13394-012-0061-4

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