Why indigenous languages matter for mathematics education: a case study of Ichishkíin


This article describes the initial work and next steps for the development of a mathematics curriculum in Ichishkíin, an Indigenous Yakama language. Framed by the Ichishkíin concept of pinak’inut’áwaas (mirror/window), our work seeks to answer the following questions: How are mathematical concepts represented in Yakama culture, and how is Yakama culture reflected in mathematical concepts? How can we respectfully and reflectively craft new Ichishkíin words to express mathematical concepts not reflected in Yakama culture? This is decolonizing work, and joins a growing body of Culturally Sustaining and Culturally Reviving Pedagogies, which center teaching and learning on the lived experiences of students while critiquing culture for the ways it both sustains and diminishes. Given the dominant nature of mathematical culture, a key tenet of our project is privileging Yakama culture and the development of Ichishkíin language. We discuss the values and respect that are foundational to our ongoing collaboration to craft curriculum.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6


  1. 1.

    The Yakama Nation changed the spelling of the Tribe’s name in 1993 from “Yakima” to “Yakama” to align with the spelling in the 1855 Treaty with the USA. In our project, we focus on the Yakama dialect of Ichishkíin. In the US context, Indigenous peoples often refer to themselves as “Indian” or “Tribal.” For example, our Yakama Tribal Elder research collaborator would rarely refer to herself as “Indigenous,” and we keep the language intact to reflect the usage of our Elder collaborator.

  2. 2.

    For an extended discussion of Ichishkíin ordinal and cardinal number systems, see Jansen (2010).


  1. Archibald, J. A. (2008). Indigenous storywork: Educating the heart, mind, body, and spirit. Vancouver: UBC press.

    Google Scholar 

  2. Archibald, J. A., & Parent, A. N. (2019). Hands back, hands forward for indigenous storywork as methodology. In S. Windchief & T. San Pedro (Eds.), Applying indigenous research methods: Storying with peoples and communities (pp. 3–20). New York: Routledge.

    Google Scholar 

  3. Askew, & Venkat. (2017). “I hate maths”: Changing primary school teachers’ relationships with mathematics. In U. X. Eligio (Ed.), Understanding emotions in mathematical thinking and learning (pp. 340–355). San Diego: Academic Press.

    Google Scholar 

  4. Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. https://amte.net/standards

  5. Barton, B. (2007). The language of mathematics: Telling mathematical tales (Vol. 44). Springer Science & Business Media.

  6. Beavert, V. R. (2017). The gift of knowledge/Ttnuwit Atawish Nch’inch’imamí: Reflections on Sahaptin ways. Seattle: University of Washington Press.

  7. Beavert, V., & Hargus, S. (2009). Ichishkíin Sínwit: Yakama/Yakima Sahaptin dictionary. Seattle: University of Washington Press.

    Google Scholar 

  8. Bishop, A. J. (1988). Mathematics education in its cultural context. Educational Studies in Mathematics, 19(2), 179–191.

    Google Scholar 

  9. Bishop, R., & Berryman, M. (2006). Culture speaks: Cultural relationships and classroom learning. Huia Publishers.

  10. Brayboy, B. M. J. (2005). Toward a tribal critical race theory in education. The Urban Review, 37(5), 425–446.

  11. Brenzinger, M., Yamamoto, A., Aikawa, N., Koundiouba, D., Minasyan, A., Dwyer, A., ... & Smeets, R. (2003). Language vitality and endangerment. Paris: UNESCO Intangible Cultural Unit, Safeguarding Endangered Languages. http://www.unesco.org/culture/ich/doc/src/00120-en.pdf. Accessed 1 July 2010.

  12. Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2018). Reconceptualizing the roles of researchers and teachers to bring research closer to teaching. Journal for Research in Mathematics Education, 49(5), 514–520.

    Google Scholar 

  13. Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119–142.

    Google Scholar 

  14. Croft, S. J., Roberts, M. A., & Stenhouse, V. L. (2015). The perfect storm of education reform: High-stakes testing and teacher evaluation. Social Justice, 42(1).

  15. Damasio, A. (2006). Descartes’ error. New York: Random House.

    Google Scholar 

  16. De Freitas, E., Sinclair, N., & Coles, A. (Eds.). (2017). What is a mathematical concept? Cambridge: Cambridge University Press.

  17. Donald, D., Glanfield, F., & Sterenberg, G. (2011). Culturally relational education in and with an indigenous community. IN Education, 17(3).

  18. Donald, D., Glanfield, F., & Sterenberg, G. (2012). Living ethically within conflicts of colonial authority and relationality. Journal of the Canadian Association for Curriculum Studies, 10(1), 53–76.

    Google Scholar 

  19. Edmonds-Wathen, C., Owens, K., Sakopa, P., & Bino, V. (2014). Indigenous languages and mathematics in elementary schools. In J. Anderson, M. Cavanagh & A. Prescott (Eds.). Curriculum in focus: Research guided practice (proceedings of the 37th annual conference of the mathematics education research Group of Australasia) (pp. 207–214). Sydney: MERGA.

  20. Fisher, A. (2012). The Misplaced Mountain: Maps, memory, and the Yakama reservation boundary dispute. American Indian Culture and Research Journal, 36(1), 79–122.

    Google Scholar 

  21. Fosnot, C. T., & Dolk, M. L. A. M. (2002). Young mathematicians at work: Constructing fractions, decimals, and percents. Portsmouth: Heinemann.

    Google Scholar 

  22. Garcia-Olp, M., Nelson, C., & Saiz, L. (2019). Conceptualizing a mathematics curriculum: Indigenous knowledge has always been mathematics education. Educational Studies, 55(6), 689–706. https://doi.org/10.1080/00131946.2019.1680374

  23. Gibeaut, J. (1999). Another broken trust: After the government’s bungling of a land allotment program for hundreds of thousands of Indians, all eyes are now on a federal judge trying to sort out the mess. American Bar Association Journal, 85, 40–47.

    Google Scholar 

  24. Goins, E. (2017). Why I’m leaving a research I university for a liberal arts college. American mathematical society’s blog on inclusion/exclusion. Retrieved from https://blogs.ams.org/inclusionexclusion/2017/09/15/why-im-leaving-a-research-i-university-for-a-liberal-arts-college/

  25. Gutiérrez, R. (2012). Context matters: How should we conceptualize equity in mathematics education? In B. Herbel-Eisenmann, J. Choppin, D. Wagner, & D. Pimm (Eds.), Equity in discourse for mathematics education: Theories, practices, and policies (Vol. 55, pp. 17–33). Dordrecht: Springer Science & Business Media.

  26. Gutiérrez, R. (2017). Political conocimiento for teaching mathematics: Why teachers need it and how to develop it. In S. E. Kastberg, A. M. Tyminski, A. E. Lischka, & W. B. Sanchez (Eds.), Building support for scholarly practices in mathematics methods (pp. 11–38). Charlotte: IAP.

  27. Gutstein, E. (2004). Home buying while brown by black: Teaching mathematics for racial justice. Learning and Teaching Mathematics, 2004(1), 31–34.

  28. Hamill, J. F. (2003). Show me your CDIB: Blood quantum and Indian identity among Indian people of Oklahoma. American Behavioral Scientist, 47(3), 267–282.

  29. Hargus, S., & Beavert, V. (2014). Northwest Sahaptin. Journal of the International Phonetic Association, 44(3), 319–342.

    Google Scholar 

  30. Hefendehl-Hebeker, L., vom Hofe, R., Büchter, A., Humenberger, H., Schulz, A., & Wartha, S. (2019). Subject-matter didactics. In Traditions in German-speaking mathematics education research (pp. 25–59). Cham: Springer.

    Google Scholar 

  31. Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32, 195–222.

  32. Hunn, E. S., & Selam, J. (1990). Nch’i-wana, “the big river”: Mid-Columbia Indians and their land. University of Washington Press.

  33. Jacob, M. M. (2013). Yakama rising: Indigenous cultural revitalization, activism, and healing. Tucson: University of Arizona Press.

    Google Scholar 

  34. Jansen, J. (2010). A grammar of Yakima Ichishkíin/Sahaptin. (xxxiv, 505). Doctoral dissertation, University of Oregon. http://hdl.handle.net/1794/10901

  35. Jilk, L. M. (2016). Supporting teacher noticing of students’ mathematical strengths. Mathematics Teacher Educator, 4(2), 188–199. https://doi.org/10.5951/mathteaceduc.4.2.0188

    Article  Google Scholar 

  36. Jorgensen, R. (2012). Exploring scholastic mortality among working-class and indigenous students. In B. Herbel-Eisenmann, J. Choppin, D. Wagner, & D. Pimm (Eds.), Equity in discourse for mathematics education: Theories, practices, and policies (Vol. 55, pp. 35–49). Dordrecht: Springer Science & Business Media.

  37. Kieren, T. E. (1976). On the mathematical, cognitive and instructional. In R. A. Lesh & D. A. Bradbard (Eds.), Number and Measurement. Papers from a Research Workshop (pp. 101–144). Columbus, OH: ERIC

  38. Kieren, T. E. (1980). The rational number construct: Its elements and mechanisms. In Recent research on number learning (pp. 125–149). Columbus: ERIC/SMEAC.

  39. Kisker, E. E., Lipka, J., Adams, B. L., Rickard, A., Andrew-Ihrke, D., Yanez, E. E., & Millard, A. (2012). The potential of a culturally based supplemental mathematics curriculum to improve the mathematics performance of Alaska native and other students. Journal for Research in Mathematics Education, 43(1), 75–113.

    Google Scholar 

  40. Lee, C. D. (2017). An ecological framework for enacting culturally sustaining pedagogy. In D. Paris & H. S. Alim (Eds.), Culturally sustaining pedagogies: Teaching and learning for justice in a changing world (pp. 261–273). New York: Teachers College Press.

    Google Scholar 

  41. Lee, T. S., & McCarty, T. L. (2017). Upholding Indigenous education sovereignty through critical culturally sustaining/revitalizing pedagogy. In Paris, D., & Alim, H. S. (Eds.). (2017). Culturally sustaining pedagogies: Teaching and learning for justice in a changing world (pp. 61–82). New York: Teachers College Press.

  42. Lipka, J., Hogan, M. P., Webster, J. P., Yanez, E., Adams, B., Clark, S., & Lacy, D. (2005). Math in a cultural context: Two case studies of a successful culturally based math project. Anthropology & Education Quarterly, 36(4), 367–385.

    Google Scholar 

  43. Lunney Borden, L. (2011). The ‘verbification’ of mathematics: Using the grammatical structures of Mi’kmaq to support student learning. For the Learning of Mathematics, 31(3), 8–13.

    Google Scholar 

  44. Lunney Borden, L. (2013). What’s the word for … ? Is there a word for … ? How understanding Mi’kmaw language can help support Mi’kmaw learners in mathematics. Mathematics Education Research Journal, 25(1), 5–22.

    Google Scholar 

  45. Lunney Borden, L., & Wagner, D. (2011). Show me your math. CMS Notes, 43(2), 10–11.

    Google Scholar 

  46. Marshall, S. A. (2018). To sustain tribal nations: Striving for indigenous sovereignty in mathematics education. The Journal of Educational Foundations, 31(1/2), 11–39.

    Google Scholar 

  47. McCarty, T., & Lee, T. (2014). Critical culturally sustaining/revitalizing pedagogy and Indigenous education sovereignty. Harvard Educational Review, 84(1), 101–124.

  48. Meaney, T., Trinick, T., & Fairhall, U. (2013). One size does not fit all: Achieving equity in Māori mathematics classrooms. Journal for Research in Mathematics Education, 44(1), 235–263.

    Google Scholar 

  49. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks: Sage.

    Google Scholar 

  50. National Governors Association. (2010). Common core state standards. Washington, DC.

  51. National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. Reston: NCTM.

  52. Norton, B. (1997). Language, identity, and the ownership of English. TESOL Quarterly, 31(3), 409–429.

    Google Scholar 

  53. Paris, D. (2012). Culturally sustaining pedagogy: A needed change in stance, terminology, and practice. Educational Researcher, 41(3), 93–97.

    Google Scholar 

  54. Paris, D., & Alim, H. S. (Eds.). (2017). Culturally sustaining pedagogies: Teaching and learning for justice in a changing world. New York: Teachers College Press.

    Google Scholar 

  55. Piaget, J. (1926/1951). The language and thought of the child (pp. 1–49). London: Routledge & Kegan.

    Google Scholar 

  56. Pine, A., & Turin, M. (2017). Oxford research encyclopedia of linguistics. Oxford University Press. https://doi.org/10.1093/acrefore/9780199384655.013.8

  57. Ruef, J. (2016). Building powerful voices: Co-constructing public Sensemaking. Unpublished doctoral dissertation, Stanford University.

  58. Ruef, J. (2018). Think you’re bad at math? You might be suffering from math trauma. The Conversation. https://theconversation.com/think-youre-bad-at-math-you-may-suffer-from-math-trauma-104209

  59. Ruef, J. (2020). What gets checked at the door? Embracing students’ complex math identities. Journal of Humanistic Mathematics, 10(1), 22–38. https://doi.org/10.5642/jhummath.202001.04

  60. Ruef, J. (in press). How Ms. Mayen and her students co-constructed “good at math.” Journal of Research in Mathematics Education.

  61. Ruef, J., & Torres, A. (in press). A menu of risk-taking scaffolds. Mathematics Teacher: Learning and Teaching PK–12.

  62. Sabzalian, L. (2019). Indigenous children’s survivance in public schools. Routledge.

  63. San Pedro, T. J. (2017). This stuff interests me”: Re-centering indigenous paradigms in colonizing schooling spaces. In Paris, D., & Alim, H. S. (Eds.). (2017). Culturally sustaining pedagogies: Teaching and learning for justice in a changing world (pp. 99–116). New York: Teachers College Press.

  64. Senate Bill 13. (2017). Oregon Department of Education. 79th Oregon Legislative Assembly. Retrieved from https://olis.leg.state.or.us/liz/2017R1/Downloads/MeasureDocument/SB13

  65. Simon, M. A., Placa, N., & Avitzur, A. (2016). Participatory and anticipatory stages of mathematical concept learning: Further empirical and theoretical development. Journal for Research in Mathematics Education, 47(1), 63–93.

  66. Sfard, A., & Prusak, A. (2005). Identity that makes a difference: Substantial learning as closing the gap between actual and designated identities. International Group for the Psychology of Mathematics Education, 1, 37–52.

    Google Scholar 

  67. Smith, L. T. (2012). Decolonizing methodologies: Research and indigenous people (2nd ed.). London: Zed Books.

    Google Scholar 

  68. Substitute Senate Bill 5433. (2015). Litzow, Rolfes, Roach, Fain, Hasagawa, Dammeier, McCoy, Nelson, Frockt, McAuliffe, Rivers, Kohl-Welles, Chase, Jayapal, Conway, and Habib. 64th Washington Legislative Assembly. Retrieved from https://app.leg.wa.gov/billsummary/?BillNumber=5433&Year=2015&Initiative=false

  69. Tate, W. F. (1994). From inner city to ivory tower: Does my voice matter in the academy? Urban Education, 29(3), 245–269.

    Google Scholar 

  70. Trinick, T., Meaney, T., & Fairhall, U. (2014). Teachers learning the registers of mathematics and mathematics education in another language: An exploratory study. ZDM, 46(6), 953–965.

    Google Scholar 

  71. Underriner, J., & Jansen, J. (2018). The role of institutions of higher education in teaching indigenous languages: Ichishkíin and Chinuk Wawa. Language and Linguistics Compass, 12(5), e12276.

    Google Scholar 

  72. United States Department of Education (2017). The federal role in education. https://www2.ed.gov/about/overview/fed/role.html

  73. Tuck, E., & Yang, K. W. (2014). R-words: Refusing research. In D. Paris & M. T. Winn (Eds.), Humanizing research: Decolonizing qualitative inquiry with youth and communities (pp. 223–248). Thousand Oakes: Sage Publications.

  74. Vithal, R., & Skovsmose, O. (1997). The end of innocence: A critique of ‘ethnomathematics’. Educational Studies in Mathematics, 34(2), 131–157.

    Google Scholar 

  75. Vygotsky, L. S. (1980). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.

    Google Scholar 

Download references


The authors thank Jill Baxter, Joana Jansen, and the anonymous reviewers whose feedback strengthened this work. Thanks to Assistant Dean Aaron Bird Bear (Mandan, Dinatsa, Diné) for sharing his family’s story. Special thanks to Tuxámshish for her unwavering support, and the Northwest Indian Language Institute for their ongoing work. We acknowledge and thank Kalapuya Ilihi, the land that nourishes us.

Author information



Corresponding author

Correspondence to Jennifer L. Ruef.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ruef, J.L., Jacob, M.M., Walker, G.K. et al. Why indigenous languages matter for mathematics education: a case study of Ichishkíin. Educ Stud Math 104, 313–332 (2020). https://doi.org/10.1007/s10649-020-09957-0

Download citation


  • Indigenous
  • Decolonizing
  • Language revitalization
  • Culturally sustaining