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Humanizing mathematics education: quantitative and arithmetic argumentation of indigenous cultural practices

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Abstract

Dehumanized and globalized mathematics education in the last centuries has led to established learning processes disconnected from indigenous knowledge. The effect of cognitive imperialism, given the systematic negation of the language and the culture, has as a disastrous consequence of the gradual and systematic loss of knowledge and indigenous reasoning. Thus, recognizing, appreciating and updating it turns into a task and challenge for the teaching and learning of math in the intercultural classroom. Therefore, the purpose of this research is to focus on analyzing the mathematical reasoning of the indigenous student while encoding and decoding an historic numeric registry artifact called püron (knot in the Mapuche language). The study was conducted in three schools on Mapuche territory of Araucanía Region in Chile, using the Participatory Action Research method. The results show that encoding/decoding quantities helps indigenous students to recognize structures and to establish a numeration system close to the historically reported cultural practices of the Mapuche people. Moreover, it extends the mathematical quantitative structure and reasoning to an arithmetic one seen in the present day cultural practices such as the measurement of fields for planting. Thus, the experience contributes to the students’ linguistic awareness of Mapudungun (Mapuche language) in a numeration system framework.

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Notes

  1. Nomenclature: (G) Girl or (B) Boy. Number relates to the school level, from 1 to 6. (B) Botronhue, (SJ) San José or (VL) Vega Larga representing each school. Number relates to the lesson in which the expression was made, from 1 to 4.

References

  • Aikenhead, G. S. (2017). Enhancing school mathematics culturally: A path of reconciliation. Canadian Journal of Science, Mathematics and Technology Education, 17(2), 73–140.

    Article  Google Scholar 

  • Arellano, C. (2009). Un khipu olvidado: el püron mapuche. Notas acerca de su función. En V. Solanilla (Ed.), Actas IV Jornadas Internacionales sobre textiles precolombinos (pp.229–240). Book Print Digital, S. A.

  • Askew, M. & Venkat, H. (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). Academic Press. https://doi.org/10.1016/B978-0-12-802218-4.00013-3.

  • Barton, B. (2008). Language and mathematics. Springer.

    Book  Google Scholar 

  • Barton, B. (2009). The language of mathematics. Springer.

    Google Scholar 

  • Battiste, M. (2004). Animating sites of postcolonial education: Indigenous knowledge and the humanities. Plenary Address.

  • Benoit, L., Lehalle, H., & Jouen, F. (2004). Do young children acquire number words through subitizing or counting? Cognitive Development, 19(3), 291–307. https://doi.org/10.1016/j.cogdev.2004.03.005

    Article  Google Scholar 

  • Bishop, A. J. (1988). Mathematical Enculturation: A Cultural Perspective on Mathematics Education. Kluwer Academic.

  • Bishop, A. J. (1998). Equilibrando las necesidades matemáticas de la educación general con las de la instrucción matemática de los especialistas. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas, 27, 25–37.

  • Borden, L., & Munroe, E. (2016). Speaking English isn’t thinking in English: Exploring young aboriginal children’s mathematical experiences through aboriginal perspectives. In A. Anderson, J. Anderson, J. Hare, & M. MacTavish (Eds.), Language, learning, and culture in early childhood. Home, school, and community contexts (pp. 64–81). Routledge.

  • D’Ambrosio, U. (2006). Ethnomathematics: Link between traditions and modernity. Sense Publishers.

    Book  Google Scholar 

  • d’Errico, F., Doyon, L., & Colagé, I., Queffelec, A., Le Vraux, E., Giacobini, G., Vandermeersch, B., & Maureille, B. (2018). From number sense to number symbols. An archaeological perspective. Philosophical Transactions of the Royal Society b: Biological Sciences, 373, 1–10. https://doi.org/10.1098/rstb.2016.0518

    Article  Google Scholar 

  • Dehaene, S. (2011). The number sense: How the mind creates mathematics. OUP USA.

  • Dehaene, S., Izard, V., Spelke, E., & Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science, 320(5880), 1217–1220. https://doi.org/10.1126/science.1156540

    Article  Google Scholar 

  • Edmonds-Wathen, C., Owens, K., & Bino, V. (2019). Identifying vernacular language to use in mathematics teaching. Language and Education, 33(1), 1–17. https://doi.org/10.1080/09500782.2018.1488863

    Article  Google Scholar 

  • Ejuu, G. (2019). African indigenous games: Using Bame Nsamenang’s Africentric thoughts to reflect on our heritage, pedagogy, and practice in a global village. Journal of Psychology in Africa, 29(4), 319–327. https://doi.org/10.1080/14330237.2019.1647496

    Article  Google Scholar 

  • Flores, J. A. (2012). Definición de buenas prácticas en larevitalización de lenguas: Una agendaen curso. CUHSO, 11(1), 27–37. https://doi.org/10.7770/cuhso-V11N1-art242

    Article  Google Scholar 

  • Geary, D. (1994). Children’s mathematical development: Research and practical applications. American Psychological Association Washington, DC. https://doi.org/10.1037/10163-000

    Article  Google Scholar 

  • Gibson, D. J., Gunderson, E. A., Spaepen, E., Levine, S. C., & Goldin- Meadow, S. (2019). Number gestures predict learning of number words. Developmental Science, 22, e12791. https://doi.org/10.1111/desc.12791.

  • Harvey, A., & Russell-Mundine, G. (2018). Decolonising the curriculum: Using graduate qualities to embed Indigenous knowledges at the academic cultural interface. Teaching in Higher Education, 24(6), 789–808. https://doi.org/10.1080/13562517.2018.1508131

    Article  Google Scholar 

  • Huencho, A. (2020). Matemática Mapuche: Promoción del aprendizaje desde el conocimiento cultural. [Unpublished doctoral dissertation]. Pontificia Universidad Católica de Chile.

  • Huencho, A., & Chandía, E. (2018). Planificar la clase de matemática con responsabilidad cultural: El registro de información cuantificable a través del Püron. UNO Revista De Didáctica De Las Matemáticas, 82, 7–15.

    Google Scholar 

  • Huencho, A., Chandía, E., Rojas., F., & Williamson, G. (2021). Model of the development of mathematical knowledge from the Knowing and Doing of the Mapuche people. Educación Matemática, 33(2), 7–36. https://doi.org/10.24844/EM3302.01.

  • Huencho, A., Rojas, F., Webb, A. (2017). Educación Matemática Intercultural: Propuestas y proyecciones desde el pueblo mapuche. En E. Treviño, L. Morawietz, C. Villalobos y E. Villalobos (Eds.), Educación intercultural en Chile. Experiencias, pueblos y territorios (pp. 303–334). Ediciones Universidad Católica de Chile.

  • 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). Teachers College Press.

    Google Scholar 

  • Leibovich, T., Katzin, N., Harel, M., & Henik, A. (2017). From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40, e164. https://doi.org/10.1017/S0140525X16000960.

  • Little Bear, L. (2000). Jagged worldviews colliding. In M. Battiste (Ed.), Reclaiming Indigenous Voice and Vision (pp. 77–85). UBC Press.

    Google Scholar 

  • Lunney Borden, L. (2010). Transforming mathematics education for Mi’kmaw students through mawikinutimatimk. [Unpublished doctoral dissertation]. University of New Brunswick.

  • McCarty, T. L. & Lee, T. (2014). Critical culturally sustaining/revitalizing pedagogy and indigenous education sovereignty. Harvard Educational Review, 84(1), 101–124. https://doi.org/10.17763/haer.84.1.q83746nl5pj34216.

  • Meaney, T., Trinick, T., & Fairhall, U. (2012). Collaborating to meet language challenges in indigenous mathematics classrooms. Springer.

    Book  Google Scholar 

  • 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. https://doi.org/10.5951/jresematheduc.44.1.0235

    Article  Google Scholar 

  • Ministerio de Educación, República de Chile [MINEDUC]. (2020). Bases curriculares Lengua y Cultura de los Pueblos Originarios Ancestrales. 1° a 6° año de Educación Básica. Ministerio de Educación.

  • Ministerio de Educación, República de Chile [MINEDUC]. (2018). Bases Curriculares Primero a Sexto Básico 2012. Unidad de Currículum y Evaluación. Ministerio de Educación. Recuperado de http://www.curriculumnacional.cl/614/articles-21322_bases.pdf.

  • Nsamenang, A. B. & Tchombe, M. S. (Eds.). (2011). Hand-book of African educational theories and practices: A generative teacher education curriculum. Presses Universitaires d’Afrique.

  • Nunes, T., Dorneles, B. V., Lin, P. J., & Rathgeb-Schnierer, E. (2016). Teaching and learning about whole numbers in primary school. Springer Nature.

  • Overmann, K. A. (2018). Constructing a concept of number. Journal of Numerical Cognition, 4, 464–493. https://doi.org/10.5964/jnc.v4i2.161

    Article  Google Scholar 

  • Owens, K., Meaney, T., Trinick, T., & Fairhall, U. (2013). Collaborating to meet language challenges in Indigenous mathematics classrooms. Mathematics Education Research Journal, 25, 185–188. https://doi.org/10.1007/s13394-013-0071-x

    Article  Google Scholar 

  • Owens, K. (2014). The impact of a teacher education culture-based project on identity as a mathematically thinking teacher. Asia-Pacific Journal of Teacher Education, 42(2), 186–207. https://doi.org/10.1080/1359866X.2014.892568

    Article  Google Scholar 

  • Owens, K. (2015). Visuospatial Reasoning: An Ecocultural Perspective for Space. Springer.

    Book  Google Scholar 

  • Paliwal, V., & Baroody, A. J. (2020). Cardinality principle understanding: The role of focusing on the subitizing ability. ZDM Mathematics Education, 52(4), 649–661. https://doi.org/10.1007/s11858-020-01150-0

    Article  Google Scholar 

  • Quintriqueo, S., & McGinity, M. (2009). Implicancias de un modelo curricular monocultural en la construcción de la identidad socio-cultural de alumnos/as Mapuches de la IX Región de la Araucanía Chile. Revista Estudios Pedagógicos, 35(2), 173–188.

    Google Scholar 

  • Rogoff, B., Moore, L., Najafi, B., Dexter, A., Correa-Chávez, M., & Solis, J. (2007). Children’s development of cultural repertoires through participation in everyday routines and practices. In J. Grusec & P. Hastings (Eds.), Handbook of socialisation (pp. 490–515). Guilford.

    Google Scholar 

  • Rogoff, B., Paradise, R., Arauz, R. M., Correa-Chávez, M., & Angelillo, C. (2003). Firsthand learning through intent partici- pation. Annual Review of Psychology, 54, 175–203. https://doi.org/10.1146/annurev.psych.54.101601.145118

    Article  Google Scholar 

  • Susman, G. (1983). Action Research: A Sociotechnical Systems Perspective. In G. Morgan (Ed.), Beyond Method: Strategies for Social Research (pp. 95–113). Sage.

    Google Scholar 

  • Testolin, A. (2020). The challenge of modeling the acquisition of mathematical concepts. Frontiers in Human Neuroscience, 14, 100. https://doi.org/10.3389/fnhum.2020.00100

    Article  Google Scholar 

  • Walsh, C. (2018). Decoloniality in/as Praxis. In M. Walter, Y.C. Walsh (Eds.), On Decoloniality. Analytics, Concepts, Praxis (pp.15–102). Durham: Duke University Press.

  • Walsh, C. (2021). (Re)existence in times of de-existence: Political–pedagogical notes to Paulo Freire. Language and Intercultural Communication, 21(4), 468–478. https://doi.org/10.1080/14708477.2021.1916025

    Article  Google Scholar 

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Acknowledgements

Special thanks to Jill Bratton for the language support as we finalized this article. Thanks are also due to FONDEF project ID21I10187 “Modelo de acompañamiento para la implementación de la intervención educativa intercultural en contexto indígena”, subsidised by the Agencia Nacional de Investigación y Desarrollo de Chile (ANID), and to the International Agreement between the Fundación Santa María Global España and the Universidad Católica de Temuco in the framework of the project “Activando la Resolución de Problemas en aula Multigrado”.

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  1. Universidad Católica de Temuco, Temuco, Chile

    Anahí Huencho

  2. Universidad de Concepción, Concepción, Chile

    Eugenio Chandía

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  1. Anahí Huencho
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  2. Eugenio Chandía
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Correspondence to Anahí Huencho.

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Huencho, A., Chandía, E. Humanizing mathematics education: quantitative and arithmetic argumentation of indigenous cultural practices. ZDM Mathematics Education 55, 1085–1099 (2023). https://doi.org/10.1007/s11858-023-01490-7

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