Abstract
This paper explores the outcomes of the first year of the implementation of a mathematics program (Representations, oral language and engagement in Mathematics: RoleM) which is framed upon research relating to effectively supporting young Indigenous students’ learning. The sample comprised 230 Indigenous students (average age 5.76 years) from 15 schools located across Queensland. The pre-test and post-test results from purposely developed language and mathematics tests indicate that young Indigenous Australian students are very capable learners of mathematics. The results of a multiple regression analysis denoted that their ability to ascertain the structure of patterns and to understand mathematical language were both strong predictors of their success in mathematics, with the latter making the larger contribution.
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Aldridge, J. (2005). The importance of oral language. Childhood Education, 81(3), 177–180.
Anghileri, J. (1995). Language, arithmetic and the negotiation of meaning. For the Learning of Mathematics, 21(3), 10–14.
Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas. New York: Brooks/Cole Publishing.
Askew, M., Brown, M., Rhodes, V., William, D., & Johnson, D. (1997). Effective teachers of numeracy. London: King’s College.
Barton, B. (1996). Making sense of Ethnomathematics: Ethnomathematics is making sense. Educational Studies in Mathematics, 31(1), 201–233.
Bikner-Ahsbahs, A. (2006). Semiotic sequence analysis: Constructing epistemic types empirically. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (pp. 161–168). Prague, Czech Republic: PME.
Bishop, A. (1996). How should mathematics teaching in modern societies relate to cultural values: Some preliminary questions. In D. T. Nguyen, T. L. Pham, C. Comiti, D. R. Green, E. Southwell, & J. Izard (Eds.), Proceedings of the seventh South East Asian conference on mathematics education (pp. 19–24). Hanoi: Vietnamese Mathematical Society.
Blanton, M., & Kaput, J. (2004). Elementary grades students’ capacity for functional thinking. In M. Hoines & A. Fuglestad (Eds.), Proceedings of the 28th conference of the international group for psychology of mathematics education (pp. 135–142). Bergen, Norway: PME.
Boehm, A. E. (1971). Boehm test of basic concepts manual. New York: The Psychological Corporation.
Burns, R. (2000). Introduction to research methods. Frenchs Forest: Pearson Education.
Cairney, T. (2003). Literacy within family life. In N. Hall, J. Larson, & J. Marsh (Eds.), Handbook of early childhood literacy (pp. 85–98). London: Sage Publications.
Castle, K., & Aichele, D. B. (1994). Professional development and teacher autonomy. In D. B. Aichele & A. F. Coxford (Eds.), Professional development for teachers of mathematics. Reston, VA: National Council of Teachers of Mathematics.
Christie, M., & Harris, S. (1985). Communication breakdown in the Aboriginal classroom. In J. B. Pride (Ed.), Cross-cultural encounters: Communication and miscommunication (pp. 81–90). Melbourne: River Seine Publications.
Cohen, J. W. (1988). Statistical power analysis for the behavioural sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.
Cooper, T., & Warren, E. (2011). Years 2 to 6 students’ ability to generalise: Models, representations and theory. In J. Cai & E. Knuth (Eds.), Early algebraization: Volume 2 of advances in mathematics education (pp. 187–214). Netherlands: Springer.
Council of Australian Governments (2009). National indigenous reform agreement. Retrieved from http://www.coag.gov.au/coag_meeting_outcomes/2009-07-02/docs/NIRA_closing_the_gap.pdf.
Dickinson, D., McCabe, A., & Essex, M. J. (2006). A window of opportunity we must open to all: The case for preschool with high-quality support for language and literacy. In D. Dickinson & B. Neuman (Eds.), Handbook of early literacy research: Volume 2 (pp. 11–28). New York: Guilford Press.
Doig, B., & de Lemos, M. (2000). I can do maths. Melbourne: ACER.
Eades, D. (1995). Aboriginal English (Aboriginal literacy resource kit). North Sydney: NSW Board of Studies.
Ellemor-Collins, D., & Wright, R. (2009). Structuring numbers 1–20: developing facile addition and subtraction. Mathematics Education Research Journal, 21(2), 50–75.
Ernest, P. (1999). Forms of knowledge in mathematics and mathematics education: philosophical and rhetorical perspectives. Educational Studies in Mathematics, 38, 67–83.
Frigo, T., & Simpson, L. (1999). Research into the numeracy development of Aboriginal students: Implications for the NSW K-10 mathematics syllabus. Canberra: New South Wales Board of Studies.
Frigo, T., Corrigan, M., Adams, I., Hughes, P., Stephens, M., & Woods, D. (2004). Supporting English literacy and numeracy learning for Indigenous students in the early years [Research Monograph]. Camberwell, Victoria: Australian Council for Education Research.
Gerdes, P. (1994). Reflections on ethnomathematics. For the Learning of Mathematics, 14(2), 19–22.
Graham, B. (1988). Mathematical education and Aboriginal children. Educational Studies in Mathematics, 19(2), 119–135.
Gutstein, E. (2003). Mathematics for social justice in an urban Latino school. Journal for Research in Mathematics Education, 34(1), 37–73.
Halliday, M. (1979). Language as social semiotic: The social interpretation of language and meaning. London: Edward Arnold Publishing.
Harris, P. (1991). Mathematics in a cultural context: Aboriginal perspectives on space, time and money. Geelong: Deakin University.
Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. New York: Routledge.
Heslop, J. (2003). Living and teaching in Aboriginal communities. In Q. Beresford & G. Partington (Eds.), Reform and resistance in Aboriginal education (pp. 208–237). Crawley, Western Australia: University of Western Australia Press.
Hewitson, R. (2007). Climbing the educational mountain: a metaphor for real culture change for Indigenous students in remote schools. The Australian Journal of Indigenous Education, 36, 6–20.
Howard, P. (1997, November). Aboriginal voices in our schools. Paper presented at the Annual Conference of the Australian Association for Research in Education, Brisbane, Australia.
Hughes, P., More, A., & Williams, M. (2004). Aboriginal ways of learning. Adelaide: University of South Australia.
Irwin, K. (1994). Maori research methods and processes: an exploration and discussion. A Journal for South Pacific Cultural Studies, 28, 25–43.
Jones, K., Kershaw, L., & Sparrow, L. (1995). Aboriginal children learning mathematics. Perth, Western Australia: MASTEC, Edith Cowan University.
Jorgensen, R. (2011). Language, culture and learning mathematics: A bourdieuian analysis of Indigenous learning. In C. Wyatt-Smith, J. Elkins, & S. Gunn (Eds.), Multiple perspectives on difficulties in learning literacy and numeracy (pp. 315–329). Netherlands: Springer.
Kemmis, S., & McTaggart, R. (2000). Participatory action research. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of qualitative research (pp. 567–605). Thousand Oaks, CA: Sage.
Krause, K.-L., Bochner, S., Duchesne, S., & McMaugh, A. (2010). Educational psychology for learning and teaching. Victoria: Thomson.
Laborde, C. (1990). Language and mathematics. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition: A research synthesis by the international group for the psychology of mathematics education (pp. 53–69). Cambridge: Cambridge University Press.
Liljedahl, P. (2004). Repeating pattern or number pattern: the distinction is blurred. Focus on Learning Problems in Mathematics, 26(3), 24–42.
Luke, A. (2009). Education 2010 and new times: Why equity and social justice still matter, but differently. Paper presented at Education Queensland online conference.
Luke, A., Land, R., Christie, P., & Kolatsis, A. (2002). Standard Australian English and language for Queensland Aboriginal and Torres Strait Islander students. Brisbane: Queensland Indigenous Education Consultative Body.
Mason, J., Stephens, M., & Watson, A. (2009). Appreciating structure for all. Mathematics Education Research Journal, 2(2), 10–32.
Meaney, T., Fairhall, U., & Trinick, T. (2008). The role of language in ethnomathematics. Journal of Mathematics and Culture, 3(1), 52–65.
Mills, C., & Gale, T. C. (2003). Transient teachers: mixed messages of schooling in regional. Australian Journal of Research in Rural Education, 18, 145–151.
Ministerial Council on Education, Employment, Training, and Youth Affairs. (2007). National report on schooling in Australia: Reading, writing and numeracy benchmark results for 2005. Canberra: MCEETYA.
Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49.
Mulligan, J. T., Mitchelmore, M. C., & Prescott, A. (2005). Case studies of children’s development of structure in early mathematics: A two-year longitudinal study. In H. Chick & J. Vincent (Eds.), Proceedings of the 29th international conference for the psychology of mathematics education (pp. 1–8). Melbourne: PME.
Munns, G., Martin, A., & Craven, R. (2008). To free the spirit? Motivation and engagement of indigenous students. Australian Journal of Indigenous Education, 37, 98–107.
Nakata, M. (2007). The cultural interface. Australian Journal of Indigenous Education, 36, 7–14.
Nichol, R. (2008, January). Pedagogical issues affecting Indigenous citizenship and education in Australia and Melanesia. Paper presented at the Social Educators of Australia Biennial Conference, Making a difference: Multidimensional citizenship education in a changing world, University of Newcastle.
Nichol, R., & Robinson, J. (2000). Pedagogical challenges in making mathematics relevant for indigenous Australians. International Journal of Mathematical Education in Science and Technology, 4, 495–504.
Nichols, S., Glass, G., & Berliner, D. (2006). High-stakes testing and student achievement: does accountability pressure increase student learning? Education Policy Analysis Archives, 14(1), 1–172.
Niesche, R. (2009). The use of home language in the mathematics classroom. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Proceedings of the 32nd annual conference of the mathematics education research group of Australasia (pp. 704–707). Palmerston North, NZ: MERGA.
Orrill, R. (2001). Mathematic, numeracy and democracy. In L. Steen (Ed.), Mathematics and democracy: A case for quantitative literacy. Reston, VA: The National Council on Education and the Disciplines.
Osborne, B. (2003). Preparing preservice teachers’ minds, hearts and actions for teaching in remote Indigenous contexts. Australian Journal of Indigenous Education, 31, 17–24.
Papic, M. (2007). Mathematical patterning in early childhood: An intervention study. Unpublished PhD thesis, Macquarie University.
Papic, M., & Mulligan, J. T. (2007). The growth of early mathematical patterning: An intervention study. In J. Watson & K. Beswick (Eds.), Proceedings of the 30th annual conference of the mathematics education research group of Australasia (pp. 591–600). Hobart: MERGA.
Pearson, N. (2009). Radical hope: education and equality in Australia. Quarterly Essay, 35, 1–106.
Rigney, L. (1999). Internationalization of an Indigenous anticolonial cultural critique of research methodologies: a guide to indigenist research methodology and its principles. Wicazo Sa Review, 14(2), 109–121.
Roberts, T. (1998). Mathematical registers in Aboriginal languages. For the Learning of Mathematics, 18(1), 10–16.
Sarra, C. (2011). Transforming indigenous education. In N. Purdie, G. Milgate, & H. Bell (Eds.), Two way teaching and learning: Toward culturally reflective and relevant education (pp. 107–117). Victoria: ACER Press.
Schleiger, H., & Gough, J. (2001). Diagnostic mathematical tasks. Sydney: UNSW Press.
Sharplin, E.D. (2008). Quality of worklife for rural and remote teachers: Perspectives of novice, interstate and overseas-qualified teachers. Unpublished doctoral dissertation, The University of Western Australia.
Smith, L. (1999). Decolonizing methodologies: Research and Indigenous peoples. London: Zed Books.
Thorpe, K., Tayler, C., Bridgstock, R., Grieshaber, S., Skoien, P., Dany, S., et al. (2004). Preparing for school: Report of the Queensland preparing for school trials 2003/4. Brisbane: Queensland University of Technology.
Warren, E. (2005). Patterns supporting the development of early algebraic thinking. Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia (pp. 759–766). Melbourne: MERGA.
Warren, E. (2009). Early childhood teachers’ professional learning in early algebraic thinking a model that supports new knowledge and pedagogy. Mathematics Teacher Education and Development, 10, 30–45.
Warren, E., & deVries, E. (2009). Young Australian Indigenous students’ engagement with numeracy: actions that assist to bridge the gap. Australian Journal of Education, 53(2), 159–175.
Warren, E., & Miller, J. (2010). Exploring four year old indigenous students’ ability to pattern. International Research in Early Childhood Education, 1(2), 42–56.
Warren, E., & Young, J. (2008). Oral language, representations and mathematical understanding: Australian Indigenous students. Australian Journal of Indigenous Education, 37, 130–137.
Warren, E., Young, J., & deVries, E. (2008). The impact of early numeracy engagement on 4 year old Indigenous students. Australian Journal of Early Childhood Education, 33(4), 2–8.
Warren, E., deVries, E., & Cole, A. (2009). Closing the gap: myths and truths behind subitisation. Australasian Journal of Early Childhood, 34(4), 46–53.
Warren, E., Quine, J., & DeVries, E. (2012). Supporting teachers’ professional learning at a distance: a model for change in at-risk contexts. Australian Journal of Teacher Education, 37(6), 11–28.
White, D. (1974). Mathematical anthropology. In J. J. Honigman (Ed.), Handbook of social and cultural anthropology (pp. 369–446). Chicago: Rand McNally.
Willis, S. (2000, October). Strengthening numeracy: Reducing risk. Paper presented at the Australian Council of Educational Research Conference, Brisbane.
Yunkaporta, T., & McGinty, S. (2009). Reclaiming Aboriginal place-based worldviews at the interface of local and non-local knowledge. Australian Education Researcher, 36(2), 55–72.
Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: the tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49, 379–402.
Zhang, H., & Alex, N.K. (1995). Oral language development across the curriculum K - 12. Retrieved from http://www.ed.gov/databases/ERIC_Digests/ed389029.html.
Acknowledgments
The research reported in this paper was supported by Australian Research Council under grant LP100100154, and the Department of Education, Employment and Workplace Relations. The authors express their thanks to Eva deVries, Antoinette Cole, participating teachers, Indigenous education officers, students and school communities for their generous support of this project.
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Many thanks to Antoinette Cole for her ongoing support and insights
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Warren, E., Miller, J. Young Australian Indigenous students’ effective engagement in mathematics: the role of language, patterns, and structure. Math Ed Res J 25, 151–171 (2013). https://doi.org/10.1007/s13394-013-0068-5
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DOI: https://doi.org/10.1007/s13394-013-0068-5