Abstract
This paper reports on part of a large study investigating how Indigenous students’ mathematical proficiency can be effectively supported in the primary years. Within this study, the problem-solving processes of thirty-six primary aged students in an Indigenous community school were evaluated. This was examined by ascertaining students’ problem-solving proficiency on a written test, conducting error analysis from written test scripts, followed by Newman interviews. The findings indicated that supporting students’ strategic competence and productive dispositions were critical in fostering students’ problem-solving success. When students’ strategic competence was supported through a scaffolded Newman interview, students’ problem-solving proficiency increased. Furthermore, the oral and personal nature of Newman interviews acted to significantly increase students’ productive dispositions towards the tasks. These findings have implications for teaching practice and provide tangible points of action that classroom teachers can implement to support Indigenous students’ success in problem-solving.
Similar content being viewed by others
References
Ashlock, R. B. (1976). Error patterns in computation (2d ed.). Columbus, Ohio: Merrill.
Attard, C., Ingram, N., Forgasz, H., Leder, G., & Grootenboer, P. (2016). Mathematics education and the affective domain. In In Research in mathematics education in Australasia 2012–2015 (pp. 73–96). Singapore: Springer.
Australian Association of Mathematics Teachers [AAMT]. (2011). Cluster finding 4.4: risk taking. Retrieved from Make it Count: https://mic.aamt.edu.au/Findings/Professional-Practice/4.-Environment/4.4-Risk-Taking. Accessed 2 June 2020.
Australian Curriculum, Assessment and Reporting Authority. (2018). Mathematics F-10. from the Australian Curriculum: http://www.australiancurriculum.edu.au/Mathematics/
Beresford, Q. (2003). The context of Aboriginal education. In Q. Beresford & G. Partington (Eds.), Reform and resistance in Aboriginal education: the Australian experience (pp. 10–68). Perth: University of Western Australia Press.
Booker, G. (2011). Building numeracy: moving from diagnosis to intervention. Oxford University Press.
Booker, G., Bond, D., Sparrow, L., & Swan, P. (2014). Teaching primary mathematics. Pearson Higher Education AU.
Botha, L. (2011). Mixing methods as a process towards indigenous methodologies. International Journal of Social Research Methodology, 14(4), 313–325.
Bruner, J. (1966). Toward a theory of instruction (Vol. 59). Harvard University Press.
Burrows, L. J. (1976). A review of the literature on computational errors with whole numbers (MEDIC Report 7-76). Vancouver: University of British Columbia, Department of Mathematics Education.
Carpenter, T. P., Hiebert, J., & Moser, J. M. (1983). The effect of instruction on children's solutions of addition and subtraction word problems. Educational Studies in Mathematics, 14(1), 55–72.
Carstairs, J., Myers, B., Shores, E., & Fogarty, G. (2006). Influence of language background on tests of cognitive abilities: Australian data. Australian Psychologist, 41(1), 48–54.
Castella, E. K., Byrne, D., & Covington, M. (2013). Unmotivated or motivated to fail? A cross-cultural study of achievement motivation, fear of failure, and student disengagement. Journal of Educational Psychology, 105(3), 861.
Clarkson, P. (1983). Types of errors made by Papua New Guinean students. Educational Studies in Mathematics, 14(4), 355–367.
Clarkson, P. C. (1991). Language comprehension errors: a further investigation. Mathematics Education Research Journal, 3(2), 24–33.
Clements, M. A. (1980). Analysing children’s errors on written mathematical tasks. Educational Studies in Mathematics, 11(1), 1–21.
Cohen, L. M., Manion, L. L., & Morrison, K. (2011). Research methods in education. New York: Routledge.
Covington, M. V., & Omelich, C. L. (1991). Need achievement revisited: verification of Atkinson’s original 2 x 2 model. In C. D. Spielberger, I. G. Sarason, Z. Kulcsar, & G. L. Van Heck (Eds.), Stress and emotion (14th ed.). New York: Hemisphere.
Davis, H. (2013). Teacher-student relationships. In J. Hattie & E. Anderman (Eds.), International guide to student achievement (pp. 219–221). New York: Routledge.
Denzin, N. K., & Lincoln, Y. S. (2008). Introduction: critical methodologies and indigenous inquiry. Handbook of critical and indigenous methodologies, 1–20.
Department of the Prime Minister and Cabinet. (2018). Closing the Gap Prime minister’s report 2018.
Desoete, A., Roeyers, H., & Buysse, A. (2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disabilities, 34, 435–449.
Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109–132.
Flavell, J. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231–236). Hillsdale: Erlbaum.
Fogarty, G. J., & White, C. (1994). Differences between values of Australian Aboriginal and non-Aboriginal students. Journal of Cross-Cultural Psychology, 25(3), 394–408.
Forgasz, H. J., Leder, G. C., & Halliday, J. (2013). The “Make It Count” project: NAPLAN achievement evaluation. Mathematics Education Research Group of Australasia.
Gorman, D., & Toombs, M. (2009). Matching research methodology with Australian indigenous culture. Aboriginal and Islander Health Worker Journal, 33(3), 4–7.
Groome, H., & Hamilton, A. (1995). Meeting the educational needs of Aboriginal adolescents. Canberra: Australian Government Publishing Service.
Grootenboer, P., & Sullivan, P. (2013). Remote indigenous students’ understanding of measurement. International Journal of Science and Mathematics Education, 11(1), 169–189.
Gutstein, E. (2006). Reading and writing the world with mathematics: toward a pedagogy for social justice. Taylor & Francis.
Guy, G. M., Cornick, J., & Beckford, I. (2015). More than math: on the affective domain in developmental mathematics. International Journal for the Scholarship of Teaching and Learning, 9(2), 7.
Hacker, D. J., & Dunlosky, J. (2003). Not all metacognition is created equal. New Directions for Teaching and Learning, 95, 73–79.
Halse, C., & Robinson, M. (1999). Towards an appropriate pedagogy for Aboriginal children. In R. Craven (Ed.), Teaching Aboriginal studies (pp. 199–213). Sydney: Allen & Unwin.
Hambleton, R. K., & Rodgers, J. (1995). Item bias review. ERIC Clearinghouse on assessment and evaluation, the Catholic University of America, Department of Education.
Harrison, N. (2007). Where do we look now? The future of research in indigenous Australian education. The Australian Journal of Indigenous Education, 36, 1–5.
Hattie, J., & Clarke, S. (2019). Visible learning: feedback. Routledge.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: the case of mathematics. Educational Researcher, 25(4), 12–21.
Hunter, B., & Schwab, R. (2003). Practical reconciliation and recent trends in indigenous education. In Centre for Aboriginal Economic Policy Research Discussion Paper, 249. Canberra: ANU.
Jorgensen, R. (2018). Final report: remote numeracy project. University of Canberra.
Jorgensen, R., Dole, S., & Larkin, K. (2020). Teaching mathematics in primary schools: principles for effective practice. Allen & Unwin.
Klenowski, V. (2014). Towards fairer assessment. The Australian Educational Researcher, 41(4), 445–470.
Leder, G. C., & Forgasz, H. J. (2006). Affect and mathematics education: PME perspectives. In Handbook of research on the psychology of mathematics education (pp. 403-427). Brill Sense.
Martin, A. J. (2006). A motivational psychology for the education of indigenous Australian students. The Australian Journal of Indigenous Education, 35, 30–43.
Martin, K. (2007). Ma (r) king tracks and reconceptualising Aboriginal early childhood education: an Aboriginal Australian perspective. Childrenz Issues: Journal of the Children’s Issues Centre, 11(1), 15.
Martin, A. J., & Marsh, H. W. (2003). Fear of failure: friend or foe? Australian Psychologist, 38, 31–38.
Martin, A. J., Marsh, H. W., & Debus, R. L. (2001). A quadripolar need achievement representation of self-handicapping and defensive pessimism. American Educational Research Journal, 38, 583–610.
Mellor, S., & Corrigan, M. (2004). The cast for change: a review of contemporary research on indigenous education outcomes. Camberwell: Australian Council for Education Research.
Montalvo, G.P. (1997) Pleasing the teacher: an exploration of the construct and its behavioral and motivational patterns. Unpublished doctoral dissertation, The University of Oklahoma.
Morris, C., & Matthews, C. (2011). Numeracy, mathematics and indigenous learners: not the same old thing. Indigenous Education: Pathways to Success, 29–33.
National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. (1st ed.). Reston.
National Health and Medical Research Council. (2015). Chapter 4.7: Aboriginal and Torres Strait Islander Peoples. Retrieved February 17, 2017, from National Statement on Ethical Conduct in Human Research: https://www.nhmrc.gov.au/book/chapter-4-7-aboriginal-and-torres-strait-islander-peoples
National Mathematics Advisory Panel. (2008). Foundations for success: the final report of the National Mathematics Advisory Panel. Washington: U.S. Department of Education.
National Research Council. (2001). Looking at mathematics and learning. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Adding it up: Helping children learn mathematics (pp. 1–16). Washington: National Academy Press.
Newman, M. A. (1983). Strategies for diagnosis and remediation. Sydney: Harcourt, Brace Jovanovich.
Nichol, R., & Robinson, J. (2000). Pedagogical challenges in making mathematics relevant for indigenous Australians. International Journal of Mathematical Education in Science and Technology, 31(4), 495–504.
OECD (2016) Low-performing students: why they fall behind and how to help them succeed, PISA, OECD Publishing, Paris, https://doi.org/10.1787/9789264250246-en.
Özsoy, G., & Ataman, A. (2017). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2), 67–82.
Philipp, R. A., & Siegfried, J. M. (2015). Studying productive disposition: the early development of a construct. Journal of Mathematics Teacher Education, 18(5), 489–499.
Polya, G. (1988). How to solve it. New Jersey: Princeton University Pres.
Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in mathematics Education, 163-172.
Reisman, F. K. (1982). Guide to the diagnostic teaching of arithmetic. Merrill Publishing Company.
Renaud, D. (2013). Attitudes and dispositions. In J. Hattie & E. Anderman (Eds.), International guide to student achievement (pp. 57–58). New York: Routledge.
Sarra, C., (2003). Young and black and deadly: strategies for improving outcomes for Indigenous students. Paper no. 5 in Australian College of Education Quality Teaching Series: Practitioner Perspectives.
Sarra, C. (2009). NAPLAN data. Dr. Chris Sarra: Changing the tide of low expectations in indigenous education.
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. 107–118). Victoria: ACER Press.
Sarra, G., Matthews, C., Ewing, B., & Cooper, T. (2011). Indigenous mathematics: creating an equitable learning environment. In N. Purdie, G. Milgate, & H. Bell (Eds.), Two way teaching and learning: toward culturally reflective and relevant education (pp. 173–185). Victoria: ACER Press.
Schwab, R. G., & Sutherland, D. (2001). Building indigenous learning communities. Discussion paper No.225/2001. Centre for Aboriginal Economic Policy Research, Canberra: The Australian National University.
Thornton, S. (2020) (Re)asserting a knowledge-building agenda in school mathematics. Mathematics Education Research Journal, 1–17.
Urdan, T. (2013). Social motivation and academic motivation. In J. Hattie & E. Anderman (Eds.), International guide to student achievement (pp. 54–56). New York: Routledge.
Vygotsky, L. S. (1978). Mind in society: the development of higher psychological processes. Cambridge: Harvard University Press.
Warren, E., & Miller, J. (2013). Young Australian indigenous students’ effective engagement in mathematics: the role of language, patterns, and structure. Mathematics Education Research Journal, 25(1), 151–171.
White, A. (2005). Active mathematics in classrooms: find out why children make mistakes - and then doing something to help them. Square One, 15(4), 15–19.
Woodward, A., Beswick, K., & Oates, G. N. (2017). The four proficiency strands plus one?: productive disposition and the Australian Curriculum: Mathematics. In MAV17 (pp. 18-24).
Yunkaporta, T. (2009). Aboriginal pedagogies at the cultural interface (Doctoral dissertation, James Cook University).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Reid O’Connor, B., Norton, S. Supporting indigenous primary students’ success in problem-solving: learning from Newman interviews. Math Ed Res J 34, 293–316 (2022). https://doi.org/10.1007/s13394-020-00345-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13394-020-00345-8