Developing a Theoretical Framework to Inform the Design of a Teacher Professional Development Program to Enable Foundation to Year 2 Teachers of Mathematics to Build on Indigenous and Low-SES Students' Cultural Capital

Robyn Anderson, Alexander Stütz, Thomas James Cooper, Rod Nason

Abstract


This paper reports on the early stages of the conceptualisation and implementation of the Accelerated Inclusive Mathematics—Early Understandings (AIM EU) project, a project whose major goals are to advance theory and practice in the improvement of Foundation to Year 2 (F–2) teachers' capacity to teach mathematics and through this to enhance F–2 Indigenous and low-SES students' levels of engagement and learning of mathematics. A design-research methodology was used to achieve the advancement of theory and practice. The major outcome of the research is a revised theoretical framework to inform the design and implementation of culturally relevant mathematics pedagogy for F–2 Indigenous and low-SES students.

Keywords


teacher professional development; multicultural capital; knowledge for teaching; Indigenous students; low-SES students

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Abrams, E., Taylor, P. C., & Guo, C-L. (2013). Contextualizing culturally relevant science and mathematics teaching for Indigenous learners. International Journal of Science and Mathematics Education, 11(1), 1–21.

Achinstein, B., & Aguirre, J. (2008). Cultural match or culturally suspect: How new teachers of color negotiate sociocultural challenges in the classroom. Teachers College Record, 110(8), 1505–1540.

Aguirre, J. M., Turner, E. E., Gau Bartell, T., Kalinec-Craig, C., Foote, M. Q., Roth McDuffie, A., & Drake, C. (2012). Making connections in practice: How prospective elementary teachers connect to children's mathematical thinking and community funds of knowledge in mathematics education. Journal of Teacher Education, 64(2), 178–192. https://doi.org/10.1177/0022487112466900

Aikenhead, G. S. (1996). Science education: Border crossing into the subculture of science. Studies in Science Education, 27(1), 1–52. doi:10.1080/03057269608560077

Australian Curriculum, Assessment and Reporting Authority. (2015). 2015 National Assessment Program—Literacy and Numeracy. Achievement in reading, persuasive writing, language conventions and numeracy: National report for 2015. Retrieved from

http://www.nap.edu.au/_resources/2015_NAPLAN_national_report.pdf

Barton, P. E. (2004). Why does the gap persist? Educational Leadership, 6(3), 8–13.

Belgarde, M., Mitchell, R., & Arquero, A. (2002). What do we have to do to create culturally responsive programs? The challenge of transforming American Indian teacher education. Action in Teacher Education, 24(2), 42–54.

Bishop, R., Berryman, M., Cavanagh, T., & Teddy, L. (2008). A culturally responsive pedagogy of relations: Effective teaching for Māori students. In A. St. George, S. Brown, & J. O'Neill (Eds.), Facing the big questions in teaching: Purpose, power and learning (pp. 165–172). Melbourne: Cengage Learning.

Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608–645.

Bourdieu, P. (1990). Reproduction in education, society, and culture. London: Sage in association with Theory, Culture & Society, Dept. of Administrative and Social Studies, Teesside Polytechnic.

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

Brett, C., Nason, R. A., & Woodruff, E. (2002). Communities of inquiry among pre-service teachers investigating mathematics. THEMES in Education, 3(1), 39–62.

Brogan, R. (2009). Relations between school outcomes and school SES. Retrieved from http://www.education.com/reference/article/socioeconomic-status/

Buckskin, P. (2012). Engaging Indigenous students: The important relationship between Aboriginal and Torres Strait Islander students and their teachers. In K. Price (Ed.), Aboriginal and Torres Strait Islander Education. Port Melbourne, VIC: Cambridge University Press.

Buxton, L. (2017). Ditching deficit thinking: Changing to a culture of high expectations. Issues in Educational Research, 27(2), 198–214.

Cambourne, B., Ferry, B., & Kiggins, J. (2003). The knowledge building community odyssey: Reflections on the journey. Change: Transformations in Education, 6(2), 57–66.

Carter, P. L. (2005). Keepin' it real: School success beyond Black and White. New York, NY: Oxford University Press.

Chalmers, C., Carter, M., Cooper, T., & Nason, R. (2017). Implementing "big ideas" to advance the teaching and learning of science, technology, engineering and mathematics (STEM). International Journal of Science and Mathematics Education, 15(Suppl 1), 25–43. doi:10.1007/s10763-017-9799-1

Chalmers, C., & Nason, R. (2017). Systems thinking approach to robotics curriculum in schools. In M. S. Khine (Ed.), Robotics in STEM education: Redesigning the learning experience (pp. 33–57). Cham, Switzerland: Springer International Publishing.

Charles, R. I. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Mathematics Education Leadership, 7(3), 9–24.

Claussen, S., & Osborne, J. (2012). Bourdieu's notion of cultural capital and its implications for the science curriculum. Science Education, 97(1), 58–79. doi:10.1002/sce.21040

Comber, B., & Hill, S. (2000) Socio-economic disadvantage, literacy and social justice: Learning from longitudinal case study research. Australian Educational Researcher, 27(3), 79–97.

Connolly, S. (2012). Students' cultural capital: A study of assessment for learning as a field of exchange (Unpublished PhD thesis). Queensland University of Technology, Brisbane, QLD.

Cooper, T. J., Carter, M. G., & Lowe, J. A. (2016). Using the big ideas of mathematics to "close the gap". In C. Csíkos, A. Rausch, & J. Szitányi (Eds.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 171–178). Szeged, Hungary: PME.

Cooper, T. J., & Warren, E. (2011). Years 2 to 6 students' ability to generalise: Models, representations and theory for teaching and learning. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 187–214), Advances in Mathematics Education. Berlin Heidelberg: Springer-Verlag. doi:10.1007/978-3-642-17735-4_12

Cuoco, A., Goldenberg, E. P., & Mark, J. (2010). Contemporary curriculum issues: Organizing a curriculum around mathematical habits of mind. Mathematics Teacher, 103(9), 682–688.

Davydov, V. V. (1975a). Logical and psychological problems of elementary mathematics as an academic subject. In L. P. Steffe (Ed.), Children's capacity for learning mathematics. Soviet studies in the psychology of learning and teaching mathematics (Vol. VII, pp. 55–107). Chicago: University of Chicago.

Davydov, V. V. (1975b). The psychological characteristics of the "prenumerical" period of mathematics instruction. In L. P. Steffe (Ed.), Children's capacity for learning mathematics. Soviet studies in the psychology of learning and teaching mathematics (Vol. VII, pp. 109–205). Chicago: University of Chicago.

Davydov, V. V. (1990). Types of generalization in instruction: Logical and psychological problems in the structuring of school curricula. Soviet studies in mathematics education (Vol. 2). Reston, VA: National Council of Teachers of Mathematics.

Delpit, L. (1992) Acquisition of literate discourse: Bowing before the master? Theory into practice, 31(4), 296–302.

Dockery, A. M. (2009). Culture and wellbeing: The case of Indigenous Australians (CLMR Discussion Paper Series 09/01). Perth: The Centre for Labour Market Research. Retrieved from http://ceebi.curtin.edu.au/local/docs/2009.01_CultureWellbeing.pdf

Dougherty, B., & Zilliox, J. (2003). Voyaging from theory and practice in teaching and learning: A view from Hawai'i. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 31–46). College of Education, Honolulu: University of Hawaii.

Enyedy, N., & Mukhopadhyay, S. (2007). They don't show nothing I didn't know: Emergent tensions between culturally relevant pedagogy and mathematics pedagogy. Journal of the Learning Sciences, 16(2), 139–174. doi:10.1080/10508400701193671

Ernest, P. (n.d.). What is the philosophy of mathematics education? Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.197.5854&rep=rep1&type=pdf

Fotheringham, P. (2012). What works. The Work Program. Success in remote schools: A research study of eleven improving remote schools. Abbotsford, VIC: National Curriculum Services Pty Ltd. Retrieved from http://www.whatworks.edu.au/upload/1341805220784_file_SuccessinRemoteSchools2012.pdf

Frigo, T., Corrigan, M., Adams, I., Hughes, C., Stephens, M., & Woods, D. (2003). Supporting English literacy and numeracy learning for Indigenous students in the early years (ACER Monograph 57). Camberwell, VIC: Australian Council for Educational Research.

Frigo, T., & Simpson, L. (2001). Research into the numeracy development of Aboriginal students: Implications for the NSW K–10 Mathematics Syllabus. Sydney: Office of the Board of Studies New South Wales.

Gay, G. (2002). Preparing for culturally responsive teaching. Journal of Teacher Education, 53(1), 106–116.

Gay, G. (2010). Culturally responsive teaching: Theory, research, and practice (2nd ed.). New York, NY: Teachers College Press.

Giroux, H. (1990). Reading texts, literacy, and textual authority. Journal of Education, 172(1), 85–103.

Goldenberg, B. M. (2014). White teachers in urban classrooms: Embracing non-white students' cultural capital for better teaching and learning. Urban Education, 49(1), 111–144.

Griffin, P., Care, E., Hutchinson, D., Arratia-Martinez, A., & McCabe, C. (2013). Assessment and learning partnerships: The influence of teaching practices on student achievement. Melbourne: Assessment Research Centre, The University of Melbourne.

Grootenboer, P., & Sullivan, P. (2013). Remote indigenous students' understanding of measurement. International Journal of Science and Mathematics Education, 11(1), 169–189.

Gurung, N., & Hayne, A. (2009). Exploring signature pedagogies: Approaches to teaching disciplinary habits of mind. Sterling, VA: Stylus Publishing.

Guskey, T. R. (2003). What makes professional development effective? Phi Delta Kappan, 84(10), 748–750.

Gutiérrez, R. (2007). Context matters: Equity, success, and the future of mathematics education. In T. Lamberg & L. R. Wiest (Eds.), Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1–18). Reno: University of Nevada.

Gutiérrez, R. (2008). A "gap-gazing" fetish in mathematics education? Problematizing research on the achievement gap. Journal for Research in Mathematics Education, 39(4), 357–364.

Howard, T. C. (2003). Culturally relevant pedagogy: Ingredients for critical teacher reflection. Theory into Practice, 42(3), 195–202. http://dx.doi.org/10.1207/s15430421tip4203_5

Huang, C-H., & Lin, F-L. (2013). Using activity theory to model Atayal students' classroom mathematical activity. International Journal of Science and Mathematics Education, 11(1), 213–236.

Kelly, A. E. (2004). Design research in education: Yes, but is it methodological? Journal of the Learning Sciences, 13(1), 115–128.

Kidman, J., Yen, C-F., & Abrams, E. (2013). Indigenous students' experiences of the hidden curriculum in science education: A cross-national study in New Zealand and Taiwan. International Journal of Science and Mathematics Education, 11(1), 43–64.

Krakouer, J. (2015). Literature review relating to the current context and discourse on Indigenous cultural awareness in the teaching space: Critical pedagogies and improving Indigenous learning outcomes through cultural responsiveness. Camberwell, VIC: Australian Council for Educational Research.

Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Education Research Journal, 32, 465–491.

Leonard, J., Brooks, W., Barnes-Johnson, J., & Berry, R. Q. (2010). The nuances and complexities of teaching mathematics for cultural relevance and social justice. Journal of Teacher Education, 61(3), 261–270.

Lewthwaite, B. E., Owen, T., Doiron, A., Renaud, R., & McMillan, B. (2014). Culturally responsive teaching in Yukon First Nations settings: What does it look like and what is its influence? Canadian Journal of Educational Administration and Policy, 155(1), 1–34.

Luitel, B. C. (2013). Mathematics as an im/pure knowledge system: Symbiosis, (w)holism and synergy in mathematics education. International Journal of Science and Mathematics Education, 11(1), 65–87.

MacDonald, A., & Lowrie, T. (2011). Developing measurement concepts within context: Children's representations of length. Mathematics Education Research Journal, 23(1), 27–42.

Martin, K. L. (2009). Aboriginal worldview, knowledge and relatedness: Reconceptualising Aboriginal schooling as a teaching-learning and research interface. Journal of Australian Indigenous Issues, 12(4), 66–78.

Martin, L. C. (2008). Folding back and the dynamical growth of mathematical understanding: Elaborating the Pirie-Kieren theory. The Journal of Mathematical Behavior, 27(1), 64–85.

Matthews, C. (2009). Stories and symbols: Maths as storytelling. Professional Voice, 6(3), 45–50. Retrieved from https://issuu.com/aeu-vic/docs/pv_6_3/1?e=1350839/5379655

Matthews, L. E. (2003). Babies overboard! The complexities of incorporating culturally relevant teaching into mathematics instruction. Educational Studies in Mathematics, 53(1), 61–82.

McKinley, E. (2007). Postcolonialism, Indigenous students, and science education. In S. K. Abell & N. G. Lederman (Eds.), Handbook of research in science education (pp. 199–226). Mahwah, NJ: Lawrence Erlbaum.

McTaggart, R., & Curró, G. (2009). Book language as a foreign language: ESL strategies for Indigenous learners. Towong, QLD: Queensland College of Teachers.

Meyer, C. K., Vines, N. A., & Shankland, R. K. (2012). Designing high-quality professional development: Scaffolding secondary content-area teachers’ discipline literacy instruction. American Reading Forum Annual Yearbook [Online] (Vol. 32). Retrieved from

www.americanreadingforum.org/yearbook/12_yearbook/documents/Meyer-C-K-Vines-N-A-Shankland-R-K-(2012).pdf

Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd ed.). Newbury Park, CA: Sage.

Mills, C. (2008). Reproduction and transformation of inequalities in schooling: The transformative potential of the theoretical constructs of Bourdieu. British Journal of Sociology of Education, 29(1), 79–89.

Moll, L. C., Amanti, C., Neff, D., & González, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory into Practice, 31 (2), 132–141.

Moll, L. C., & González, N. (2004). Engaging life: A funds-of-knowledge approach to multicultural education. In J. Banks & C. A. McGee Banks (Eds.), Handbook of research on multicultural education (pp. 699–715). San Francisco, CA: Jossey-Bass.

Nakata, M. (2007). The cultural interface. The Australian Journal of Indigenous Education, 36(Supplement), 7–14.

Nam, Y., Roehrig, G., Kern, A., & Reynolds, B. (2013). Perceptions and practices of culturally relevant science teaching in American Indian classrooms. International Journal of Science and Mathematics Education, 11(1), 143–167.

Nason, R. A., Chalmers, C. A., & Yeh, A. (2012). Facilitating growth in prospective teachers' knowledge: Teaching geometry in primary schools. Journal of Mathematics Teacher Education, 15(3), 227–249.

Niemi, D., Vallone, J., & Vendlinski, T. (2006). The power of big ideas in mathematics education: Development and pilot testing of POWERSOURCE assessments (CSE Report 697). Los Angeles, CA: National Center for Research on Evaluation, Standards, and Student Testing (CRESST), University of California.

Nieto, S. (2004). Affirming diversity: The sociopolitical context of multicultural education (4th ed.). New York, NY: Pearson.

Owens, K. (2015). Changing the teaching of mathematics for improved Indigenous education in a rural Australian city. Journal of Mathematics Teacher Education, 18(1), 53–78.

Parhar, N., & Sensoy, O. (2011). Culturally relevant pedagogy redux: Canadian teachers' conceptions of their work and its challenges. Canadian Journal of Education, 34(2), 189–218.

Parker, F., Bartell, T. G., & Novak, J. D. (2017). Developing culturally responsive mathematics teachers: secondary teachers' evolving conceptions of knowing students. Journal of Mathematics Teacher Education, 20(3), 385–407.

Renshaw, P. (1992, November). The sociocultural theory of teaching and learning: Implications for the curriculum in the Australian context. Paper presented at the Twenty-Second Annual Conference of the Australian Association for Research in Education, Deakin University, Geelong, Victoria. Retrieved from http://webpages.charter.net/schmolze1/vygotsky/renshaw.html

Renshaw, P., Baroutsis, A., van Kraayenoord, C., Goos, M., & Dole, S. (2013). Teachers using classroom data well: Identifying key features of effective practices (Final Report). Brisbane: The University of Queensland.

Roehrig, G. H., Campbell, K. M., Dalbotten, D., & Varma, K. (2012). CYCLES: A culturally-relevant approach to climate change education in native communities. Journal of Curriculum and Instruction, 6(1), 73–89.

Sarra, C. (2009, September). Indigenous leadership in education institute. Paper presented at the Stronger Smarter Summit, Brisbane.

Sarra, C. (2010). Stronger smarter approaches to Indigenous leadership in Australia. In I. Snyder & J. Nieuwenhuysen (Eds.), Closing the gap in education? Melbourne: Monash University Publishing. Retrieved from http://www.publishing.monash.edu.au/books/cge.html

Sarra, C. (2011). Strong and Smart – Towards a pedagogy for emancipation: Education for first peoples. Abingdon, UK: Routledge.

Schmittau, J., & Morris, A. (2004). The development of algebra in the elementary mathematics curriculum of V. V. Davydov. The Mathematics Teacher, 8(1), 60–87.

Schoenfeld, A. H. (2016). Solving the problem of powerful instruction. In C. Csíkos, A. Rausch, & J. Szitányi, (Eds.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 3–18). Szeged, Hungary: PME.

Snow, C. E., Griffin, P., & Burns, M. S. (Eds.). (2005). Knowledge to support the teaching of reading: Preparing teachers for a changing world. San Francisco, CA: Jossey-Bass.

Spina, N., Carter, M., Cooper, T., Cottier, C., Farrington, G., & Stütz, A. (2017). YuMi Deadly Centre impact evaluation report, March 2017. Retrieved from http://ydc.qut.edu.au/about/evidence-of-effectiveness.jsp

Sullivan, A. (2002). Bourdieu and education: How useful is Bourdieu's theory for researchers? The Netherlands' Journal of Social Sciences, 38(2), 144–166.

Teach For Australia. (2016). Australia's PISA results show educational disadvantage gap remains. Retrieved from http://www.teachforaustralia.org/2016/12/07/australias-pisa-results-show-educational-disadvantage-gap-remains/

Thornton, S., De Bortoli, L., & Buckley, S. (2013). PISA 2012: How Australia measures up. Camberwell, VIC: Australian Council for Educational Research.

Trumbull, E., & Pacheco, M. (2005). The teacher's guide to diversity: Building a knowledge base. Volume 1: Human development, culture and cognition. The Education Alliance at Brown University. Retrieved from http://indiana.edu/~pbisin/resources/TeacherGuideVol1.pdf

Valencia, R. R., & Solórzano, D. G. (1997). Contemporary deficit thinking. In R. R. Valencia (Ed.). The evolution of deficit thinking: Educational thought and practice (pp. 160–210). London: Routledge Falmer.

Venenciano, L. & Dougherty, B. (2014). Addressing priorities for elementary school mathematics. For the Learning of Mathematics, 34(1), 18–24.

Warren, E., & Cooper, T. J. (2009). Developing mathematics understanding and abstraction: The case of equivalence in the elementary years. Mathematics Education Research Journal, 21(2), 76–95.

Warren, E. A., 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). http://dx.doi.org/10.14221/ajte.2012v37n6.1

Weinstein, C. S., Tomlinson-Clarke, S., & Curran, M. (2004). Toward a conception of culturally responsive classroom management. Journal of Teacher Education, 55(1), 25–38. doi:10.1177/0022487103259812

Yin, R. K. (2003). Case study research: Design and methods (3rd ed., Vol. 5). Thousand Oaks: Sage Publications.

Yosso, T. (2005). Whose culture has capital? A critical race theory discussion of community cultural wealth. Race, Ethnicity and Education, 8(1), 69–91.

YuMi Deadly Centre. (2014a). YuMi Deadly Maths: Big ideas for mathematics – Prep to Year 9. Kelvin Grove: Queensland University of Technology.

YuMi Deadly Centre. (2014b). YuMi Deadly Maths: Overview – philosophy, pedagogy, change and culture. Kelvin Grove: Queensland University of Technology.


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