Forging New Opportunities for Problem Solving in Australian Mathematics Classrooms through the First National Mathematics Curriculum

Abstract

Although the Federal government in Australia has tried on previous occasions to exert a greater influence on curriculum development, curriculum development was the responsibility of each of the eight states and territories until quite recently. The new Labour Government in 2007 has employed increased central control and accountability measures, with national testing in grades 3, 5, 7 and 9 from 2008, publication of school results on a MySchool website, and the development of the first national curriculum in English, Mathematics, Science and History. States are still responsible for implementation, but the new funding model means they must comply with national curriculum implementation up to grade 10. Developing the first national curriculum for mathematics has been a challenge, but a plan of mathematics learning for each grade level organised into three content strands has now been developed. In addition, four proficiency (or process) strands describe the actions associated with doing mathematics. Since problem solving has been a key component of previous curriculum documents and there is evidence of limited use of complex problem solving in some Australian mathematics classrooms, the representation of problem solving in curriculum documents is examined in this chapter to explore whether the new national curriculum for Australia forges new opportunities for teachers and students.

Keywords

National curriculum Historical perspectives Problem solving Proficiencies Teacher interpretation Authentic problems 

References

  1. ACARA (2010a). Australian curriculum information sheet: why have an Australian curriculum? Sydney: ACARA. Google Scholar
  2. ACARA (2010b). Australian curriculum: mathematics F to 10. Sydney: ACARA. Google Scholar
  3. ACARA (2012). Australian curriculum: mathematics, version 3.0. Downloaded 3rd February 2012 from http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10.
  4. Anderson, J. (1996). Some teachers’ beliefs and perceptions of problem solving. In P. Clarkson (Ed.), Technology in mathematics education, Proceedings of the 19 th annual conference of MERGA (pp. 30–37). Melbourne: Deakin University Press. Google Scholar
  5. Anderson, J. (1997). Teachers’ reported use of problem-solving teaching strategies in primary mathematics classrooms. In F. Biddulph & K. Carr (Eds.), People in mathematics education, Proceedings of the 20th annual conference of MERGA (pp. 50–57). Melbourne: Deakin University Press. Google Scholar
  6. Anderson, J. (2002). Development and overall changes to the K_10 mathematics syllabuses. Reflections, 27(4), 14–20. Google Scholar
  7. Anderson, J. (2003). Teachers’ choice of tasks: a window into beliefs about the role of problem solving in learning mathematics. In L. Bragg, C. Campbell, G. Herbert, & J. Mousley (Eds.), Mathematics education research: innovation, networking, opportunity, Proceedings of the 26th annual conference of the mathematics education research group of Australasia, Geelong, Victoria (pp. 72–79). Google Scholar
  8. Anderson, J. (2005). Implementing problem solving in mathematics classrooms: what support do teachers want? In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: theory, research and practice, Proceedings of the 28th annual conference of the mathematics education research group of Australasia, Melbourne, Victoria (pp. 89–96). Google Scholar
  9. Anderson, J., & Bobis, J. (2005). Reform-oriented teaching practices: a survey of primary school teachers. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 65–72). Melbourne: PME. Google Scholar
  10. Anderson, J., & Moore, M. (2005). Evaluating the professional learning of secondary mathematics teachers: reflecting on their reflections! In Proceedings of the Australian association for research in education’s 35th annual international education research conference, Sydney, Australia (ISSN 1324-9320). Published at http://www.aare.edu.au/05pap/and05154.pdf. Google Scholar
  11. Anderson, J., Sullivan, P., & White, P. (2004). The influence of perceived constraints on teachers’ problem-solving beliefs and practices. In I. Putt, R. Faragher, & M. McLean (Eds.), Mathematics education for the third millennium: towards 2010, Proceedings of the 27th annual conference of the mathematics education research group of Australasia (pp. 39–46). Townsville: MERGA. Google Scholar
  12. Anderson, J., White, P., & Wong, M. (2012). Mathematics curriculum in the schooling years. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenlees (Eds.), Research in mathematics education in Australasia 2008-2011 (pp. 219–244). Rotterdam: Sense Publishers. CrossRefGoogle Scholar
  13. Atweh, B., & Goos, M. (2011). The Australian mathematics curriculum: a move forward or back to the future? Australian Journal of Education, 55(3), 214–228. CrossRefGoogle Scholar
  14. Atweh, B., Goos, M., Jorgensen, R., & Siemon, D. (Eds.) (2012a). Engaging the Australian curriculum mathematics: perspectives from the field. Online publication of MERGA. http://www.merga.net.au/sites/default/files/editor/books/1/Book.pdf.
  15. Atweh, B., Miller, D., & Thornton, S. (2012b). The Australian curriculum: mathematics—world class or déjà vu? In B. Atweh, M. Goos, R. Jorgensen, & D. Siemon (Eds.), Engaging the Australian curriculum mathematics: perspectives from the field (pp. 1–18). Online publication of MERGA http://www.merga.net.au/sites/default/files/editor/books/1/Book.pdf.
  16. Atweh, B., & Singh, P. (2011). The Australian curriculum: continuing the national conversation. Australian Journal of Education, 55(3), 189–196. CrossRefGoogle Scholar
  17. Australian Association of Mathematics Teachers [AAMT] (2010). AAMT response to the draft K-10 Australian curriculum: mathematics. Adelaide: AAMT. Google Scholar
  18. Barry, B., et al. (1988). HBJ year 6 mathematics. Sydney: Harcourt Brace Jovanovich. Google Scholar
  19. Board of Secondary Education NSW (1989). Syllabus years 7–8. North Sydney: Board of Secondary Education. Google Scholar
  20. Board of Studies NSW [BOSNSW] (1996). Mathematics years 9–10 syllabus—advanced, intermediate and standard courses. Sydney: BOS NSW. Google Scholar
  21. Board of Studies NSW (1998). Mathematics K-6 outcomes and indicators. Sydney: BOS NSW. Google Scholar
  22. Board of Studies NSW (1999). Mathematics years 7–8 syllabus outcomes. Sydney: BOS NSW. Google Scholar
  23. Board of Studies NSW (2003). Mathematics years 7–10 syllabus. Sydney: BOS NSW. Google Scholar
  24. Cavanagh, M. (2006). Mathematics teachers and working mathematically: responses to curriculum change. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures and learning spaces, Proceedings of the 29th annual conference of the mathematics research group of Australasia (pp. 115–122). Adelaide: MERGA. Google Scholar
  25. Clarke, B. (2009). Using tasks involving models, tools and representations: insights from a middle years mathematics project. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides. Proceedings of the 32nd MERGA annual conference (Vol. 2, pp. 718–721). Palmerston North: MERGA. Google Scholar
  26. Clarke, D., Goos, M., & Morony, W. (2007). Problem solving and working mathematically: an Australian perspective. ZDM Mathematics Education, 39(5–6), 475–490. CrossRefGoogle Scholar
  27. Clements, D. H. (2007). Curriculum research: towards a framework for research-based curricula. Journal for Research in Mathematics Education, 38, 35–70. Google Scholar
  28. Curriculum Corporation (1994). Mathematics—a curriculum profile for Australian schools. Carlton: Curriculum Corporation. Google Scholar
  29. Ellerton, N., & Clements, M. (Ken) (1994). The national curriculum debacle. Perth: Meridian Press. Google Scholar
  30. Handal, B., & Herrington, A. (2003). Mathematics teachers’ beliefs and curriculum reform. Mathematics Education Research Journal, 15(1), 59–69. CrossRefGoogle Scholar
  31. Harel, G. & Confrey, J. (Eds.) (1994). The development of multiplicative reasoning in the learning of mathematics. Albany: State University of New York Press. Google Scholar
  32. Hollingsworth, H., Lokan, J., & McCrae, B. (2003). Teaching mathematics in Australia: results from the TIMSS 1999 video study. Camberwell: Australian Council of Educational Research. Google Scholar
  33. Kennedy, K. (2005). Charting the global contexts of the school curriculum: why curriculum solutions are never simple. In C. Harris & C. Marsh (Eds.), Curriculum developments in Australia: promising initiatives, impasses and dead-ends (pp. 1–14). Deakin West: Australian Curriculum Studies Association. Google Scholar
  34. Kennedy, K. (2009). The idea of a national curriculum in Australia: what do Susan Ryan, John Dawkins and Julia Gillard have in common? Curriculum Perspectives, 29(1). Google Scholar
  35. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.) (2001). Adding it up: helping children learn mathematics. Washington: National Academy Press. Google Scholar
  36. Lester, F. K. (1994). Musings about problem-solving research: 1970–1994. Journal for Research in Mathematics Education, 25(6), 660–675. CrossRefGoogle Scholar
  37. Lovitt, C., & Clarke, D. (1988). Mathematics curriculum and teaching program (MCTP) activity bank—volumes 1 and 2. Canberra: Curriculum Development Centre. Google Scholar
  38. Lovitt, S., & Clarke, D. (2011). The features of a rich and balanced mathematics lesson: teacher as designer. Educational Designer, 1(4), 1–25. Google Scholar
  39. Marsh, C. (Ed.) (2010). Curriculum over 30 years: what have we achieved? Canberra: Australian Curriculum Studies Association. Google Scholar
  40. Mathematics Education Research Group of Australasia [MERGA] (2010). MERGA response to the Australian curriculum (mathematics), MERGA, May 2010. http://www.merga.net.au/node/49.
  41. McGaw, B. (2010). President’s report: transforming school education. Dialogue, 29(1). Available: www.assa.edu.au/publications/dialogue/2010_Vol29_No1.php.
  42. Ministerial Council of Education, Employment, Training and Youth Affairs [MCEETYA] (2008). Melbourne declaration on educational goals for young Australians. Carlton Sth: MCEETYA. Google Scholar
  43. Morony, W. (2011). Messages about progress to date on the Australian curriculum: mathematics. Curriculum Perspectives, 11(1), 62–65. Google Scholar
  44. National Council of Teachers of Mathematics [NCTM] (1989). Curriculum and evaluation standards for school mathematics. Reston: NCTM. Google Scholar
  45. National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston: NCTM. Google Scholar
  46. National Curriculum Board (2008). National mathematics curriculum: framing paper. Barton: NCB. Google Scholar
  47. National Curriculum Board (2009). Shape of the Australian curriculum: mathematics. Barton: NCB. Google Scholar
  48. NSW Department of Education (1989). Mathematics K-6. Sydney: NSW Department of Education. Google Scholar
  49. Piper, K. (1989). National curriculum: prospects and possibilities. Curriculum Perspectives, 9(3), 3–7. Google Scholar
  50. Polya, G. (1945). How to solve it. Princeton: Princeton University Press. Google Scholar
  51. Reid, A. (2005). The politics of national curriculum collaboration: how can Australia move beyond the railway gauge metaphor? In C. Harris & C. Marsh (Eds.), Curriculum developments in Australia: promising initiatives, impasses and dead-ends (pp. 39–51). Deakin West: Australian Curriculum Studies Association. Google Scholar
  52. Robitaille, D., Schmidt, W., Raizen, S., & McKnight, C. (1996). Curriculum frameworks for mathematics and science. Google Scholar
  53. Schoenfeld, A. H. (2007). Problem solving in the United States, 1970–2008: research and theory, practice and politics. ZDM Mathematics Education, 39(5–6), 537–551. CrossRefGoogle Scholar
  54. Siemon, D. (2011). Realising the ‘big ideas’ in number—vision impossible? Curriculum Perspectives, 31(1), 66–69. Google Scholar
  55. Siemon, D., & Booker, G. (1990). Teaching and learning FOR, ABOUT and THROUGH problem solving. Vinculum, 27(2), 4–12. Google Scholar
  56. Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents. Journal of Mathematical Behaviour, 24, 341–350. CrossRefGoogle Scholar
  57. Sullivan, P. (2011). Teaching mathematics: using research-informed strategies. Camberwell: Australian Council for Educational Research. Google Scholar
  58. Sullivan, P. (2012). The Australian curriculum: mathematics as an opportunity to support teachers and improve student learning. In B. Atweh, M. Goos, R. Jorgensen, & D. Siemon (Eds.), Engaging the Australian curriculum mathematics: perspectives from the field (pp. 175–189). Online publication of MERGA http://www.merga.net.au/sites/default/files/editor/books/1/Book.pdf. Google Scholar
  59. Thomson, S., De Bortoli, L., Nicholas, M., Hillman, K., & Buckley, S. (2010). Challenges for Australian education: results from PISA 2009. Melbourne: Australian Council for Educational Research. Google Scholar
  60. Thornton, S. (2011). In search of uncertainty. Curriculum Perspectives, 31(1), 74–76. Google Scholar
  61. Vincent, J. (2004). The numeracy research and development initiative projects. Australian Primary Mathematics Classroom, 9(4), 4–9. Google Scholar
  62. Yates, L., Collins, C., & O’Connor, K. (Eds.) (2011a). Australia’s curriculum dilemmas: state cultures and the big issues. Carlton: Melbourne University Press. Google Scholar
  63. Yates, L., Collins, C., & O’Connor, K. (2011b). Australian curriculum making. In L. Yates, C. Collins, & K. O’Connor (Eds.), Australia’s curriculum dilemmas: state cultures and the big issues (pp. 3–22). Carlton: Melbourne University Press. Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.The University of SydneySydneyAustralia

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