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Teaching Simultaneous Linear Equations: A Case of Realistic Ambitious Pedagogy

  • Yew Hoong LeongEmail author
  • Eng Guan Tay
  • Khiok Seng Quek
  • Sook Fwe Yap
Chapter
Part of the Mathematics Education – An Asian Perspective book series (MATHEDUCASPER)

Abstract

In this chapter, we present a conceptualisation of mathematics teaching and learning which we term realistic ambitious pedagogy. We locate this pedagogy within the domains of teaching goals and teaching enactment, and the interactions between them. We argue that it is a suitable pedagogy for use in teacher development enterprises because it takes into deliberate consideration the realistic constraints within which teachers work while pursuing ambitious goals of mathematics teaching. To illustrate, we provide an example taken from our work of redesigning a curriculum unit on simultaneous linear equations in two variables with some Year 8 mathematics teachers in Singapore.

Keywords

Realistic ambitious pedagogy Teaching goals Teacher professional development 

References

  1. Amador, J., & Lamberg, T. (2013). Learning trajectories, lesson planning, affordances, and constraints in the design and enactment of mathematics teaching. Mathematical Thinking and Learning, 15(2), 146–170.  https://doi.org/10.1080/10986065.2013.770719.CrossRefGoogle Scholar
  2. Assude, T. (2005). Time management in the work economy of a class, a case study: Integration of Cabri in primary school mathematics teaching. Educational Studies in Mathematics, 59(1–3), 183–203.  https://doi.org/10.1007/s10649-005-5888-0.CrossRefGoogle Scholar
  3. Barksdale-Ladd, M. A., & Thomas, K. F. (2000). What’s at stake in high-stakes testing: Teachers and parents speak out. Journal of Teacher Education, 51(5), 384–397.  https://doi.org/10.1177/0022487100051005006.CrossRefGoogle Scholar
  4. Charles, R. I. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. NCSM Journal of Mathematics Education Leadership, 7(3), 9–24.Google Scholar
  5. Diamond, J. B., & Spillane, J. P. (2004). High-stakes accountability in urban elementary schools: Challenging or reproducing inequality. Teachers College Record, 106(6), 1145–1176.CrossRefGoogle Scholar
  6. Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York, NY: Macmiillan Publishing Company.Google Scholar
  7. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., et al. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Education Researcher, 25(4), 12–21.  https://doi.org/10.3102/0013189X025004012.CrossRefGoogle Scholar
  8. Jones, A. M. (2012). Mathematics teacher time allocation (Master’s thesis, Brigham Young University, Provo, UT). Retrieved from http://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4492&context=etd
  9. Kazemi, E., Lampert, M., & Franke, M. (2009). Developing pedagogies in teacher education to support novice teacher’s ability to enact ambitious instruction. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia. Wellington, New Zealand (Vol. 1, pp. 11–29). Palmerston North, New Zealand: Mathematics Education Research Group of Australasia.Google Scholar
  10. Keiser, J. M., & Lambdin, D. V. (1996). The clock is ticking: Time constraint issues in mathematics teaching reform. The Journal of Educational Research, 90(1), 23.CrossRefGoogle Scholar
  11. Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge, United Kingdom: Cambridge University Press.CrossRefGoogle Scholar
  12. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29–63.  https://doi.org/10.3102/00028312027001029.CrossRefGoogle Scholar
  13. Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.Google Scholar
  14. Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., & Franke, M. (2010). Using designed instructional activities to enable novices to manage ambitious mathematics teaching. In M. K. Stein & L. Kucan (Eds.), Instructional Explanations in the Disciplines (pp. 129–141). New York, NY: Springer Science + Business Media.CrossRefGoogle Scholar
  15. Leong, Y. H., & Chick, H. L. (2007/2008). An insight into the ‘Balancing Act’ of teaching. Mathematics Teacher Education and Development, 9, 51–65.Google Scholar
  16. Leong, Y. H., & Chick, H. L. (2011). Time pressure and instructional choices when teaching mathematics. Mathematics Education Research Journal, 23(3), 347–362.CrossRefGoogle Scholar
  17. Leong, Y. H., Chick, H. L., & Moss, J. (2007). Classroom research as teacher-researcher. The Mathematics Educator, 10(2), 1–26.Google Scholar
  18. Leong, Y. H., Tay, E. G., Toh, T. L., Quek, K. S., Toh, P. C., & Dindyal, J. (2016a). Infusing mathematical problem snolving in the mathematics curriculum: Replacement Units. In P. Felmer, E. Perhkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 309–326). Geneva: Springer.CrossRefGoogle Scholar
  19. Leong, Y. H., Tay, E. G., Toh, T. L., Yap, R. A. S, Toh, P. C., Quek, K. S., & Dindyal, J. (2016b). Boundary objects within a replacement unit strategy for mathematics teacher development. In B. Kaur, O. N. Kwon, & Y. H. Leong (Eds.), Professional development of mathematics teachers: An Asian perspective (pp. 189–208). Singapore: Springer.Google Scholar
  20. Lester, F. K. (Ed.). (2003). Teaching mathematics through problem solving: Prekindergarten - Grade 6. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  21. Meek, C. (2003). Classroom crisis: It’s about time. Phi Delta Kappan, 84(8), 592.CrossRefGoogle Scholar
  22. National Education Commission on Time and Learning. (1994/2005). Prisoners of time: Report of the National Education Commission on Time and Learning. Washington, DC: Education Commission of the States.Google Scholar
  23. Plank, S. B., & Condliffe, B. F. (2013). Pressures of the season: An examination of classroom quality and high-stakes accountability. American Educational Research Journal, 50(5), 1152–1182.  https://doi.org/10.3102/0002831213500691.CrossRefGoogle Scholar
  24. Schielack, J. F., & Chancellor, D. (2010). Mathematics in focus, K-6: How to help students understand big ideas and make critical connections. Portsmouth, NH: Heinemann.Google Scholar
  25. Schoen, H. L. (Ed.). (2003). Teaching mathematics through problem solving: Grades 6-12. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  26. Valli, L., & Buese, D. (2007). The changing role of teachers in an era of high-stakes accountability. American Educational Research Journal, 44(3), 519–558.  https://doi.org/10.3102/0002831207306859.CrossRefGoogle Scholar
  27. Wu, M., & Zhang, D. (2006). An overview of the mathematics curricula in the West and East. In F. K. S. Leung, K.-D. Graf, & F. Lopez-Real (Eds.), Mathematics education in different cultural traditions: A comparative study of East Asia and the West (pp. 181–193). New York, NY: Springer.CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Yew Hoong Leong
    • 1
    Email author
  • Eng Guan Tay
    • 1
  • Khiok Seng Quek
    • 1
  • Sook Fwe Yap
    • 1
  1. 1.National Institute of EducationSingaporeSingapore

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