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Teaching Simultaneous Linear Equations: A Case of Realistic Ambitious Pedagogy

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Mathematics Education in Singapore

Part of the book series: Mathematics Education – An Asian Perspective ((MATHEDUCASPER))

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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.

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Notes

  1. 1.

    Here, the lower case letters r and d are used to label the goals. This is to make a distinction between this set of goals and the goals listed in the previous section of this paper where they were labelled with capital letters R and D. The relationship between the r- and d-goals and the R- and D-goals respectively is roughly one of subordination. For example, fulfilling r1 within the teaching of this unit supports the fulfilment of some more broad-grained R-goals (such as R1).

  2. 2.

    The task may appear at first look to be a repetition of contents taught in earlier lessons. In Lesson 4, the teacher has moved to teaching the method of elimination. Here, students were asked to use this newly learnt method to solve equations they would have solved in earlier lessons using the substitution method.

References

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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

  • 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 

  • 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.

    Article  Google Scholar 

  • Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge, United Kingdom: Cambridge University Press.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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 

  • Leong, Y. H., & Chick, H. L. (2011). Time pressure and instructional choices when teaching mathematics. Mathematics Education Research Journal, 23(3), 347–362.

    Article  Google Scholar 

  • Leong, Y. H., Chick, H. L., & Moss, J. (2007). Classroom research as teacher-researcher. The Mathematics Educator, 10(2), 1–26.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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 

  • Lester, F. K. (Ed.). (2003). Teaching mathematics through problem solving: Prekindergarten - Grade 6. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Meek, C. (2003). Classroom crisis: It’s about time. Phi Delta Kappan, 84(8), 592.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • Schoen, H. L. (Ed.). (2003). Teaching mathematics through problem solving: Grades 6-12. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. National Institute of Education, Singapore, Singapore

    Yew Hoong Leong, Eng Guan Tay, Khiok Seng Quek & Sook Fwe Yap

Authors
  1. Yew Hoong Leong
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  2. Eng Guan Tay
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  3. Khiok Seng Quek
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  4. Sook Fwe Yap
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Corresponding author

Correspondence to Yew Hoong Leong .

Editor information

Editors and Affiliations

  1. National Institute of Education, Nanyang Technological University, Singapore, Singapore

    Tin Lam Toh

  2. National Institute of Education, Nanyang Technological University, Singapore, Singapore

    Berinderjeet Kaur

  3. National Institute of Education, Nanyang Technological University, Singapore, Singapore

    Eng Guan Tay

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Leong, Y.H., Tay, E.G., Quek, K.S., Yap, S.F. (2019). Teaching Simultaneous Linear Equations: A Case of Realistic Ambitious Pedagogy. In: Toh, T., Kaur, B., Tay, E. (eds) Mathematics Education in Singapore. Mathematics Education – An Asian Perspective. Springer, Singapore. https://doi.org/10.1007/978-981-13-3573-0_19

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  • DOI: https://doi.org/10.1007/978-981-13-3573-0_19

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-3572-3

  • Online ISBN: 978-981-13-3573-0

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