Skip to main content

Advertisement

Log in

Scaling up of Continual Professional Development for Mathematics Problem Solving in Singapore Schools

  • Published:
International Journal of Science and Mathematics Education Aims and scope Submit manuscript

Abstract

The more ambitious an educational innovation, the greater the challenge in scaling up. In this paper, we focus on the scaling up of an ambitious pedagogical practice—mathematics problem solving as a regular feature in the classroom. We adopt a long-term approach to continual professional development (CPD) that began with intensive work with one school before we broadened the programme to four other schools which span the spectrum of schools in Singapore. To evaluate this overall design, we examine the current state of each school’s capacity in sustaining mathematics problem-solving instruction. In particular, we study and report findings on these areas: the readiness of teachers, the instructional materials and supporting structures. Based on the findings, we reflect on our CPD strategies and our theory of action which guided the CPD programme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abbott, M., Walton, C., Tapia, Y., & Greenwood, C. R. (1999). Research to practice: A “blueprint” for closing the gap in local schools. Exceptional Children, 65, 339–352.

    Article  Google Scholar 

  • Argyris, C., & Schon, D. A. (1978). Organizational learning: A theory of action perspective. Reading: Addison-Wesley.

  • Bobis, J. (2011). Mechanisms affecting the sustainability and scale-up of a system-wide numeracy reform. Mathematics Teacher Education and Development, 13(1), 34–53.

    Google Scholar 

  • Bogdan, R. C., & Biklen, S. K. (1998). Qualitative research for education: An introduction to theory and methods (3rd ed.). Boston: Allyn andBacon.

  • Bradley, A. (1996). Teachers as learners. Teacher Magazine, 7(9), 31–36.

    Google Scholar 

  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.

    Article  Google Scholar 

  • Cobb, P., & Smith, T. (2008). District development as a means of improving mathematics teaching and learning at scale. In K. Krainer & T. Woods (Eds.), The international handbook of mathematics teacher education: Participants in mathematics teacher education (Vol. 3, pp. 231–254). Rotterdam: Sense Publishers.

    Google Scholar 

  • Coburn, C. E. (2003). Rethinking scale: Moving beyond numbers to deep and lasting change. Educational Researcher, 32(6), 3–12.

    Article  Google Scholar 

  • Cohen, D. K., & Ball, D. L. (2007). Educational innovation and the problem of scale. In B. Schneider & S. McDonald (Eds.), Scale-up in education: Ideas in principle (Vol. 1, pp. 19–36). Lanham: Rowman and Littlefield.

    Google Scholar 

  • Dindyal, J., Quek, K.S., Leong, Y.H., Toh, T.L., Tay, E.G., Lou, S.T. (2010). Problems for a problem solving curriculum. In Sparrow, L., Kissane, B., Hurst, C. (Ed.) Shaping the future of mathematics education (pp. 749–752). Fremantle, Australia: The Mathematics Education Research Group of Australasia.

  • Dindyal, J., Tay, E. G., Toh, T. L., Leong, Y. H., & Quek, K. S. (2012). Mathematical problem solving for everyone: A new beginning. The Mathematics Educator, 13, 51–70.

  • Darling-Hammond, L., Wei, R. C., Andree, A., Richardson, N., & Orphanos, S. (2009). Professional learning in the learning profession: A status report on teacher development in the United States and beyond. Dallas: National Staff Development Council.

    Google Scholar 

  • Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational Researcher, 34(3), 3–14.

    Article  Google Scholar 

  • Henrick, E., Cobb, P., & Jackson, K. (2015). Educational design to support system-wide instructional improvement. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods (pp. 497–530). Dordrecht: Springer.

    Google Scholar 

  • Kazemi, E. (2008). School development as a means of improving mathematics teaching and learning: Towards a multidirectional analyses of learning across contexts. In K. Krainer & T. Woods (Eds.), The international handbook of mathematics teacher education: Participants in mathematics teacher education (Vol. 3, pp. 209–230). Rotterdam: Sense Publishers.

    Google Scholar 

  • Kazemi, E., Franke, M., & Lampert, M. (2009). Developing pedagogies in teacher education to support novice teachers’ 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 Australiasia (Vol. 1, pp. 11–21). Palmerston North: MERGA.

    Google Scholar 

  • Kho, T. H., Yeo, S. M., & Fan, L. (2014). Model method in Singapore primary mathematics textbooks. In K. Jones, C. Bokhove, G. Howson, & L. Fan (Eds.), Proceedings of the International Conference on Mathematics Textbook Research and Development (ICMT-2014) (pp. 275–282). Southampton: University of Southampton.

    Google Scholar 

  • Krainer, K., Zehetmeier, S., Hangfstingl, B., Rauch, F., & Tscheinig, T. (2019). Insights into scaling up a nationwide learning and teaching initiative on various levels. Educational Studies in Mathematics, 102(3), 395–415.

    Article  Google Scholar 

  • Krainer, K., & Zehetmeier, S. (2013). Inquiry-based learning for students, teachers, researchers, and representatives of educational administration and policy: Reflections on a nation-wide initiative fostering educational innovations. ZDM - The International Journal on Mathematics Education, 45(6), 875–886.

    Article  Google Scholar 

  • Kuzle, A. (2018). Assessing the metacognition of grade 2 and grade 4 students using an adaptation of a multi-method interview approach during mathematics problem solving. Mathematics Education Research Journal, 30(2), 185–207.

    Article  Google Scholar 

  • Leong, Y.H., Dindyal, J., Toh, T.L. Quek, K.S., Tay, E.G., & Lou, S.T. (2011). Teacher education for a problem-solving curriculum in Singapore. ZDM: The International Journal on Mathematics Education, 43(6-7), 819–831.

  • Leong, Y. H., Tay, E. G., Quek, K. S., Toh, T. L., Toh, P. C., Dindyal, J., & Yap, R. A. S. (Eds.). (2014). Making mathematics more practical: Implementation in the schools. Singapore: World Scientific Publishing Co. Pte. Ltd.

  • Leong, Y. H., Kaur, B., & Kwon, O. (2017). Mathematics teacher professional development: An Asian perspective. In B. Kaur, O. Kwon, & Y.H. Leong (Eds.), Professional development of mathematics teachers - An Asian perspective (pp. 1–14). Singapore: Springer.

  • Leong, Y.H., Tay, E.G., Toh, T.L., Quek, K.S., & Yap, R.A. (2019). Concretisations: A support for teachers to carry out instructional innovations in the mathematics classroom. International Journal of Science and Mathematics Education, 17(2), 365–384.

  • Lampert, M., & Graziani, F. (2009). Instructional activities as a tool for teachers’ and teacher educators’ learning. The Elementary School Journal, 109(5), 491–509.

    Article  Google Scholar 

  • Lampert, M., Boerst, T. A., & Graziani, F. (2011). Organizational resources in the service of school-wide ambitious teaching practice. Teachers College Record, 113(7), 1361–1400.

    Google Scholar 

  • Langer-Osuna, J. M. (2016). The social construction of authority among peers and its implications for collaborative mathematics problem solving. Mathematical Thinking and Learning, 18(2), 107–124.

    Article  Google Scholar 

  • Lemke, J. L., & Sabelli, N. H. (2008). Complex systems and educational change: Towards a new research agenda. Educational Philosophy and Theory, 40(1), 118–129.

    Article  Google Scholar 

  • Maaβ, K., & Artigue, M. (2013). Implementation of inquiry-based learning in day-to-day teaching: A synthesis. ZDM - The International Journal on Mathematics Education, 45(6), 779–795.

    Article  Google Scholar 

  • Maciejewski, W. Future-oriented thinking and activity in mathematical problem solving. In P. Liljedahl & M. Santos-Trigo (Eds.), Mathematical problem solving: Current themes, trends, and research (pp. 2140). Switzerland: Springer Nature.

  • Pólya, G. (1945). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton: Princeton University Press.

    Book  Google Scholar 

  • Quek, K. S., Dindyal, J., Toh, T. L., Leong, Y. H., & Tay, E. G. (2011). Problem solving for everyone: A design experiment. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 15(1), 31–44.

  • Quek, K.S., Leong, Y.H., Tay, E.G., Toh, T.L., Dindyal, J. (2012). Diffusion of the mathematics practical paradigm in the teaching of problem solving: Theory and praxis. In Dindyal, J., Cheng, L.P., Ng, S.F. (Ed.) Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 618 - 624). Singapore: MERGA.

  • Roesken-Winter, B., Schüler, S., Stahnke, R., & Blömeke, S. (2015). Effective CPD on a large scale: Examining the development of multipliers. ZDM - The International Journal on Mathematics Education, 47(1), 13–25.

    Article  Google Scholar 

  • Rogers, E. M. (2003). Diffusion of innovations (5th ed.). New York: Simon and Schuster.

    Google Scholar 

  • Schildkamp, K., Poortman, C. L., Ebbeler, J., & Pieters, J. M. (2019). How school leaders can build effective data teams: Five building blocks for a new wave of data-informed decision making. Journal of Educational Change, 20, 283–325.

    Article  Google Scholar 

  • Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic Press.

    Google Scholar 

  • Schoenfeld, A. H. (2007). Problem solving in the United States, 1970–2008: Research and theory, practice and politics. ZDM - The International Journal on Mathematics Education, 39(5–6), 537–551.

    Article  Google Scholar 

  • Sfard, A. (2004). What could be more practical than good research? On mutual relations between research and practice of mathematics education. In M. Niss (Ed.), Proceedings of the 10th international congress on mathematical education (pp. 76–92). Copenhagen: IMFUFA.

    Google Scholar 

  • Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents. The Journal of Mathematical Behavior, 24(3–4), 341–350.

    Article  Google Scholar 

  • Toh, T. L., Quek, K. S., Leong, Y. H., Dindyal, J., & Tay, E. G. (2011a). Making mathematics practical: An approach to problem solving. Singapore: World Scientific Publishing Co. Pte. Ltd.

  • Toh, T.L., Quek, K.S., Leong, Y.H., Dindyal, J., Tay, E.G. (2011b). Assessing problem solving in the mathematics curriculum: A new approach. In Wong, K.Y., Kaur, B. (Ed.), AME Yearbook 2011: Assessment (pp. 1–35). Singapore: World Scientific.

  • Tatar, D., Roschelle, J., Knudsen, J., Shectman, N., Kaput, J., & Hopkins, B. (2008). Scaling up innovative technology-based mathematics. The Journal of the Learning Sciences, 17, 248–286.

    Article  Google Scholar 

  • Tirosh, D., Tsamir, P., & Levenson, E. (2015). Fundamental issues concerning the sustainment and scaling up of professional development programs. ZDM - The International Journal on Mathematics Education, 47, 153–159.

    Article  Google Scholar 

  • Woolner, P., Thomas, U., & Tiplady, L. (2018). Structural change from physical foundations: The role of the environment in enacting school change. Journal of Educational Change, 18, 223–242.

    Article  Google Scholar 

  • Zehetmeier, S. (2015). Sustaining and scaling up the impact of professional development programmes. ZDM - The International Journal on Mathematics Education, 47(1), 117–128.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yew Hoong Leong.

Electronic supplementary material

ESM 1

(DOCX 37 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Leong, Y.H., Toh, T.L., Tay, E.G. et al. Scaling up of Continual Professional Development for Mathematics Problem Solving in Singapore Schools. Int J of Sci and Math Educ 19, 1291–1310 (2021). https://doi.org/10.1007/s10763-020-10097-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10763-020-10097-3

Keywords

Navigation