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Problems in Real-World Context and Mathematical Modelling

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Mathematics Education in Singapore

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

Abstract

This chapter discusses teacher education efforts and analyses the research outcomes in the domain of solving problems in real-world contexts, particularly in the field of mathematical modelling among other tasks situated in real-world contexts in Singapore mathematics classrooms. The first part of this chapter begins with an understanding of “applications and modelling” from the perspective of the Singapore school mathematics curriculum framework. The second part of this chapter reports on the efforts made in supporting applications and modelling in teacher education through professional development opportunities. This chapter continues with a discussion of findings from local research in solving problems in real-world contexts (applications and/or modelling) carried out with students in primary and secondary schools to add to the repertoire of knowledge in this domain. Challenges are surfaced in the light of the preceding sections with implications for teacher education and research with the acknowledgement that there is still some distance to go to know more about applications and modelling and actualizing the curriculum in a more holistic sense through teacher education and the implementing of modelling lessons. This chapter discusses the way forward in supporting the advancement of mathematical modelling in the mathematics curriculum.

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References

  • Ang, K. C. (2009). Mathematical modelling in the secondary and Junior College classroom. Singapore: Pearson.

    Google Scholar 

  • Ang, K. C. (2010). Mathematical modelling in the Singapore curriculum: Opportunities and challenges. In A. Araújo, A. Fernandes, A. Azevedo & J. F. Rodrigues (Eds.), Proceedings of the EIMI 2010 Conference on Educational Interfaces Between Mathematics and Industry (pp. 53–62). New York: Springer.

    Google Scholar 

  • Ang, K. C. (2013). Real-life modelling within a traditional curriculum: Lessons from a Singapore experience. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 131–140). Dordrecht: Springer.

    Google Scholar 

  • Ang, K. C. (2015). Mathematical modelling in Singapore schools: A framework for instruction. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 57–72). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work: Experiences from an in-service course for upper secondary teachers. ZDM—The International Journal on Mathematics Education, 38(2), 163–177.

    Article  Google Scholar 

  • Blum, G. W., Galbraith, P., Hans-Wolfgang, H., & Niss, M. (Eds.). (2007a). Modelling and applications in mathematics education: The 14th ICMI Study. New York: Springer.

    Google Scholar 

  • Blum, W., Galbraith, P. L., Henn, H., & Niss, M. (Eds.). (2007b). Modelling and applications in mathematics education: 14th ICMI Study. New York: Springer.

    Google Scholar 

  • Brown, R., Redmond, T., Sheehy, J., & Lang, D. (2015). Mathematical modelling—An example from an inter-school modelling challenge. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice (pp. 143–160). Singapore: World Scientific Publishing Co., Pte. Ltd.

    Chapter  Google Scholar 

  • Chan, C. M. E. (2009). Mathematical modelling as problem solving for children in the Singapore mathematics classroom. Journal of Science and Mathematics Education in Southeast Asia, 32(1), 36–61.

    Google Scholar 

  • Chan, C. M. E. (2011). Primary 6 students’ attitudes towards mathematical problem-solving in a problem-based learning setting. The Mathematics Educator, 13(1), 15–31.

    Google Scholar 

  • Chan, C. M. E. (2013). Initial perspectives of teacher professional development on mathematical modelling in Singapore: Conceptions of mathematical modelling. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 405–413). Dordrecht: Springer.

    Google Scholar 

  • Chan, C. M. E., Ng, K. E. D., Widjaja, W., & Seto, C. (2012). Assessment of primary 5 students’ mathematical modelling competencies. Journal of Science and Mathematics Education in Southeast Asia, 35(2), 146–178.

    Google Scholar 

  • Chan, C. M. E., Ng, K. E. D., Widjaja, W., & Seto, C. (2015). A case study on developing a teacher’s capacity in mathematical modelling. The Mathematics Educator, 16(1), 45–74.

    Google Scholar 

  • Chan, C. M. E., Vapumarican, R., Oh, K. V., Liu, H. T., & Seah, Y. H. S. (2016). Fostering mathematical reasoning of P5 students during mathematical modelling. Journal of Science and Mathematics Education in Southeast Asia, 39(2), 138–167.

    Google Scholar 

  • Chan, C. M. E., Vapumarican, R., Oh, K. V., Liu, H. T., & Seah, Y. H. S. (2017). Empowering students’ mathematics learning through mathematical modelling. In B. Kaur & N. H. Lee (Eds.), Empowering mathematics learners: Yearbook 2017 association of mathematics educators (pp. 355–375). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Cheng, L. P. (2013a). The design of a mathematics problem using real-life context for young children. Journal of Science and Mathematics Education in Southeast Asia, 36(1), 23–43.

    Google Scholar 

  • Cheng, L. P. (2013b). Posing problems to understand children’s learning of fractions. In V. Steinle, L. Ball, & C. Bardini (Eds.) Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 162–169). Melbourne, Victoria, Australia: Mathematics Education Research Group of Australasia Inc.

    Google Scholar 

  • Cheng, L. P., & Toh, T. L. (2015). Mathematical problem solving using real-world problems. In Y. H. Cho, I. S. Caleon, & M. Kapur (Eds.), Authentic problem solving and learning in the 21st century (pp. 57–71). Singapore: Springer.

    Chapter  Google Scholar 

  • Dindyal, J. (2009). Applications and modelling for the primary mathematics classroom. Singapore: Pearson.

    Google Scholar 

  • Dindyal, J., & Kaur, B. (2010). Mathematical applications and modelling: Concluding comments. In B. Kaur & J. Dindyal (Eds.), Mathematical applications and modelling (pp. 325–335). Singapore: World Scientific Publishing.

    Chapter  Google Scholar 

  • Dolk, M., Widjaja, W., Zonneveld, E., & Fauzan, A. (2010). Examining teacher’s role in relation to their beliefs and expectations about students’ thinking in design research. In R. K. Sembiring, K. Hoogland, & M. Dolk (Eds.), A decade of PMRI in Indonesia (pp. 175–187). Bandung, Utrecht: APS International.

    Google Scholar 

  • Gravemeijer, K., & van Eerde, D. (2015). Design research as a means for building a knowledge base for teaching in mathematics education. The Elementary School Journal, 109(5), 510–524.

    Article  Google Scholar 

  • Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 503–510). New York: Springer.

    Chapter  Google Scholar 

  • Kaiser, G., & Schwarz, B. (2010). Authentic modelling problems in mathematics education—Examples and experiences. Journal Fur Mathematik - Didaktic, 31(1), 51–76.

    Article  Google Scholar 

  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM—The International Journal of Mathematics Education, 38(3), 302–310.

    Article  Google Scholar 

  • Kaur, B., & Dindyal, J. (2010). A prelude to mathematical applications and modelling in Singapore schools. In B. Kaur & J. Dindyal (Eds.), Mathematical applications and modelling (pp. 3–18). Singapore: World Scientific Publishing.

    Chapter  Google Scholar 

  • Kwek, M. L., & Ko, H. C. (2011). The teaching and learning of mathematical modelling in a secondary school. Paper presented at the 15th International Conference on the Teaching of Mathematical Modelling and Applications: Connecting to practice—Teaching Practice and the Practice of Applied Mathematicians, Australian Catholic University (St. Patrick), Melbourne, Australia.

    Google Scholar 

  • Lee, N. H. (2013). Initial perspectives of teacher professional development on mathematical modelling in Singapore: Problem posing and task design. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 415–425). Dordrecht: Springer.

    Google Scholar 

  • Lee, N. H., & Ang, K. C. (2015). Developing teachers’ competencies in the teaching of mathematical modelling. Singapore: National Institute of Education.

    Google Scholar 

  • Lee, N. H., & Ng, K. E. D. (Eds.). (2015). Mathematical modelling: From theory to practice (1st ed.). Singapore: World Scientific Co. Pte. Ltd.

    Google Scholar 

  • Lesh, R., & Doerr, H. M. (2003). Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum Associates.

    Book  Google Scholar 

  • Lesh, R., & Kelly, A. (2000). Multitiered teaching experiments. In A. Kelly & R. Lesh (Eds.), Research design in mathematics and science education (pp. 197–230). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 763–803). Charlotte, NC: Image Age Publishing.

    Google Scholar 

  • Ministry of Education [MOE]. (1999). Project work: Guidelines. Singapore: Author.

    Google Scholar 

  • Ministry of Education [MOE]. (2006a). Primary mathematics syllabus. Singapore: Author.

    Google Scholar 

  • Ministry of Education [MOE]. (2006b). Secondary mathematics syllabus. Singapore: Author.

    Google Scholar 

  • Ministry of Education [MOE]. (2012a). Ordinary-level and normal (academic)-level mathematics teaching and learning syllabus. Singapore: Author.

    Google Scholar 

  • Ministry of Education [MOE]. (2012b). Mathematical modelling resource kit. Singapore: Author.

    Google Scholar 

  • Ministry of Education [MOE]. (2014). Career information: Supporting you in every way—TEACH framework. Retrieved October 5, 2017 from http://www.moe.gov.sg/careers/teach/images/teach-framework.jpg.

  • Ministry of Education [MOE]. (2015). Secondary mathematics assessment guide. Singapore: Author.

    Google Scholar 

  • Ng, K. E. D. (2009). Thinking, small group interactions, and interdisciplinary project work (Doctoral dissertation), The University of Melbourne, Australia.

    Google Scholar 

  • Ng, K. E. D. (2010). Partial metacognitive blindness in collaborative problem solving. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 446–453). Fremantle, Australia: Adelaide: MERGA.

    Google Scholar 

  • Ng, K. E. D. (2011). Mathematical knowledge application and student difficulties in a design-based interdisciplinary project. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), International perspectives on the teaching and learning of mathematical modelling: Trends in the teaching and learning of mathematical modelling (Vol. 1, pp. 107–116). New York: Springer.

    Google Scholar 

  • Ng, K. E. D. (2013). Teacher readiness in mathematical modelling: Are there differences between pre-service and experienced teachers? In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Connecting to practice: Teaching practice and the practice of applied mathematicians (pp. 339–348). Dordrecht: Springer.

    Google Scholar 

  • Ng, K. E. D., Chan, C. M. E., Widjaja, W., & Seto, C. (2013, March). Fostering teacher competencies in incorporating mathematical modelling in Singapore primary mathematics classrooms. Paper presented at Innovations and Exemplary Practices in Mathematics Education: 6th East Asia Regional Conference on Mathematics Education, Phuket, Thailand.

    Google Scholar 

  • Ng, K. E. D., & Lee, N. H. (2012). Mathematical modelling: A collection of classroom tasks. Singapore: Alston Publishing House Private Limited.

    Google Scholar 

  • Ng, K. E. D., Stillman, G. A., & Stacey, K. (2007). Interdisciplinary learning and perceptions of interconnectedness of mathematics. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 185–192). Seoul, Korea: PME.

    Google Scholar 

  • Ng, K. E. D., Widjaja, W., Chan, C. M. E., & Seto, C. (2012). Activating teacher critical moments through reflection on mathematical modelling facilitation. In J. Brown & T. Ikeda (Eds.), ICME 12 Electronic Pre-Conference Proceedings TSG17: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics (pp. 3347–3356). Seoul, Korea: ICME12.

    Google Scholar 

  • Ng, K. E. D., Widjaja, W., Chan, C. M. E., & Seto, C. (2015). Developing teaching competencies through videos for facilitation of mathematical modelling in Singapore primary schools. In S. F. Ng (Ed.), The contributions of video and audio technology towards professional development of mathematics teachers (pp. 15–38). New York: Springer.

    Google Scholar 

  • Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. Galbraith, C. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 43–59). New York: Springer.

    Chapter  Google Scholar 

  • Seto, C., Thomas, M., Ng, K. E. D., Chan, C. M. E., & Widjaja, W. (2012). Mathematical modelling for Singapore primary classrooms: From a teacher’s lens. In Dindyal, J., Cheng, L. P., & Ng, S. F. (Eds.), Mathematics education—Expanding horizons: Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 674–681). Singapore: MERGA Inc.

    Google Scholar 

  • Stillman, G., Brown, J., & Galbraith, P. L. (2008). Research into the teaching and learning of applications and modelling in Australasia. In H. Forgasz, A. Barkatsas, A. J. Bishop, B. Clarke, S. Keast, W. T. Seah, & P. Sullivan (Eds.), Research in mathematics education in Australasia: 2004–2007 (pp. 141–164). The Netherlands: Sense Publishers.

    Google Scholar 

  • Stillman, G., Brown, J., Galbraith, P. L., & Ng, K. E. D. (2016). Research into mathematical applications and modelling. In K. Makar, S. Dole, J. Visnovska, M. Goos, A. Bennison, & K. Fry (Eds.), Research in mathematics education in Australasia: 2012–2015 (pp. 281–304). The Netherlands: Springer.

    Chapter  Google Scholar 

  • Tan, L. S. (2015). Professional development for teachers of mathematical modelling in Singapore (Unpublished doctoral thesis). Nanyang Technological University, Singapore.

    Google Scholar 

  • Tan, L. S., & Ang, K. C. (2016). A school-based professional development programme for teachers of mathematical modelling in Singapore. Journal of Mathematics Teacher Education, 19, 399–432.

    Article  Google Scholar 

  • Yeo, B. W. J., Choy, B. H., Ng, K. E. D., & Ho, W. K. (2018). Problems in real-world contexts: Principles of design, assessment and implementation. Singapore: Shinglee.

    Google Scholar 

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Author information

Authors and Affiliations

  1. National Institute of Education, Singapore, Singapore

    Chun Ming Eric Chan, Kit Ee Dawn Ng, Ngan Hoe Lee & Jaguthsing Dindyal

Authors
  1. Chun Ming Eric Chan
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  2. Kit Ee Dawn Ng
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  3. Ngan Hoe Lee
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  4. Jaguthsing Dindyal
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Correspondence to Chun Ming Eric Chan .

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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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Chan, C.M.E., Ng, K.E.D., Lee, N.H., Dindyal, J. (2019). Problems in Real-World Context and Mathematical Modelling. 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_9

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  • DOI: https://doi.org/10.1007/978-981-13-3573-0_9

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  • Online ISBN: 978-981-13-3573-0

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