Abstract
This chapter describes some innovative pedagogical practices in Singapore. It is divided into two main sections: pedagogies that engage the minds, and those that engage the hearts, of mathematics learners. Examples of such classroom practices include the Singapore Model Method to solve word problems in primary schools, the Singapore AlgeDisc™ to teach algebra in secondary schools, and guided-discovery learning. The main principle that underlies all these pedagogies that engage the minds of mathematics students is the Concrete-Pictorial-Abstract (C-P-A) approach. We also describe a theoretical framework on engaging the hearts of mathematics learners and the use of various strategies to make lessons interesting. Examples of such strategies include the use of mathematics songs and videos, television shows and movies, mathematics storybooks, drama, magic tricks, and mathematics puzzles and games. Some of these practices are not unique to Singapore but many local teachers are using them in their classrooms. Finally, this chapter also reviews limited local research on these pedagogical practices, and where there is no local research, we suggest some directions for future research.
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Aiken, L. R. (1972). Research on attitudes toward mathematics. Arithmetic Teacher, 19, 229–234.
Bruner, J. S. (1961). The act of discovery. Harvard Educational Review, 31, 21–32.
Bruner, J. S. (1964). The course of cognitive growth. American Psychologist, 19, 1–15.
Bruner, J. S. (1966). Toward a theory of instruction. MA: Harvard University Press.
Bryk, A. S. (2015). Accelerating how we learn to improve. Educational Researcher, 44(9), 467–477.
Burns, M. (2003). Using games in your math teaching. Connect Magazine, 17(2), 1–4.
Chang, S. H., Lee, N. H., & Koay, P. L. (2017). Teaching and learning with concrete-pictorial-abstract sequence—A proposed model. The Mathematics Educator, 17(1), 1–28.
Choy, B. H. (2013). Productive mathematical noticing: What it is and why it matters. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 186–193). Melbourne: MERGA.
Chua, B. L. (2017). Empowering learning in an algebra class: The case of expansion and factorisation. In B. Kaur & N. H. Lee (Eds.), Empowering mathematics learners (Association of Mathematics Educators 2017 Yearbook, pp. 9–29). Singapore: World Scientific.
Davies, B. (1995). The role of games in mathematics. Square One, 5(2), 7–17.
Ernest, P. (1991). The philosophy of mathematics education. London: Falmer Press.
Franke, M. L., Kazemi, E., & Battey, D. (2007). Understanding teaching and classroom practice in mathematics. In J. Frank & K. Lester (Eds.), Second handbook of research on mathematics teaching and learning (pp. 225–256). Charlotte, NC: Information Age Publishing.
Gardner, H. (2006). Multiple intelligences: New horizons. New York: Basic Books.
Goh, S. P. (2009). Primary 5 pupils’ difficulties in using the Model Method for solving complex relational word problems (Unpublished master’s thesis). National Institute of Education, Nanyang Technological University, Singapore.
Hart, L. E. (1989). Describing the affective domain: Saying what we mean. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 37–45). New York: Springer.
Hough, B. H., & Hough, S. (2012). The play was always the thing: Drama’s effect on brain function. Psychology, 3(6), 454–456.
Huang, Y. (2016). Effects of crafted video lessons incorporating multi-modal representations on learning of factorization of quadratic expressions (Unpublished master’s thesis). National Institute of Education, Nanyang Technological University, Singapore.
Hunter, R., Hunter, J., Jorgensen, R., & Choy, B. H. (2016). Innovative and powerful pedagogical practices in mathematics education. In K. Makar, S. Dole, J. Visnovska, M. Goos, A. Bennison, & K. Fry (Eds.), Research in mathematics education in Australasia 2012–2015 (pp. 213–234). Singapore: Springer.
Jaworski, B. (1994). Investigating mathematics teaching: A constructivist enquiry. London: Falmer Press.
Kho, T. H. (1987). Mathematical models for solving arithmetic problems. Paper presented at the 4th Southeast Asian Conference on Mathematics Education, Singapore.
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.
Kho, T. H., Yeo, S. M., & Lim, J. (2009). The Singapore Model Method for learning mathematics. Singapore: EPB Pan Pacific.
Kintsch, W., & Greeno, J. G. (1985). Understanding and solving arithmetic word problems. Psychological Review, 92(1), 109–129.
Koirala, H. P., & Goodwin, P. M. (2000). Teaching algebra in the middle grades using math magic. Mathematics Teaching in the Middle School, 5(9), 562–566.
Lang, P., Katz, Y. J., & Menezes, I. (Eds.). (1998). Affective education: A comparative view. London: Cassell.
Langley, G. J., Moen, R. D., Nolan, K. M., Nolan, T. W., Norman, C. L., & Provost, L. P. (2009). The improvement guide: A practical approach to enhancing organizational performance. San Francisco: Jossey-Bass.
Leach, G., Hunter, R., & Hunter, J. (2014). Teachers repositioning culturally diverse students as doers and thinkers of mathematics. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 381–388). Sydney: MERGA.
Lemire, S., Christie, C. A., & Inkelas, M. (2017). The methods and tools of improvement science. In C. A. Christie, M. Inkelas, & S. Lemire (Eds.), Improvement science in evaluation: Methods and uses. new directions for evaluation (pp. 23–33).
Leong, S. L. (2015). Effects of a mathematics instructional sequence on the conceptual and procedural understanding of algebraic expressions for secondary students with mathematics difficulties (Unpublished doctoral dissertation). National Institute of Education, Nanyang Technological University, Singapore.
Leong, Y. H., Ho, W. K., & Cheng, L. P. (2015). Concrete-Pictorial-Abstract: Surveying its origins and charting its future. The Mathematics Educator, 16(1), 1–18.
Leong, Y. H., Yap, S. F., Teo, M. L., Thilagam, S., Karen, I., Quek, E. C., & Tan, K. L. K. (2010). Concretising factorisation of quadratic expressions. The Australian Mathematics Teacher, 66(3), 19–24.
Lesser, L. M., & Glickman, M. E. (2009). Using magic in the teaching of probability and statistics. Model Assisted Statistics and Applications, 4, 265–274.
Lewis, C. (2015). What is improvement science? Do we need it in education? Educational Researcher, 44(1), 54–61.
Lim, P., Fu, S., & Foong, P. H. S. (2014). Magic tricks in the teaching of the arithmetic mean. In J. Vincent, G. FitzSimons, & J. Steinle (Eds.), Proceedings of the 51st Mathematical Association of Victoria Annual Conference: Maths Rocks (pp. 94–101). Victoria, Australia: MAV.
Lowrie, T., & Jorgensen (Zevenbergen), R. (Eds.). (2015). Digital games and mathematics learning: Potential, promises and pitfalls. Dordrecht, The Netherlands: Springer.
Marshman, M., & Brown, R. (2014). Coming to know and do mathematics with disengaged students. Mathematics Teacher Education and Development, 16(2), 71–88.
McLeod, D. B. (1989). Beliefs, attitudes, and emotions: New views of affect in mathematics education. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 245–258). New York: Springer.
McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: MacMillan.
Ministry of Education of Singapore. (2007). Mathematics syllabus: Primary. Singapore: Curriculum Planning and Development Division.
Ministry of Education of Singapore. (2012a). Mathematics syllabus: Primary. Singapore: Curriculum Planning and Development Division.
Ministry of Education of Singapore. (2012b). Mathematics syllabus: Secondary. Singapore: Curriculum Planning and Development Division.
Murphy, C. (2015). Changing teachers’ practices through exploratory talk in mathematics: A discursive pedagogical perspective. The Australian Journal of Teacher Education, 40(5), 61–84.
National Arts Council. (2017). Teaching through the arts programme. Retrieved from https://aep.nac.gov.sg.
Nesher, P., Greeno, J. G., & Riley, M. S. (1982). The development of semantic categories for addition and subtraction. Educational Studies in Mathematics, 13(4), 373–394.
Ng, S. F. (2003). How Secondary Two Express stream students used algebra and the Model Method to solve problems. The Mathematics Educator, 7(1), 1–17.
Ng, S. F., & Lee, K. (2005). How Primary Five pupils use the Model Method to solve word problems. The Mathematics Educator, 9(1), 60–83.
Ng, S. F., & Lee, K. (2009). The Model Method: Singapore children’s tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282–313.
Pekrun, R. (Ed.) (2014). Emotions and learning (Vol. 24). Switzerland: UNESCO.
Pirie, S. (1987). Mathematical investigations in your classroom: A guide for teachers. Basingstoke, England: Macmillan.
Poh, B. K. (2007). Model method: Primary three pupils’ ability to use models for representing and solving word problems (Unpublished master’s thesis). National Institute of Education, Nanyang Technological University, Singapore.
Shanmugaratnam, T. (2005). Teach less learn more (TLLM). Speech by Mr Tharman Shanmugaratnam, Minister of Education, at the MOE Work Plan seminar 2005. Singapore: National Archives of Singapore.
Sullivan, P., & Davidson, A. (2014). The role of challenging mathematical tasks in creating opportunities for student reasoning. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 605–612). Sydney: MERGA.
Wong, K. Y. (2015). Effective mathematics lessons through an eclectic Singapore approach (Association of Mathematics Educators 2017 Yearbook, pp. 219–248). Singapore: World Scientific.
Yeo, J. B. W. (2013). The nature and development of processes in mathematical investigation (Unpublished doctoral thesis). National Institute of Education, Nanyang Technological University, Singapore.
Yeo, J. B. W. (2018a). Engaging the hearts of mathematics learners. In P. C. Toh & B. L. Chua (Eds.), Mathematics instruction: Goals, tasks and activities (Association of Mathematics Educators 2018 Yearbook, pp. 115–132). Singapore: World Scientific.
Yeo, J. B. W. (2018b). Maths songs, videos and games for secondary school maths. Retrieved from http://math.nie.edu.sg/bwjyeo/videos.
Yeo, J. B. W., Teh, K. S., Loh, C. Y., & Chow, I. (2013a). New syllabus additional mathematics (9th ed.). Singapore: Shinglee.
Yeo, J. B. W., Teh, K. S., Loh, C. Y., Chow, I., Neo, C. M., & Liew, J. (2013b). New syllabus mathematics 1 (7th ed.). Singapore: Shinglee.
Yeo, J. B. W., Teh, K. S., Loh, C. Y., Chow, I., Ong, C. H., & Liew, J. (2015). New syllabus mathematics 3 (7th ed.). Singapore: Shinglee.
Yeo, J. B. W., & Yeap, B. H. (2010). Characterising the cognitive processes in mathematical investigation. International Journal for Mathematics Teaching and Learning. Retrieved from http://www.cimt.org.uk/journal.
Yeo, S. M., Thong, C. H., & Kho, T. H. (2008, July). Algebra discs: Digital manipulatives for learning algebra. Paper presented at the 11th International Congress on Mathematics Education, Monterrey, Mexico.
Yuen, S. (2016, March 14). Drama-based teaching on the rise. The Straits Times. Retrieved from www.straitstimes.com.
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Yeo, J.B.W., Choy, B.H., Lim, L.G.P., Wong, L.F. (2019). Innovative Pedagogical Practices. 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_8
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