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Low Attainers and Learning of Mathematics

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Mathematics Education in Singapore

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

Abstract

This chapter describes the main studies which have been carried out in the Singapore mathematics classrooms to identify and address the learning needs of low attainers in mathematics at the primary and secondary levels. This chapter begins with describing two research projects on low attainers: the first is an exploratory study on low attainers at the primary level and the second a survey on teachers’ perception of low attainers from the Normal (Technical) stream at the secondary level. These two studies identified the characteristics of low attainers and their content knowledge, teachers’ perception about their motivation and competency in mathematics, and provide a preliminary knowledge of how teachers have attempted to facilitate them to learn mathematics better. The chapter further presents three intervention research projects that were conducted by researchers from the Singapore National Institute of Education (NIE) in collaboration with school teachers to facilitate the low attainers in learning mathematics. The first project was an action research proposed by a school to facilitate the mathematics learning of students from the Normal (Academic) stream through the use of cooperative learning strategies. The researchers proposed a framework of cooperative learning that was trialled in their school setting. The second project was another research project initiated by researchers from NIE on using comics and storytelling in teaching mathematics in the Normal (Technical) stream. The study shows that there was an overall positive impact of this approach on students’ motivation in learning mathematics and their performance in mathematics achievement test. In the third project, another team of researchers from NIE attempting to use the Concrete–Pictorial–Abstract heuristic to help Normal (Academic) students learn mathematics by assisting them to make abstract algebra meaningful and manageable. This chapter concludes with describing the projected initiated by the Ministry of Education at the national level on building teacher capacity to facilitate learning of mathematics among the low attainers in mathematics.

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References

  • Amir, N., & Subramaniam, R. (2007). Making a fun cartesian diver: A simple project to engage kinaesthetic learners. Physics Education, 42(5), 478–480.

    Article  Google Scholar 

  • Burns, M. (1990). The math solution: Using groups of four. In N. Davidson (Ed.), Cooperative learning in mathematics: A handbook for teachers, 1–11. California: Addison-Wesley.

    Google Scholar 

  • Bruner, J. S. (1966). Toward a theory of instruction. MA: Harvard University Press.

    Google Scholar 

  • Cardelle-Elawar, M. (1995). Effects of metacognitive instruction on low achievers in mathematics problems. Teaching and Teacher Education, 11(1), 81–95.

    Article  Google Scholar 

  • Chang, S. H., Koay, P. L., & Kaur, B. (2010). Performance of low attainers in numeracy from Singapore. In M. Westbrook, et al. (Eds.), New curriculum new opportunities (pp. 79–88). Melbourne: The Mathematical Association of Victoria.

    Google Scholar 

  • Denvir, B., Stolz, C., & Brown, M. (1982). Low attainers in mathematics 5–16: Policies and practices in schools. London: Methuen Educational.

    Google Scholar 

  • Dunne, M., Humphreys, S., Sebba, J., Dyson, A., Gallannaugh, F., & Muijs, D. (2007). Effective teaching and learning for pupils in low attaining groups. Research Report DCSF-RR011, Department for children, schools and families. Author: University of Sussex.

    Google Scholar 

  • Fong, P. Y., Ghani, M., & Chang, S. H. (2012). Characteristics of low attainers: Behaviours affects and home backgrounds (Chap. 3). In B. Kaur & M. Ghani (Eds.), Low attainers in primary mathematics (pp. 87–132). Singapore: World Scientific.

    Google Scholar 

  • Glass, S. (2003). The uses and applications of learning technologies in the modern classroom: Finding a common ground between kinaesthetic and theoretical delivery. Educational Research Report. Information Analyses (070).

    Google Scholar 

  • Goh, K. S., & the Education Study Team. (1979). Report on the Ministry of Education 1978. Singapore: Singapore National Printers.

    Google Scholar 

  • Haylock, D. (1991). Teaching mathematics to low attainers, 8–12. London: Paul Chapman.

    Google Scholar 

  • Karsenty, R. (2010). Mathematical creativity and low achievers in secondary schools: Can the two meet? In M. Avotina, D. Bonka, H. Meissner, L. Ramana, L. Sheffield, & E. Velikova (Eds.), Abstracts of the 6th international conference on creativity in mathematics and the education of gifted students (pp. 50–51). Riga, Latvia: University of Latvia.

    Google Scholar 

  • Karsenty, R., Arcavi, A., & Hadas, N. (2007). Exploring informal products of low achievers in mathematics. Journal of Mathematical Behavior, 26(2), 156–177.

    Article  Google Scholar 

  • Kaur, B., & Ghani, M. (Eds.). (2012). Low attainers in primary mathematics. Singapore: World Scientific.

    Google Scholar 

  • Kaur, B., Koay, P. L., Foong, P. Y., & Sudarshan, A. (2012). An exploratory study on low attainers in primary mathematics (LAPM) (Chap. 1). In B. Kaur & M. Ghani (Eds.), Low attainers in primary mathematics (pp. 1–18). Singapore: World Scientific.

    Google Scholar 

  • Keijzer, R., & Terwei, J. (2004). A low-achiever’s learning process in mathematics: Shirley’s fraction learning. Journal of Classroom Interaction, 39(2), 10–23.

    Google Scholar 

  • Koay, P. L., Chang, S. H., & Ghani, M. (2012). Mathematics content knowledge of low attainers (Chap. 2). In B. Kaur & M. Ghani (Eds.), Low attainers in primary mathematics (pp. 19–86). Singapore: World Scientific.

    Google Scholar 

  • Kraemer, J. M. (2000). Met handen en voeten rekenen. Naareen natuurlijke benadering van rekenzwakke kinderen [Arithmetic with hands and feet. Towards a natural approach for low arithmetic achievers]. Tijdschrift voor Onderwijs en Opvoeding, 59(1), 29–32.

    Google Scholar 

  • Kraemer, J. M., & Janssen, J. (2000). Druppels op een gloeiende plaat—aandachtspunten voor een grondige discussie over de continue ontwikkeling van rekenzwakke leerlingen tussen vier en zestien jaar [Drops in the ocean—points of attention for a thorough discussion on the continuous development of low-attainers in arithmetic between four and sixteen years of age]. Tijdschrift voor Nascholing en Onderzoek van het Reken-wiskundeonderwijs, 18(3), 3–14.

    Google Scholar 

  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. In: J. Kilpatrick & Wirzup, I. (Eds.), (trans: Teller, J.). Chicago, IL: University of Chicago.

    Google Scholar 

  • Lee, K. Y. (1979). Letter in response to the report on the Ministry of Education by Dr Goh and his team. In Ministry of Education, Report on the Ministry of Education by Dr Goh and his team. Singapore: Ministry of Education.

    Google Scholar 

  • Lehr, J. B., & Harris, H. W. (1988) At risk, low-achieving students in the classroom: Analysis and action series. Washington, DC: National Education Association.

    Google Scholar 

  • 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), 1–19.

    Google Scholar 

  • Leong, Y. H., Yap, S. F., Teo, M. L., Thilagam, S., Karen, I., Quek, E. C., et al. (2010). Concretising factorisation of quadratic expressions. The Australian Mathematics Teacher, 66(3), 19–25.

    Google Scholar 

  • Lui, H. W. E., Liu W. C., Lim K. M., & Toh T. L. (2003). Students’ math self-concept and correlates: Some preliminary findings. In NA (Ed.), ERAS Conference “Research in and on the Classroom” (pp. 405–413). Singapore: National Institute of Education.

    Google Scholar 

  • Lui, H. W. E., Liu, W. C., Lim, K. M., & Toh, T. L. (2005). Positive social climate for enhancing students’ Mathematics self-concept: Research findings. In NA (Ed.), Conference of the Centre for Research, Pedagogy and Practice, National Institute of Education. Singapore: National Institute of Education.

    Google Scholar 

  • Lui, H. W. E., Toh, T. L., & Chung, S. P. (2009). Positive social climate and cooperative learning in mathematics classrooms (Chap. 14). In K. Y. Wong, P. Y. Lee, B. Kaur, P. Y. Foong, & S. F. Ng (Eds.), Mathematics education: The Singapore journey (Series on mathematics education, Vol. 2) (pp. 337–356). Singapore: World Scientific.

    Google Scholar 

  • Mercer, C. D., & Mercer, A. R. (2005). Teaching students with learning problems. Columbus, OH: Pearson.

    Google Scholar 

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

    Google Scholar 

  • Nelissen, J. M. C., & Tomic, W. (1998). Representations in mathematics education. Washington, DC: ERIC Clearinghouse.

    Google Scholar 

  • Quek, K. S., Leong, Y. H., Tay, E. G., Yap, S. F., Tong, C. L., Lee, H. T. C., & Toh, W. Y. K. (2016, July). Algebra that makes sense and that ‘works’. In Paper presented at 13th International Congress on Mathematical Education, Hamburg, Germany.

    Google Scholar 

  • Rayneri, L. J., Gerber, B. L., & Wiley, L. P. (2003). Gifted achievers and gifted underachievers: The impact of learning style preferences in the classroom. Journal of Secondary Gifted Education, 14(4), 197–204.

    Article  Google Scholar 

  • Shahrill, M., Mahalle, S., Matzin, R., Hamid, M. H. S., & Mundia, L. (2013). A comparison of learning styles and study strategies used by low and high achieving Brunei secondary school students: Implications for teacher. International Education Studies, 6(10), 39–46.

    Article  Google Scholar 

  • Teng, A. (2016, May 30). Reading comics in class? It’s just a way to learn math. Retrieved from http://www.straitstimes.com/singapore/education/reading-comics-in-class-its-just-a-way-to-learn-maths?login=true.

  • Toh, T. L. (2009). Use of cartoons and comics to teach algebra in mathematics classrooms. In D. Martin, T. Fitzpatrick, R. Hunting, D. Itter, C. Lenard, T. Mills, & L. Milne (Eds.), Mathematics of prime importance: MAV yearbook 2009 (pp. 230–239). Melbourne: The Mathematical Association of Victoria.

    Google Scholar 

  • Toh, T. L., Cheng, L. P., Ho, S. Y., Jiang, H., & Lim, K. M. (2017). Use of comics to enhance students’ learning for the development of the twenty-first century competencies in the mathematics classroom. Asia Pacific Journal of Education, 2017, 1–16.

    Google Scholar 

  • Toh, T. L., & Lui, H. W. E. (2014). Helping normal technical students with learning mathematics—A preliminary survey. Learning Science and Mathematics Online Journal, 2014(1), 1–10.

    Google Scholar 

  • Verschaffel, L., & De Corte, E. (1995). Teaching realistic mathematical modeling in the elementary school: A teaching experiment with fifth graders. In L. Meira & D. Carraher (Eds.), Proceedings of the 19th PME Conference (pp. 105–112). Recife, Brazil: Universidade Federal de Pernambuco, Graduate Program in Cognitive Psychology.

    Google Scholar 

  • Vygotsky, L. S. (1982). Thought and language. In L. S. Vygotsky (Ed.), The collected works of LS Vygotsky (pp. 5–36). Moscow: Pedagogika.

    Google Scholar 

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Correspondence to Tin Lam Toh .

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Toh, T.L., Kaur, B. (2019). Low Attainers and Learning of Mathematics. 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_13

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  • DOI: https://doi.org/10.1007/978-981-13-3573-0_13

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