Abstract
Although the part-part-whole concept and its related pictorial representation conceptualised as the Singapore model drawing may seem beguilingly simple, it is not. Comparing the data from the two videoed lessons showed that the very prescriptive mediational processes of the teacher in the second lesson helped the children to discern and identify the critical components of the part-part-whole representation. Repetition of the related mathematical language and the specific relationships until these stuck in the consciousness enabled the children to engage with the lesson. The children could state the desired rule. More importantly facility with the mathematical terms gave children a means to request for further clarifications about the concept and to extend the concept. The MISC framework gave the participating teacher greater structure to her teaching actions. Watching videoed episodes of herself at work helped improved her practice in two ways. She designed meaningful instructional materials to address the intellectual needs of the children. The entire process challenged her assumptions on how children process information and the difficulties they may have with making sense of what seems to be a simple representation of part-part-whole nature of numbers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ball, D. L. (2009, June 1). Making mathematics learnable in school: What is the work of teaching mathematics. Keynote address at the 3rd redesigning pedagogy international conference. Singapore: National Institute of Education.
Cazden, C. B. (1988). Classroom discourse – The language of teaching and learning. Portsmouth, NH: Heinemann.
Collars, C., Koay, P. L., Lee, N. H., Ong, B. L., & Tan, C. S. (2007). Shaping maths coursebook 4A (2nd ed.). Singapore: Marshall Cavendish Education.
Collars, C., Koay, P. L., Lee, N. H., Ong, B. L., & Tan, C. S. (2008). Shaping maths coursebook 5A (2nd ed.). Singapore: Marshall Cavendish Education.
Collars, C., Koay, P. L., Lee, N. H., & Tan, C. S. (2007a). Shaping maths coursebook 1A (2nd ed.). Singapore: Marshall Cavendish Education.
Collars, C., Koay, P. L., Lee, N. H., & Tan, C. S. (2007b). Shaping maths coursebook 3A (2nd ed.). Singapore: Marshall Cavendish Education.
Collis, K. F. (1973). A study of children’s ability to work with elementary mathematical systems. Australian Journal of Psychology, 25(2), 121–130.
Gladwell, M. (2000). The tipping point: How little things can make a big difference. London: Abacus.
Hattie, J. (1999, August 2). Influences on student learning. John Hattie Inaugural Lecture: Professor of Education, University of Auckland.
Inhelder, B., & Piaget, J. (1964). The early growth of logic in the child: Classification and seriation. London: Routledge & Kegan Paul.
Jaegermann, N., & Klein, P. (2010). Enhancing mothers’ interactions with toddlers who have sensory processing disorders. Infant Mental Health Journal, 31(3), 291–311.
Klein, P. S. (1988). Stability and change in interaction of Israeli mothers and infants. Infant Behaviour and Development, 11, 55–70.
Klein, P. S. (1992). Assessing cognitive modifiability of infants and toddlers: Observations based on mediated learning experience. In H. C. Haywood & D. Tzuriel (Eds.), Interactive assessment (pp. 223–250). New York: Springer.
Klein, P. S. (1996). Early intervention: Cross –cultural experiences with a mediational approach. New York: Garland.
Klein, P. S. (2003). Early intervention: Mediated intervention for sensitizing caregivers. In A. S. H. Seng, L. K. H. Pon, & O. S. Tan (Eds.), Mediated learning experience with children: Applications across countries. Singapore: McGraw-Hill Education.
Klein, P. S., Nil-Gar, O., & Darom, E. (2000). The use of computers in kindergarten, with or without adult mediation; effects on children’s cognitive performance and behavior. Computers in Human Behavior, 16, 591–608.
Klibanoff, R., Levine, S., Huttenlocher, J., Vasilyeva, M., & Hedges, L. (2006). Preschool children’s mathematical knowledge: The effect of teacher’s “math talk”. Developmental Psychology, 42, 59–69.
Marton, F., Runesson, U., & Tsui, A. B. (2004). The space of learning. In F. Marton & A. B. M. Tsui (Eds.), Classroom discourse and the space of learning (pp. 3–40). Mahwah, NJ: Lawrence Erlbaum Associates.
Ministry of Education. (2009). The Singapore model method for learning mathematics. Singapore: EPB Pan Pacific.
Neuman, D. (1987). The origin of arithmetic skills. Goteborg, Sweden: Acta Universitalis Gothenburgensis.
Piaget, J. (1952). The child’s conception of number. London: Routledge & Kegan Paul.
Resnick, L. B. (1983). A developmental theory of number understanding. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 109–151). Orlando, FL: Academic.
Runesson, U., & Mok, I. A. C. (2004). Discernment and the question, “What can be learned”. In F. Marton & A. B. M. Tsui (Eds.), Classroom discourse and the space of learning (pp. 63–87). Mahwah, NJ: Lawrence Erlbaum Associates.
Van de Walle, J. (2001). Elementary and middle school mathematics. Teaching developmentally (4th ed.). New York: Addison Wesley Longman.
Watson, A., & Mason, J. (2002). Extending examples spaces as a learning/teaching strategy in mathematics. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 378–385). Norwich, UK: PME.
Watson, A., & Mason, J. (2006). Mathematics as a constructive activity. Learners generating examples. Mahwah, NJ: Lawrence Erlbaum Associates.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media Singapore
About this chapter
Cite this chapter
Ng, S.F. (2015). How a Singapore Teacher Used Videos to Help Improve Her Teaching of the Part-Whole Concept of Numbers and the Model Method. In: Ng, S. (eds) Cases of Mathematics Professional Development in East Asian Countries. Mathematics Teacher Education, vol 10. Springer, Singapore. https://doi.org/10.1007/978-981-287-405-4_5
Download citation
DOI: https://doi.org/10.1007/978-981-287-405-4_5
Publisher Name: Springer, Singapore
Print ISBN: 978-981-287-404-7
Online ISBN: 978-981-287-405-4
eBook Packages: Humanities, Social Sciences and LawEducation (R0)