RESEARCH PAPER
Conceptions in Making Sense of Multiplication
Kin Eng Chin 1  
,  
Fui Fong Jiew 2
,  
 
 
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1
Flinders University, AUSTRALIA
2
Queensland University of Technology, AUSTRALIA
3
Universiti Malaysia Sabah, MALAYSIA
Online publish date: 2019-07-05
Publish date: 2019-07-05
 
EURASIA J. Math., Sci Tech. Ed 2019;15(12):em1779
KEYWORDS
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ABSTRACT
This paper aims to explore how three secondary school teachers make sense of multiplication based on their conceptions of multiplication. The framework of supportive and problematic conceptions in making sense of mathematics proposed by Chin (2013) is exemplified in this study. Initially, data were collected through a survey assessment that consists of a set of mathematical tasks. Then follow-up interviews were conducted with these participants. Three secondary school teachers (Jessica, Sarah and Claire – pseudonyms) participated in this study. Findings revealed that the changes of meanings in multiplication have impacted the sense-making of Sarah and Claire. On the other hand, Jessica who sensed these mathematical changes could talk about multiplication sensibly.
 
REFERENCES (22)
1.
Abdullah, N., Halim, L., & Zakaria, E. (2014). VStops: a thinking strategy and visual representation approach in mathematical word problem solving toward enhancing stem literacy. EURASIA Journal of Mathematics, Science & Technology Education, 10(3), 165-174.
 
2.
Baharam, B. H., Baharam, B. H., Ahmad, N. J., Tahir, N. M., & Hanafiah, M. N. M. (2017). Matematik tingkatan 2.
 
3.
Burris, A. C. (2005). Understanding the Math You Teach Content and Methods for Prekindergarten Through Grade 4.
 
4.
Byers, W. (2007). How mathematicians think: using ambiguity, contradiction, and paradox to create mathematics.
 
5.
Chan, Y. L., & Puteh, M. (2016). Matematik tahun 6 sekolah kebangsaan.
 
6.
Chin, K. E. (2013). Making sense of mathematics: supportive and problematic conceptions with special reference to trigonometry (Unpublished doctoral thesis). Retrieved from http://wrap.warwick.ac.uk/5840....
 
7.
Chin, K. E., & Jiew, F. F. (2018). A framework for making sense of mathematics. In F. J. Hsieh (Ed.), Proceedings of the 8th ICMI-East Asia Regional Conference on Mathematics Education, Vol. 2, (pp. 309-319).
 
8.
Chin, K. E., & Jiew, F. F. (2019). Changes of meanings in multiplication across different contexts: The case of Amy and Beth. EURASIA Journal of Mathematics, Science and Technology Education, 15(8), em1739. https://doi.org/10.29333/ejmst....
 
9.
Chin, K. E., & Pierce, R. (2019). University students' conceptions of mathematical symbols and expressions. EURASIA Journal of Mathematics, Science and Technology Education, 15(9), em1748. https://doi.org/10.29333/ejmst....
 
10.
Devlin, K. (2007). What is conceptual understanding? Retrieved from http://www.maa.org/external_ar....
 
11.
Harkness, S. S., & Thomas, J. (2008). Reflections on “Multiplication as original sin”: The implications of using a case to help preservice teachers understand invented algorithms. Journal of Mathematical Behavior, 27(2), 128–137. https://doi.org/10.1016/j.jmat....
 
12.
Jiew, F. F., & Chin, K. E. (in press). Supportive and problematic conceptions in making sense of multiplication: A case study. The Mathematics Enthusiast.
 
13.
Kilhamn, C. (2011). Making sense of negative numbers (Doctoral thesis). Retrieved from https://gupea.ub.gu.se/handle/....
 
14.
Larsson, K., Pettersson, K., & Andrews, P. (2017). Students’ conceptualisations of multiplication as repeated addition or equal groups in relation to multi-digit and decimal numbers. The Journal of Mathematical Behavior, 48, 1-13. https://doi.org/10.1016/j.jmat....
 
15.
National Council of Teachers of Mathematics (2009). Focus in High School Mathematics: Reasoning and Sense Making. Retrieved from https://www.nctm.org/Standards....
 
16.
Ooi, S. H., Yong, K. Y., & Ng, S. H. (2017). Matematik tingkatan 1.
 
17.
Piaget, J. (1952). The origins of intelligence in children (M. Cook, Trans.). https://doi.org/10.1037/11494-....
 
18.
Saleh, S., Saleh, F., Rahman, S. A., & Mohamed, A. R. (2010). Diagnosing year two pupils understanding of the certain concepts of multiplication at selected schools in Sabah. Procedia Social and Behavioral Sciences (Elsevier Ltd.), 8, 114-120. https://doi.org/10.1016/j.sbsp....
 
19.
Skemp, R. (1971). The Psychology of Learning Mathematics.
 
20.
Southwell, B., & Penglase, M. (2005). Mathematical knowledge of pre-service primary teachers. In H. L. Chick, & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 4, 209.
 
21.
Vosniadou, S., & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching. Learning and Instruction, 14(5), 445–451. https://doi.org/10.1016/j.lear....
 
22.
Whitacre, I., & Nickerson, S. D. (2016). Investigating the improvement of prospective elementary teachers’ number sense in reasoning about fraction magnitude. Journal of Mathematics Teacher Education, 19(1), 57–77. https://doi.org/10.1007/s10857....
 
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