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The purpose of this paper is to review the research on representation creation and its usage in classrooms to facilitate mathematical understanding. In the first part, the paper reviews the importance of representation in respect to mathematical learning. Then, a model linking representation usage with understanding is discussed. In conclusion, the paper proposes that learners utilize multiple representations including manipulatives, drawings, verbal and symbol forms in future research in an effort to obtain a congruent picture concerning the mathematical understanding of young children.
Ainsworth, S., Bibby, P., & Wood, D. (2002). Examining the effects of different multiple
representational systems in learning primary mathematics. The Journal of the Learning Sciences, 11(1), 25-61.
Bakar, K. A., & Karim, A. A. (2019). Young Children’s Photographs of Addition in the School
Environment. International Journal of Academic Research in Business and Social
Sciences, 9(8), 1–14.
Ballard, J. W. (2000). Students' use of multiple representations in mathematical problem
solving. Unpublished PhD dissertation, Montana State University, Bozeman, Montana.
Bobis, J. (2007). The empty number line: A useful tool or just another procedure? Teaching
Children Mathematics, 13(8), 410-413.
Chigeza, P. (2013). Translating between and within representations: Mathematics as lived
experiences and interactions. Paper presented at the Annual Meeting of the Mathematics Education Research Group of Australasia (MERGA, 36th, Melbourne, Victoria, Australia, 2013).
Council of Chief State School Officers & National Governers Association Center for Best
Practices. (2010). Common Core State Standards for Mathematics.
Diezmann, C., & English, L. (2001). The Roles of Representation in School Mathematics: 2001
YearBook (pp. 1-23). Virginia: NCTM.
Friedlander, A., & Tabach, M. (2001). Promoting multiple representations in algebra. In A.
Cuoco (Ed.), The roles of representation in school mathematics (pp. 173-184). Reston, VA: NCTM.
Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the
Concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645-657. doi: 10.1080/0144341042000262953
Gonsalves, N., & Krawec, J. (2014). Using number lines to solve Math word problems: A
strategy for students with learning disabilities. Learning Disabilities Research & Practice, 29(4), 160-170.
Goldin, G. (1998). Representational systems, learning, and problem solving in mathematics.
Journal of Mathematical Behavior, 17(2), 137-165. doi: 10.1016/S0364-0213(99)80056-1
Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of
mathematical concepts. In A.A. Cuoco & F.R. Curcio (Eds.), The roles of representation in school mathematics (pp 1-23). Reston, VA: NCTM
Hiebert, J. (1997). Making sense: teaching and learning mathematics with understanding.
Portsmouth, NH: Heinemann.
Johns, K. (2015). How do kindergarteners express their mathematics understanding?
Universal Journal of Educational Research 3(12),1015-1023.
Kato, Y., Kamii, C., Ozaki, K., & Nagahiro, M. (2002). Young children's representations of
groups of objects: The relationship between abstraction and representation. Journal for Research in Mathematics Education, 33(1), 30-45.
Krawec, J. L. (2014). Problem representation and mathematical problem solving of students of
varying math ability. Journal of Learning Disabilities, 47(2), 103-115.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among
representations in mathematics learning and problem solving. In C.Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale,NJ: Erlbaum.
MacDonald, A. (2010). Heavy thinking: Young children's theorising about mass. Australian
Primary Mathematics Classroom, 15(4), 4-8.
MacDonald, A., & Lowrie, T. (2011). Developing measurement concepts within context:
Children’s representations of length. Mathematics Education Research Journal, 23(1), 27-42. doi: 10.1007/s13394-011-0002-7
Ministry of Education Malaysia. (2006). Integrated Curriculum for Primary Schools, Curriculum
Development Centre.
Mokwebu, D. J. (2013). An exploration of the growth in mathematical understanding of grade 10 learners. University of Limpopo, Turfloop Campus.
Moomaw, S., & Dorsey, A. G. (2013). The Use of Numeric and Non-Numeric Symbols by Preschool Children in Early Addition. Journal of Research in Childhood Education, 27(3), 319-329
In-Text Citation: (Bakar et al., 2019)
To Cite this Article: Bakar, K. A., Mohamed, S., & Yunus, F. (2019). Young Children’s Representations: A Model for Using and Understanding Representations. International Journal of Academic Research in Progressive Education and Development, 8(4), 921–930.
Copyright: © 2019 The Author(s)
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