Use of Multiple Representations in Understanding Addition: The Case of Pre-school Children

Kamariah Abu Bakar, Suziyani Mohamed, Faridah Yunus, Aidah Abdul Karim

Abstract


An important objective in mathematics education is to ensure learners’ comprehension of the subject through effective teaching and learning, as emphasized by many countries worldwide, such as the United States, Australia, Singapore, and Malaysia in terms of the organization of mathematics and its curriculum documents. This paper explores young children’s (6 years old) use of multiple representations in understanding the concept of addition during problem-solving activities. The study employed a case study research design, comprising two young children in one preschool centre. Data collection included observation, dialogue with the children, and an analysis of various creations and usage of representation that shed light into both children’s capacity in utilizing different representation forms and performing translations. The findings unveiled the children’s capability in using a variety of representation forms, and performing translations within, and between different representation forms (with prompting). This study discusses the importance of facilitating the early development of young children’s use of multiple representations and performing translations to support their deep comprehension of the concept of addition.

https://doi.org/10.26803/ijlter.19.2.18


Keywords


addition; multiple representations; problem-solving; understanding; young children

Full Text:

PDF

References


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.

Abdullah, N., Zakaria, E., & Halim, L. (2012). The effect of a thinking strategy approach through visual representation on achievement and conceptual understanding in solving mathematical word problems. Asian Social Science, 8(16), 30-37.

Ahmad, A., Tarmizi, R. A., & Nawawi, M. (2010). Visual representations in mathematical word problem solving among form four students in Malacca. Procedia-Social and Behavioral Sciences, 8, 356-361.

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.

Ainsworth, S., Prain, V., & Tytler, R. (2011). Drawing to learn in science. Science, 333(6046), 1096-1097.

Anghileri, J. (1995). Children’s mathematical thinking in the primary years. Perspectives on Children’s Learning. New York: Cassell.

Ayub, A., Ghazali, M., & Othman, A. R. (2013). Preschool children's understanding of numbers from multiple representation perspective. IOSR Journal of humanities and social science, 6, 93-100.

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.

Baroody, A. J., Wilkins, J. L., & Tiilikainen, S. H. (2003). The development of children’s understanding of additive commutativity: From protoquantitive concept to general concept? In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 127–160). Mahwah, NJ: Erlbaum.

Bautista, A., Habib, M., Ong, R., Eng, A., & Bull, R. (2019). Multiple Representations in Preschool Numeracy: Teaching a Lesson on More-or-Less. Asia-Pacific Journal of Research in Early Childhood Education, 13(2).

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).

Davis, R. B. (1984). Learning Mathematics. The Cognitive Science Approach to Mathematics Education, Ablex, New Jersey.

Diezmann, C., & English, L. (2001). The roles of representation in school Mathematics: 2001 Year Book. Virginia: NCTM.

Elia, I., Gagatsis, A., & Demetriou, A. (2007). The effects of different modes of representation on the solution of one-step additive problems. Learning and Instruction, 17(6), 658-672.

Francis, F., & Tom, R. (2001). Representation: An important process for teaching and learning mathematics. Teaching Children Mathematics, 7(5), 288.

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

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.

Kaur, D., Koval, A., & Chaney, H. (2017). Potential of using iPad as a supplement to teach math to students with learning disabilities. International Journal of Research in Education and Science, 3(1), 114-121.

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.

Lipton, J. S., & Spelke, E. S. (2005). Preschool children's mapping of number words to nonsymbolic numerosities. Child Development, 76(5), 978-988.

Mokwebu, D. J. (2013). An exploration of the growth in mathematical understanding of grade 10 learners. Retrieved from http://hdl.handle.net/10386/1110

NCTM. (2000). National Council of Teachers of Mathematics, Principles and Standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

Papadakis, S., Kalogiannakis, M., & Zaranis, N. (2017). Improving mathematics teaching in kindergarten with realistic mathematical education. Early Childhood Education Journal, 45(3), 369-378.

Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation (s) in developing mathematical understanding. Theory into Practice, 40(2), 118-127.

Rosli, R., Goldsby, D., & Capraro, M. M. (2015). Using Manipulatives in Solving and Posing Mathematical Problems. Creative Education, 6(16), 1718.

Shiakalli, M., & Gagatsis, A. (2006). Compartmentalization of representation in tasks related to addition and subtraction using the number line. In Novotná, J., Moraová, H., Krátká, M. & Stehlíková, N. (Eds.). Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (pp. 105-112). Prague, Czech Republic: PME.

Suh, J., Johnston, C., Jamieson, S., & Mills, M. (2008). Promoting decimal number sense and representational fluency. Mathematics Teaching in the Middle School, 14(1), 44-50.

Tyng, K. S., Zaman, H. B., & Ahmad, A. (2011). Visual application in multi-touch tabletop for mathematics learning: A preliminary study. Paper presented at the International Visual Informatics Conference (pp. 319-328), Springer, Berlin: Heidelberg.

Ulusoy, F., & Incikabi, L. (2019). Incorporating Representation-Based Instruction into Mathematics Teaching: Engaging Middle Schoolers with Multiple Representations of Adding Fractions. In Handbook of Research on Promoting Higher-Order Skills and Global Competencies in Life and Work (pp. 311-336). IGI Global.

Yuanita, P., Zulnaidi, H., & Zakaria, E. (2018). The effectiveness of Realistic Mathematics Education approach: The role of mathematical representation as mediator between mathematical belief and problem solving. PloS one, 13(9), e0204847.

Zhou, X., Wang, Y., Wang, L., & Wang, B. (2006). Kindergarten children's representation and understanding of written number symbols. Early Child Development and Care, 176(1), 33-45. doi:10.1080/0300443042000302645


Refbacks

  • There are currently no refbacks.


e-ISSN: 1694-2116

p-ISSN: 1694-2493