# Young Children’s Use of Manipulatives to Represent Addition Concept

Keywords:
Young children, Addition concept, Manipulatives, Representation.

### Abstract

One of the first fundamental arithmetic concepts that young children learn in school is addition. This article explores how young children use manipulatives while working on tasks relating to number and addition. The study employed case study research design and involved six children (aged six years) in one preschool center. Observation of children’s work during mathematical tasks revealed children’s early understanding of the addition concept. Hence, it is important that educators value and support the early development of children’s mathematical representations to facilitate their successful use in learning and understanding mathematics concepts.

### References

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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.

Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33(2), 131-152.

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. (2017). Young Children’s Representations of Addition in Problem Solving. Creative Education, 8(14), 2232.

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.

Bakar, K.A. (2018) Young Malaysian Children’s Representations of Addition in Problem-Solving. (Unpublished doctoral thesis), The University of Sydney, Australia.

Baroody, A. J. (1987a). Children’s mathematical thinking: A developmental framework for preschool, primary, and special education teachers. New York: Teachers College Press.

Baroody, A. J. (1987b). The development of counting strategies for single-digit addition. Journal for Research in Mathematics Education, 18(2), 141-157.

Batchelor, S., Keeble, S., & Gilmore, C. (2015). Magnitude representations and counting skills in preschool children. Mathematical Thinking and Learning, 17(2-3), 116-135.

Edens, K., & Potter, E. (2007). The relationship of drawing and mathematical problem solving: “Draw for math” tasks. Studies in Art Education, 48(3), 282-298.

Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243-275). New York: Macmillan.

Gelman, R., & Gallistel, C. (1978). The children’s understanding of number: Cambridge, MA: Harvard University Press.

Gibbons, S. J. (2012). Manipulatives and the growth of Mathematical understanding. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4211&context=etd

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.

Hiebert, J., & Wearne, D. (1992). Links between teaching and learning place value with understanding in first grade. Journal for Research in Mathematics Education, 23(2), 98-122.

Howard, P., & Perry, B. (1997). Manipulatives in primary mathematics: Implications for learning and teaching. Australian Primary Mathematics Classroom, 2(2), 25.

Johns, K. (2015). How do kindergarteners express their mathematics understanding? Universal Journal of Educational Research 3(12), 1015-1023.

Krajewski, K., & Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study. Learning and Instruction, 19(6), 513-526.

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.

Levine, S. C., Jordan, N. C., & Huttenlocher, J. (1992). Development of calculation abilities in young children. Journal of Experimental Child Psychology, 53(1), 72-103.

Manches, A., & O’Malley, C. (2016). The effects of physical manipulatives on children’s numerical strategies. Cognition and Instruction, 34(1), 27-50.

Ministry of Education Malaysia. (2010). National Standard Preschool Curriculum. Kuala Lumpur: Curriculum Development Centre.

Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175-197.

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

Patel, P., & Canobi, K. H. (2010). The role of number words in preschoolers’ addition concepts and problems solving procedures. Educational Psychology, 30(2), 107-124.

Puchner, L., Taylor, A., O’Donnell, B., & Fick, K. (2008). Teacher learning and mathematics manipulatives: A collective case study about teacher use of manipulatives in elementary and middle school mathematics lessons. School Science and Mathematics, 108(7), 313-325.

Resnick, L. B. (1992). From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge. In G. Leinhardt, R. Putnam & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 373-429). Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.

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

Siegler, R. S., & Jenkins, E. (1989). How children discover new strategies. Hillsdale, NJ: Erlbaum.

Thomas, J. N., & Tabor, P. D. (2012). Developing Quantitative Mental Imagery. Teaching Children’s Mathematics, 19(3), 174-183.

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.

Uesaka, Y., Manalo, E., & Ichikawa, S. (2007). What kinds of perceptions and daily learning behaviors promote students’ use of diagrams in mathematics problem solving? Learning and Instruction, 17(3), 322-335.

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.

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.

Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33(2), 131-152.

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. (2017). Young Children’s Representations of Addition in Problem Solving. Creative Education, 8(14), 2232.

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.

Bakar, K.A. (2018) Young Malaysian Children’s Representations of Addition in Problem-Solving. (Unpublished doctoral thesis), The University of Sydney, Australia.

Baroody, A. J. (1987a). Children’s mathematical thinking: A developmental framework for preschool, primary, and special education teachers. New York: Teachers College Press.

Baroody, A. J. (1987b). The development of counting strategies for single-digit addition. Journal for Research in Mathematics Education, 18(2), 141-157.

Batchelor, S., Keeble, S., & Gilmore, C. (2015). Magnitude representations and counting skills in preschool children. Mathematical Thinking and Learning, 17(2-3), 116-135.

Edens, K., & Potter, E. (2007). The relationship of drawing and mathematical problem solving: “Draw for math” tasks. Studies in Art Education, 48(3), 282-298.

Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243-275). New York: Macmillan.

Gelman, R., & Gallistel, C. (1978). The children’s understanding of number: Cambridge, MA: Harvard University Press.

Gibbons, S. J. (2012). Manipulatives and the growth of Mathematical understanding. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4211&context=etd

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.

Hiebert, J., & Wearne, D. (1992). Links between teaching and learning place value with understanding in first grade. Journal for Research in Mathematics Education, 23(2), 98-122.

Howard, P., & Perry, B. (1997). Manipulatives in primary mathematics: Implications for learning and teaching. Australian Primary Mathematics Classroom, 2(2), 25.

Johns, K. (2015). How do kindergarteners express their mathematics understanding? Universal Journal of Educational Research 3(12), 1015-1023.

Krajewski, K., & Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study. Learning and Instruction, 19(6), 513-526.

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.

Levine, S. C., Jordan, N. C., & Huttenlocher, J. (1992). Development of calculation abilities in young children. Journal of Experimental Child Psychology, 53(1), 72-103.

Manches, A., & O’Malley, C. (2016). The effects of physical manipulatives on children’s numerical strategies. Cognition and Instruction, 34(1), 27-50.

Ministry of Education Malaysia. (2010). National Standard Preschool Curriculum. Kuala Lumpur: Curriculum Development Centre.

Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175-197.

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

Patel, P., & Canobi, K. H. (2010). The role of number words in preschoolers’ addition concepts and problems solving procedures. Educational Psychology, 30(2), 107-124.

Puchner, L., Taylor, A., O’Donnell, B., & Fick, K. (2008). Teacher learning and mathematics manipulatives: A collective case study about teacher use of manipulatives in elementary and middle school mathematics lessons. School Science and Mathematics, 108(7), 313-325.

Resnick, L. B. (1992). From protoquantities to operators: Building mathematical competence on a foundation of everyday knowledge. In G. Leinhardt, R. Putnam & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 373-429). Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.

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

Siegler, R. S., & Jenkins, E. (1989). How children discover new strategies. Hillsdale, NJ: Erlbaum.

Thomas, J. N., & Tabor, P. D. (2012). Developing Quantitative Mental Imagery. Teaching Children’s Mathematics, 19(3), 174-183.

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.

Uesaka, Y., Manalo, E., & Ichikawa, S. (2007). What kinds of perceptions and daily learning behaviors promote students’ use of diagrams in mathematics problem solving? Learning and Instruction, 17(3), 322-335.

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.

Published

2019-12-30

How to Cite

*Religación. Revista De Ciencias Sociales Y Humanidades*,

*4*(22), 39-45. Retrieved from http://revista.religacion.com/index.php/religacion/article/view/546

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General Section