Year Five Pupils’ Understanding of Generalised Arithmetic

This paper reports on the research on year five pupils’ understanding of generalised arithmetic, which aimed to investigate the understanding of year five pupils’ commutative property and the property of zero together with its correlation with their mathematical achievement. Data for the study were collected via paper and pencil assessment answers for two items. Findings showed moderate achievement for both of the tasks. The pupils’ explanation illustrated their poor conceptual understanding of commutative property and the property of zero. However, this understanding is not correlated with their mathematical achievement in school. It shows that an outstanding student in school did not necessarily acquire conceptual understanding of commutative principle and the property of zero.

Carpenter, T.P., Franke, M.L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
Carraher, D.W., Schliemann, A.D., & Schwartz, 1.L. (2008). Early algebra is not the same as algebra early. In 1.1. Kaput, D.W. Carraher, & M.L. Blanton, Algebra in the early grades (pp. 235-272). New York, NY: Taylor & Francis.
Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59-78. doi: 10.1007/BFo1284528
Hunter, 1. (2010, April). Developing early algebraic reasoning through exploration of the commutative principle. In M. ]oubert, & P. Andrews, Developing early algebraic reasoning through exploration of the commutative principle. Symposium conducted at the British Congress for Mathematics Education, Manchester, UK. Retrieved from http://www.bsrlm.org.uk/IPs/ip30- 1/BSRLM-IP-30-1-14pdf
Kaput, 1.1. (2008). What is algebra? What is algebraic reasoning? In 1.1. Kaput, D.W. Carraher, & M.L. Blanton (Eds.), Algebra in the early grades (pp. 5- 17). New York, NY: Taylor and Francis.
Knuth, E.1., Alibali, M.W., McNeil, N.M., Weinberg, A., & Stephens, A.C. (2005). Middle school students’ understanding of core algebraic concepts: Equivalence & variable. Zentralblattfur Didaktik der Mathematik, 37(1), 68-76. doi: 10.1007/BFo2655899
McNeil, N.M., Fyfe, E.R., Petersen, L.A., Dunwiddie, A.E., & Brletic-Shipley, H. (2011). Benefits of practicing 4:2+2: Nontraditional problem formats facilitate children’s understanding of mathematical equivalence. Child Development, 82(5), 1620-1633. doi: 10.1111/j.1467-8624.2011.01622.X.
Moss, I., & McNab, S.L. (2011). An approach to geometric and numeric patterning that fosters second grade students’ reasoning and generalizing about functions and co-variation. In ]. Cai, & E. Knuth (Eds.), Advances in mathematics education (pp. 277-301). New York, NY: Springer.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Ralston, N.C. (2013). The development and validation of a diagnostic assessment of algebraic thinking skills for students in the elementary grades (Doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 3588844)
Schifter, D., Monk, S., Russell, S.J., & Bastable, V. (2008). Early algebra: What does under- standing the laws of arithmetic mean in the elementary grades? In ]. Kaput, D. Carraher, M. Blanton (Eds.), Algebra in the early grades (pp. 413-447). Mahwah, NJ: Erlbaum.
SlaVit, D. (1999). The role of operation sense in transitions from arithmetic to algebraic thought. Educational Studies in Mathematics, 37(3), 251-274. doi: 10.1023/A:1003602322232