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http://dx.doi.org/10.7468/jksmed.2014.18.4.237

Primary School Students' Understanding of Equation Structure and the Meaning of Equal Sign: A Chinese Sample Study  

Yang, Xinrong (School of Mathematics and Statistics, Southwest University)
Huo, Yujia (Faculty of Psychology, Southwest University)
Yan, Yanxiong (School of Mathematics and Statistics, Southwest University)
Publication Information
Research in Mathematical Education / v.18, no.4, 2014 , pp. 237-256 More about this Journal
Abstract
This paper reports findings from a written assessment which was designed to investigate Chinese primary school students' understanding of the equal sign and equation structure. The investigation included a sample of 110 Grade 3, 112 Grade 4, and 110 Grade 5 students from four schools in China. Significant differences were identified among the three grades and no gender differences were found. The majority of Grades 3 and 4 students were found to view the equal sign as a place indicator meaning "write the answer here" or "do something like computation", that is, holding an operational view of the equal sign. A part of Grade 5 students were found to be able to interpret the equal sign as meaning "the same as", that is, holding a relational view of the equal sign. In addition, even though it was difficult for Grade 3 students to recognize the underlying structure in arithmetic equation, quite a number of Grades 4 and 5 students were able to recognize the underlying structure on some tasks. Findings in this study suggest that Chinese primary school students demonstrate a relational understanding of the equal sign and a strong structural sense of equations in an earlier grade. Moreover, what found in the study support the argument that students' understanding of the equal sign is influenced by the context in which the equal sign is presented.
Keywords
equal sign; equations; Chinese primary school students; early algebra;
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1 Alibali, M. W.; Knuth, E. J.; Hattikudur, S.; McNeil, N. M. & Stephens, A. C. (2007). A longitudinal examination of middle school students' understanding of the equal sign and equivalent equations. Math. Think. Learn. 9(3), 221-246. ME 2007b.00352   DOI
2 Asquith, P.; Stephens, A. C.; Knuth, E. J. & Alibali, M. W. (2007). Middle school mathematics teachers' knowledge of students' understanding of core algebraic concepts: Equal sign and variable. Math. Think. Learn. 9(3), 247-270. ME 2007b.00353
3 Baroody, A. J. & Ginsburg, H. P. (1983). The effects of instruction on children's understanding of the "equals" sign. Elementary School Journal 84, 199-212.   DOI
4 Behr, M.; Erlwanger, S. & Nichols, E. (1980). How children view the equal sign. Math, Teaching, 92, 13-15. ME 1981x.00631
5 Cai, J.; Ng, S. F. & Moyer, J. (2011). Developing students' algebraic thinking in earlier grades: Lessons from China and Singapore. In: J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 25-41). Berlin: Springer. ME 2011d.00630
6 Cajori, F. (1928). A history of mathematical notations: Vol. I, Notations in Elementary Mathematics. LaSalle, IL, USA: Open Court.
7 Carpenter, T. P.; Franke, M. L. & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in the elementary school. Portsmouth, NH, USA: Heinemann.
8 Falkner, K. P.; Levi, L. & Carpenter, T. P. (1999). Children's understanding of equality: A foundation for algebra. Teach. Child. Math. 6(4), 232-236. ME 2000e.03407
9 Hattikudur, S., & Alibali, M. W. (2010). Learning about the equal sign: Does comparing with inequality symbols help?. Journal of experimental child psychology 107(1), 15-30.   DOI
10 Jones, I.; Inglis, M.; Gilmore, C. & Dowens, M. (2012). Substitution and sameness: Two components of a relational conception of the equals sign. Journal of experimental child psychology 113(1), 166-176.   DOI
11 Jones, I.; Inglis, M.; Gilmore, C. & Evans, R. (2013). Teaching the substitutive conception of the equals sign. Res. Math. Educ. 15(1), 34-49. ME 2014c.00701   DOI
12 Jones, I. & Pratt, D. (2012). A substituting meaning for the equals sign in arithmetic notating tasks. J. Res. Math. Educ. 43(1), 2-33. ME 2012f.00762   DOI
13 Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics 12(3), 317-326. ME 1982x.00022   DOI   ScienceOn
14 Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In: F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707-762). Charlotte, NC, USA: Information Age. ME 06332594
15 Matthews, P.; Rittle-Johnson, B.; McEldoon, K. & Taylor, R. (2012). Measure for measure: What combining diverse measures reveals about children's understanding of the equal sign as an indicator of mathematical equality. J. Res. Math. Educ. 43(3), 316-334. ME 2012f.00766   DOI
16 Knuth, E. J.; Alibali, M. W.;, McNeil, N. M.; Weinberg, A. & Stephens, A. C. (2005). Middle school students' understanding of core algebraic concepts: Equivalence & variable. ZDM, Zentralbl. Didakt. Math. 37(1), 68-76. ME 2009b.00392   DOI
17 Knuth, E. J.; Stephens, A. C.; McNeil, N. M. & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. J. Res. Math. Educ. 37(4), 297-312. ME 2008f.00383
18 Li, X.; Ding, M.; Capraro, M. M. & Capraro, R. M. (2008). Sources of differences in children's understandings of mathematical equality: Comparative analysis of teacher guides and student texts in China and the United States. Cogn. Instr. 26(2), 195-217. ME 2012a.00383   DOI
19 McNeil, N. M. (2007). U-shaped development in math: 7-Year-olds outperform 9-year-olds on equivalence problems. Developmental Psychology 43(3), 687-695.   DOI
20 McNeil, N. M. & Alibali, M. W. (2005). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition & Development 6, 385-406.
21 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
22 Seo, K.-H. & Ginsburg, H. P. (2003). "You've got to carefully read the math sentence": Classroom context and children's interpretations of the equals sign. In: A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 161-187). Mahwah, NJ: Lawrence Erlbaum Associates. ME 2003c.02295
23 McNeil, N. M.; Grandau, L.; Knuth, E.; Alibali, M.; Stephens, A.; Hattikudur, S. et al. (2006). Middle-school students' understanding of the equal sign: The books they read can't help. Cognition and Instruction 24(3), 367-385.   DOI
24 Powell, S. R. (2012). Equations and the equal sign in elementary mathematics textbooks. Elementary School Journal 112(4), 627-648.   DOI
25 Rittle-Johnson, B., Matthews, P., Taylor, R. S., & McEldoon, K. L. (2011). Assessing knowledge of mathematical equivalence. A construct-modeling approach. Journal of Educational Psychology, 103, 85-104.   DOI
26 Stephens, A. C.; Knuth, E. J.; Blanton, M. L.; Isler, I.; Murphy Gardiner, A. & Marum, T. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students' understandings. J. Math. Behav. 32(2), 173-182. ME 2013c.00613   DOI
27 Stigler, J. W., & Baranes, R. (1988). Culture and mathematics learning. In: E. Z. Rothkoft (Ed.), Review of research in education (vol. 15, pp. 253-306). Washington, DC: American Educational research Association.