RESEARCH PAPER
Grade 9 Learners’ Structural and Operational Conceptions of the Equal Sign: A Case Study of a Secondary School in Soshanguve
 
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Department of Mathematics Education, University of South Africa, SOUTH AFRICA
 
 
Online publication date: 2017-10-05
 
 
Publication date: 2017-10-30
 
 
Corresponding author
France Masilo Machaba   

University of South Africa, 194 Block CC, Soshanguve, 0152, 0152 Pretoria, South Africa
 
 
EURASIA J. Math., Sci Tech. Ed 2017;13(11):7243-7255
 
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ABSTRACT
This article gives an account of Grade 9 learners’ understanding of the concept of the equal sign and how they move from an arithmetic to an algebraic equation. A case study, using a sequential mixed method research design, was conducted in a secondary school in Soshanguve, a township in Gauteng, South Africa. Out of the 49 learners who wrote a test on the concept of the equal sign, eight were selected for an interview. The study revealed that Grade 9 learners in this school interpreted the equal sign as a ‘do something’ and unidirectional (one-sided) sign, not as the concept that represents an equivalent (concept of keeping both sides of the equal sign equal) of two quantities. The researchers attributed misinterpretation of the equal sign to how learners had been taught the concept of number sentences in lower grades, where greater emphasis was placed on rules than on the meaning of a concept.
REFERENCES (36)
1.
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. Mathematical Thinking and Learning, 9(3), 249–272.
 
2.
Braithwaite, D. W., Goldstone, R. L., Van der Maas, H. L., & Landy, D. H. (2016). Non-formal mechanisms in mathematical cognitive development: The case of arithmetic. Cognition, 149, 40–55.
 
3.
Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A review. The Journal of Mathematical Behavior, 32(3), 613–632.
 
4.
Byrd, C. E., McNeil, N. M., Chesney, D. L., & Matthews, P. G. (2015). A specific misconception of the equal sign acts as a barrier to children’s learning of early algebra. Learning and Individual Differences, 38, 61-67.
 
5.
Capraro, R. M., Capraro, M. M., Yetkiner, Z. E., Özel, S., Kim, H. G., & Küçük, A. R. (2010). An international comparison of grade 6 students’ understanding of the equal sign. Psychological reports, 106(1), 49-53.
 
6.
Carpenter, T., Franke, M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth: Heinemann.
 
7.
Creswell. J. W. (2014). Research design: Qualitative, quantitative and mixed methods approaches. Singapore: Sage.
 
8.
Department of Basic Education. (2013). Report on the Annual National Assessment of 2013. (2013). Pretoria: Government Printing Works.
 
9.
Didis, M. G., & Erbas, A. K. (2015). Performance and difficulties of students in formulating and solving quadratic equations with one unknown. Educational Sciences: Theory & Practice, 15(4), 1137–1150.
 
10.
Essien, A. (2009). An analysis of the introduction of the equal sign in three grade 1 textbooks. Pythagoras, 69, 28–35.
 
11.
Essien, A., & Setati, M. (2006). Revisiting the equal sign: Some grade 8 and 9 learners’ interpretations. African Journal of Research in SMT Education, 10(1), 47–58.
 
12.
Grobman, K. H., & Alibali, M. W. (2007). Understanding the equal sign and learning algebra. Paper presented at the biennial meeting of the Society for Research in Child Development, Boston, MA.
 
13.
Hattikudur, A., & Alibali, M. W. (2010). Learning about the equal sign: Does comparing with inequality symbols help? Journal of Experimental Child Psychology, 107, 15–30.
 
14.
Herscovics, N., & Kieran, C. (1980). Constructing meaning for the concept of equation. Mathematics Teacher, 73(8), 572–581.
 
15.
Hohensee, C. (2017). Preparing elementary prospective teachers to teach early algebra. Journal of Mathematics Teacher Education, 1–27.
 
16.
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, 166–176.
 
17.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317–326.
 
18.
Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 36, 297–312.
 
19.
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. Cognition and Instruction, 26, 195–217.
 
20.
Linchevski, L., & Herscovics, N. (1996). Crossing the cognitive gap between arithmetic and algebra: Operating on the unknown in the context of equations. Educational Studies in Mathematics, 30(1), 39–65.
 
21.
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. Journal for Research in Mathematics Education, 43(3), 316-350.
 
22.
McNeil, N. M. (2007). U-shaped development in math: 7-year-olds outperform 9-year-olds on equivalence problems. Developmental Psychology, 43, 687–695.
 
23.
McNeil, N. M. (2008). Limitations to teaching children 2 + 2 = 4: Typical arithmetic problems can hinder learning of mathematical equivalence. Child Development, 79, 1524–1537.
 
24.
McNeil, N. M., & Alibali, M. W. (2005a). Knowledge change as a function of mathematics experience: All contexts are not created equal. Journal of Cognition and Development, 6, 285–306.
 
25.
McNeil, N. M., & Alibali, M. W. (2005b). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76, 883–899.
 
26.
National Council of Teachers of Mathematics. (2000). Principles and standards for school Mathematics. Reston, VA: Author.
 
27.
National Governors Association. (2010). The Common Core State Standards. Retrieved from http://www.corestandards.org/t....
 
28.
Osana, H. P., Cooperman, A., Adrien, E., Rayner, V., Bisanz, J., Watchorn, R., & Sherman LeVos, J. (2012). Examining teacher knowledge and classroom practices during inquiry teaching on the equal sign. American Educational Research Association, Vancouver, Canada.
 
29.
Perry, M., Church, R. B., & Goldin-Meadow, S. (1988). Transitional knowledge in the acquisition of concepts. Cognitive Development, 3, 359–400.
 
30.
Powell, S. R. (2012). Equations and the equal sign in elementary mathematics textbooks. The Elementary school journal, 112(4), 627-648.
 
31.
Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 91, 175–189.
 
32.
Rittle-Johnson, B., Matthews, P., Taylor, R. S., & McEldoon, K. L. (2011). Assessing knowledge of mathematical equivalence. A construct-modelling approach. Journal of Educational Psychology, 103, 85–104.
 
33.
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.
 
34.
Stephens, A. C., Knuth, E. J., Blanton, M. L., Isler, I., Gardiner, A. M., & Marum, T. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings. The Journal of Mathematical Behavior, 32(2), 173-182.
 
35.
Tashakkori, A., & Teddlie, C. (2010). Mixed methods in social behavioral research. Thousand Oaks, CA: Sage.
 
36.
Van de Walle, JA., Karp, KS & Bay-Williams, JM. (Eds.). (2014). Elementary and Middle School Mathematics: Teaching developmentally. New Jersey: Pearson Education.
 
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