RESEARCH PAPER
The structural and operational complementarity: Grade nine learners’ pitfalls and gains of simplifying algebraic expressions
 
More details
Hide details
1
Department of Mathematics Science and Technology Education, University of Limpopo, Limpopo, SOUTH AFRICA
 
 
Online publication date: 2023-09-07
 
 
Publication date: 2023-10-01
 
 
EURASIA J. Math., Sci Tech. Ed 2023;19(10):em2344
 
KEYWORDS
ABSTRACT
This study focused on the investigation of the structural and operational complementarity in the simplification of algebraic expressions. The dual nature of mathematical conceptions is the theoretical framework that underpin this study. Qualitative content analysis was employed as a method and research design to investigate the complementarity between the operational and structural learners’ conceptions of the simplification. The findings revealed that learners’ undeveloped and fragmented structures of algebra caused the inability to simplify expressions. Ironically, for the very few learners who managed to simplify expressions, used skills and knowledge of the previous grade. Irrespective of this, the complementarity of learners’ conceptions of systems and components is undoubtfully key to their success during the simplification of expressions. This study recommends teaching and learning of algebra should address the complementarity of the operational and structural notions.
REFERENCES (43)
1.
AL-Rababaha, Y, Y., Yew, W. T., & Meng, C. C. (2020). Misconceptions in school algebra. International Journal of Academic Research in Business and Social Sciences, 10(5), 803-812. https://doi.org/10.6007/IJARBS....
 
2.
Arzarello, F., Bazzini, L., & Chiappini, G. (2001). A model for analyzing algebraic processes of thinking. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 61-81). Kluwer. https://doi.org/10.1007/0-306-....
 
3.
Baidoo, J. (2019). Dealing with grade 10 learners’ misconceptions and errors when simplifying algebraic fractions. Journal of Emerging Trends in Educational Research and Policy Studies, 10(1), 47-55.
 
4.
Baidoo, J., Adane, M., & Luneta, K. (2020). Solving algebraic fractions in high schools: An error analysis. Journal of Educational Studies, 19(2), 96-118.
 
5.
Bansilal, S., & Ubah, I. (2020). The use of multiplication and other mal rules in fraction operations by pre-service teachers. Journal of mathematical Behavior, 58, 100781. https://doi.org/10.1016/j.jmat....
 
6.
Booth, J. L., Newton, K. J., & Twiss-Garrity, L. K. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118, 110-118. https://doi.org/10.1016/j.jecp....
 
7.
Booth, L. R. (1988). Children’s difficulties in the beginning algebra. In A. F. Coxford (Ed.), The ideas of algebra, K-12, NCTM yearbook (pp. 20-32). NCTM.
 
8.
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/147808....
 
9.
Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 669-705). Information Age Publishing. https://doi.org/10.1007/978-94....
 
10.
Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2007). Early algebra and mathematical generalization. ZDM Mathematics Education, 49, 3-22. https://doi.org/10.1007/S11858....
 
11.
Chalouh, L., & Herscovics, N. (1988). Teaching algebraic expressions in a meaningful way. In A. F. Coxford (Ed.), The ideas of algebra, K-12, NCTM yearbook (pp. 33-42). NCTM.
 
12.
Chimoni, M., & Pitta-Pantazi, D. (2017). Parsing the notion of algebraic thinking within a cognitive perspective. Educational Psychology, 37(10), 1186-1205. https://doi.org/10.1080/014434....
 
13.
DBE. (2011). Curriculum and assessment policy statements grades 7-9. Department of Basic Education. http://www.education.gov.za.
 
14.
Dhlamini, Z. B. (2018). The effectiveness of annual national assessment in monitoring mathematics education standard in South Africa [PhD thesis, University of Limpopo].
 
15.
Elo. S., & Kyngäs, H. (2008). The qualitative content analysis process. Journal of Advanced Nursing, 62(1),107-115. https://doi.org/10.1111/j.1365....
 
16.
Faramarzpoor, N., & Fadaee, M. R. (2020). The investigation of students’ mistakes in simplifying algebraic expressions and finding the source of these mistakes from the viewpoint of math teachers. Technology of Education Journal, 14(4), 959-970. https://doi.org/10.22061/TEJ.2....
 
17.
Harwood, T. G., & Garry, T. (2003). An overview of content analysis. The Marketing Review, 3, 479-498. https://doi.org/10.1362/146934....
 
18.
Irwati, C. M. Z., & Ali, R. M. (2018). Cognitive conflict strategy to minimize students’ misconceptions on the topic of addition of algebraic expression. In Journal of Physics: Conference Series, 1088, 012084. https://doi.org/10.1088/1742-6....
 
19.
Jiang, M. J. Cooper, J. L., & Alibali, M. W. (2014). Spatial factors influence arithmetic performance: The case of the minus sign. The Quarterly Journal of Experimental Psychology, 67(8), 1626-1642. https://doi.org/10.1080/174702....
 
20.
Kieran, C. (1992). The learning and teaching of algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). Macmillan.
 
21.
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707-762). Information Age Publishing.
 
22.
Linchevski, L., & Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40, 176-196. https://doi.org/10.1023/A:1003....
 
23.
Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). Kluwer. https://doi.org/10.1007/978-94....
 
24.
Moodliar, J., & Abdulhamid, L. (2021). Novice and expert grade 9 teachers’ responses to unexpected learner offers in the teaching of algebra. Pythagoras, 42(1), a624. https://doi.org/10.4102/pythag....
 
25.
Ndemo, O., & Ndemo, Z. (2018). Secondary school students’ errors and misconceptions in learning algebra. Journal of Education and Learning, 12(4), 690-701. https://doi.org/10.11591/edule....
 
26.
Novotná, J., & Hoch, M. (2008). How structure sense for algebraic expressions or equations is related to structure sense for abstract algebra. Mathematics Education Research Journal, 20(2), 93-104. https://doi.org/10.1007/BF0321....
 
27.
Otte, M. (1990). Arithmetic and geometry: Some remarks on the concept of complementarity. Studies in Philosophy and Education, 10, 37-62. https://doi.org/10.1007/BF0036....
 
28.
Pournara, C. (2020). Grade 9 learners’ algebra performance: Comparisons across quintiles, insights from errors and curriculum implications. South African Journal of Science, 116(9/10), 41-47. https://doi.org/10.17159/sajs.....
 
29.
Pournara, C., Hodgen, J., Sanders, Y., & Adler, J. (2016). Learners’ errors in secondary algebra: Insights from tracking a cohort from grade 9 to grade 11 on a diagnostic algebra test. Pythagoras, 37(1), a334. https://doi.org/10.4102/pythag....
 
30.
Scheiner, T. (2016). New light on old horizon: Constructing mathematical concepts, underlying abstraction processes, and sense making strategies. Educational Studies in Mathematics, 91, 165-183. https://doi.org/10.1007/s10649....
 
31.
Schneider, T., & Pinto, M. F. (2019). Emerging perspectives in mathematical cognition: contextualizing, complementizing, and complexifying. Educational Studies in Mathematics, 101, 357-372. https://doi.org/10.1007/s10649....
 
32.
Schreier, M. (2012). Qualitative content analysis in practice. SAGE.
 
33.
Seng, L. K. (2010). An error analysis of form 2 (grade7) students in simplifying algebraic expressions: A descriptive study. Electronic Journal of Research in Educational Psychology, 8(1), 139-162. https://doi.org/10.25115/ejrep....
 
34.
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. https://doi.org/10.1007/BF0030....
 
35.
Sfard, A. (1995). The development of algebra: confronting historical and psychological perspectives. Journal of Mathematical Behavior, 14, 15-39. https://doi.org/10.1016/0732-3....
 
36.
Sfard, A., & Linchevski, L. (1995). The gains and the pitfalls of reification: A case of algebra. Educational Studies in Mathematics, 26, 191-228. https://doi.org/10.1007/BF0127....
 
37.
Thompson, P. W., & Sfard, A. (1994). Problems of reification: Representations and mathematical objects. In D. Kirshner (Ed.), Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education (pp. 1-32).
 
38.
Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51-64. https://doi.org/10.1023/A:1003....
 
39.
van Oers, B. (1998). From context to contextualizing. Learning and Instruction, 8(6), 473-488. https://doi.org/10.1016/S0959-....
 
40.
Vithal, R. (2008). Complementarity, mathematics and context. Journal of Education, 45, 43-64.
 
41.
Warren, E. (2003). The role of arithmetic structure in the transition from arithmetic to algebra. Mathematics Education Research Journal, 15, 122-137. https://doi.org/10.1007/BF0321....
 
42.
Zeljić, M. (2015). Modelling the relationships between quantities: Meaning in literal expressions. EURASIA Journal of Mathematics, Science & Technology Education, 11(2), 431-442. https://doi.org/10.12973/euras....
 
43.
Zulfa, B. I., Suryadi, D., Fatimah, S & Jupri, A. (2020). Student’s mistake in algebraic fraction: An analysis using AVAE categories. Journal of Physics: Conference Series, 1521, 032029. https://doi.org/10.1088/1742-6....
 
eISSN:1305-8223
ISSN:1305-8215
Journals System - logo
Scroll to top