EXPLORING GRADE 11 LEARNERS’ ALGEBRAIC THINKING IN THE FORMULATION OF QUADRATIC EQUATIONS FROM GRAPHS

Reinhard Selowa, Zwelithini Bongani Dhlamini

Abstract


Algebraic thinking enables learners to devise algebra generalization when configuring quadratic equations from their graphical representations. Noticeable, learners grapple with this topic and there are some silent issues in the literature that should be explored in this discourse. Consequently, this prompted the current study, aimed to explore Grade 11 learners’ algebraic thinking when formulating quadratic equations from drawn graphs. The study adopted three tenets of the Lesh’s Translational model, pictorial and symbolic representations. An exploratory case study was used with 22 purposively sampled learners to explore algebraic thinking exhibited in learners’ responses to the graphical questions and transcripts from unstructured interviews. The algebraic thinking came from the exploration documents and interviews analysed through thematic analysis. The findings revealed that 17 learners lacked basic knowledge of algebra concepts which prevented the formulation of equations from graphs. This resulted from learners exploiting improper properties of algebra which were the requirement for the formulation of equations. The implication is that teaching, and learning should focus on the establishment of skills that permit exploiting appropriate prior knowledge relevant to this topic. Last, we suggest that empirical studies be conducted to focus on improving the instruction for the crafting of equations from graphs.


Keywords


algebraic thinking, equation representation, graph, quadratic functions

Full Text:

PDF

References


Adamuz-Povedano, N., Fernández-Ahumada, E., García-Pérez, M. T., & Montejo-Gámez, J. (2021). Developing number sense: An approach to initiate algebraic thinking in primary education. Mathematics, 9(5), 518. https://doi.org/10.3390/math9050518

Alkhateeb, M. (2019). Multiple representations in 8th Grade mathematics textbook and the extent to which teachers implement them. International Electronic Journal of Mathematics Education, 14(1), 137-145. https://doi.org/10.12973/iejme/3982

Appah, M. K., Brown, I. G., & Baidoo, S. R. (2020). Algebraic thinking among primary pupils: a boost for interest in mathematics. Pedagogical Research, 5(2), em0057. https://doi.org/10.29333/pr/7878

Apsari, R. A., Putri, R. I. I., Abels, M., & Prayitno, S. (2020). Geometry representation to develop algebraic thinking: a recommendation for a pattern investigation in pre-algebra class. Journal on Mathematics, 11(1), 45-58. https://doi.org/10.22342/jme.11.1.9535.45-58

Bakar, K. A., Mohamed, S., Yunus, F., & Karim, A. A. (2020). Use of multiple representations in understanding addition: The case of pre-school children. International Journal of Learning, Teaching and Educational Research, 19(2), 292-304. https://doi.org/10.26803/ijlter.19.2.18

Bal, A. P. (2015). Skills of using and transform multiple representations of the prospective teachers. Procedia-Social and Behavioral Sciences, 197, 582-588. https://doi.org/10.1016/j.sbspro.2015.07.197

Bayazit, I. (2018). Prospective teachers’ inclination of single representation and their development of the function concept. Educational Research and Reviews, 6(5), 436-446.

Blanton, M., Stroud, R., Stephens, A., Gardiner, A. M., Stylianou, D. A., Knuth, E., & Strachota, S. (2019). Does early algebra matter? The effectiveness of an early algebra intervention in grades 3 to 5. American Educational Research Journal, 56(5), 1930-1972. https://doi.org/10.3102/0002831219832301

Bolondi, G., Ferretti, F., & Maffia, A. (2020). Monomials and polynomials: the long march towards a definition. Teaching Mathematics and its Applications: An International Journal of the IMA, 39(1), 1-12. https://doi.org/10.1093/teamat/hry015

Brating, K., & Kilhamn, C. (2020). Exploring interaction of algebraic and computational thinking. Mathematics Thinking and Learning, 23(2), 170-185. https://doi.org/10.1080/10986065.2020.1779012

Damayanti, N. W., Parta, I. N., & Chandra, T. D. (2019). Student algebraic reasoning to solve quadratic equation problem. In Journal of Physics: Conference Series, 1227(1), 12025. https://doi.org/10.1088/1742-6596/1227/1/012025

Didis, M. G., & Erbas, A. K. (2015). Performance and difference in students in formulating & solving quadratic equations with one unknown. Educational Science Theory & Practice, 15(3), 1137-1150. http://doi.org/10.12738/estp.2015.4.2743

Rahmawati, D., Hidayanto, E., & Anwar, R. B. (2017). Process of mathematical representation translation from verbal into graphic. International Electronic Journal of Mathematics Education, 12(3), 367-381. https://doi.org/10.29333/iejme/618

Eriksson, H., & Eriksson, I. (2021). Learning actions indicating algebraic thinking in multilingual classrooms. Educational Studies in Mathematics, 106(3), 363-378. https://doi.org/10.1007/s10649-020-10007-y

Federica. F. (2019). The manipulation of algebraic expressions: Deepening of a widespread difficulties and new characterizations. International Electronic Journal of Mathematics Education, 15(1). https://doi.org/10.29333/iejme/5884

Gray, M., Downer, T., Hartz, D., Andersen, P., Hanson, J., & Gao, Y. (2022). The impact of three-dimensional visualisation on midwifery student learning, compared with traditional education for teaching the third stage of labour: A pilot randomised controlled trial. Nurse Education Today, 108, 105184. https://doi.org/10.1016/j.nedt.2021.105184

How, R. P. T. K., Zulnaidi, H., & Rahim, S. S. A. (2022). The importance of digital literacy in quadratic equations, strategies used, and issues faced by educators. Contemporary Educational Technology, 14(3), 372. https://doi.org/10.30935/cedtech/12023

Johnson, E. L. (2018). A new look at the representations for mathematical concepts: Expanding on Lesh's model of representations of mathematical concepts. Forum on Public Policy Online, 2018(1). 1-11.

Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139-151.

Kotsopoulos, D. (2007). Unraveling student challenges with quadratics: A cognitive approach. Australian Mathematics Teacher, 63(2), 19-24.

Kim How, R. P. T., Zulnaidi, H., & Abdul Rahim, S. S. (2022). The importance of digital literacy in quadratic equations, strategies used, and issues faced by educators. Contemporary Educational Technology, 14(3). https://doi.org/10.30935/cedtech/12023

Morales Carballo, A., Damián Mojica, A., & Marmolejo Vega, J. E. (2022). Hypothetical learning trajectory for assimilating the articulated concepts of quadratic function and equation through variational ideas and the use of GeoGebra in pre-university students. International Electronic Journal of Mathematics Education, 17(2), em0678. https://doi.org/10.29333/iejme/11714

Mutambara, L. H. N., Tendere, J., & Chagwiza, C. J. (2019). Exploring the conceptual understanding of the quadratic function concept in teachers’ colleges in Zimbabwe. EURASIA Journal of Mathematics, Science and Technology Education, 16(2), em1817. https://doi.org/10.29333/ejmste/112617

Radford, L. (2014). The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, 26(2), 257-277. https://doi.org/10.1007/s13394-013-0087-2

Sibgatullin, I. R., Korzhuev, A. V., Khairullina, E. R., Sadykova, A. R., Baturina, R. V., & Chauzova, V. (2022). A systematic review on algebraic thinking in education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), em2065. https://doi.org/10.29333/ejmste/11486

Taher, A.B., Mamouni, M. I, & Wahbi, B.E. (2023).The generalization as a tool to develop the algebraic thinking process. Journal of Hunan University (Natural Sciences), 50(2). https://doi.org/10.55463/issn.1674-2974.50.2.16

Tall, D., de Lima, R. N., & Healy, L. (2014). Evolving a three-world framework for solving algebraic equations in the light of what a student has met before. The Journal of Mathematical Behaviour, 34, 1–13. https://doi.org/10.1016/j.jmathb.2013.12.003

Tonapi, A. (2022). Factorising non-monic quadratic equations. At Right Angles, (12), 70-73.

Ubah, I. J. A., & Bansilal, S. (2018). Pre-service mathematics teachers’ knowledge of mathematics for teaching: quadratic functions. Problems of Education in the 21st Century, 76(6), 847-863. https://doi.org/10.33225/pec/18.76.847

Wilkie, K. J. (2021). Seeing quadratics in a new light: secondary mathematics pre-service teachers’ creation of figural growing patterns. Educational Studies in Mathematics, 106(1), 91-116. https://doi.org/10.1007/s10649-020-09997-6

Yazan, B. (2015). Three approaches to case study methods in education: Yin, Merriam, and Stake. The Qualitative Report, 20(2), 134-152. https://doi.org/10.46743/2160-3715/2015.2102




DOI: https://doi.org/10.17509/ije.v16i2.50496

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Reinhard Selowa, Zwelithini Bongani Dhlamini



Lisensi Creative Commons
This work is licensed under Creative Commons Attribution-ShareAlike 4.0 International License.