Journal of Pedagogical Sociology and Psychology
Impact of multiple representations-based instruction on teaching and learning of linear equations
Kofi Nkonkonya Mpuangnan 1 * , Blankson Kwaku Adjei 2, Samantha Nkonkonya Govender 1
More Detail
1 Department of Curriculum & Instructional Studies, University of Zululand, South Africa
2 University of Education Winneba, Ghana
* Corresponding Author
Open Access Full Text (PDF)
ARTICLE INFO

Journal of Pedagogical Sociology and Psychology, 2024 - Volume 6 Issue 1, pp. 58-76
https://doi.org/10.33902/jpsp.202425242

Article Type: Research Article

Published Online: 10 Mar 2024

Views: 142 | Downloads: 129

ABSTRACT
This paper investigates the impact of multiple representations-based instruction on the teaching and learning processes of linear equations among students in Standard VIII. It focuses on how different representations, such as graphs, tables, and equations, affect comprehension, retention, and overall mastery of linear equations in this educational context. An experimental design was employed, involving 159 students selected from Techiman Municipality in the Brong Ahafo Region of Ghana using a simple random sampling technique. Also, 86 mathematics teachers were randomly chosen to gather diverse viewpoints and valuable insights aimed at improving the teaching methods for this concept. Data collection instruments included a linear equations achievement test (pre-test & post-test) and a questionnaire. The collected data were analysed by using descriptive and inferential statistics. The study revealed that most teachers primarily relied on algebraic representation but only a few incorporated multiple representations due to various challenges such as time constraints, difficulty for students, lack of materials, and absence from the syllabus. It was further found that the implementation of multiple representations-based instructions resulted in a significant improvement in learners' scores in the linear equations achievement test, highlighting the effectiveness of this instructional approach. It was recommended that teachers teach linear equations in one variable using other representations such as manipulatives and graphics to enhance understanding. Also, students are encouraged to cultivate proficiency in integrating multiple representations when tackling problems related to linear equations. Further research should be conducted on equipping teachers with ample resources and designing robust training programs to enable them to adeptly incorporate multiple representations-based instruction for teaching linear equations.
KEYWORDS
Ghana linear equation mathematics multiple representation-based instructions standard viii
In-text citation: (Mpuangnan et al., 2024)
Reference: Mpuangnan, K. N., Adjei, B. K., & Govender, S. N. (2024). Impact of multiple representations-based instruction on teaching and learning of linear equations. Journal of Pedagogical Sociology and Psychology, 6(1), 58-76. https://doi.org/10.33902/jpsp.202425242
In-text citation: (1), (2), (3), etc.
Reference: Mpuangnan KN, Adjei BK, Govender SN. Impact of multiple representations-based instruction on teaching and learning of linear equations. Journal of Pedagogical Sociology and Psychology. 2024;6(1), 58-76. https://doi.org/10.33902/jpsp.202425242
In-text citation: (1), (2), (3), etc.
Reference: Mpuangnan KN, Adjei BK, Govender SN. Impact of multiple representations-based instruction on teaching and learning of linear equations. Journal of Pedagogical Sociology and Psychology. 2024;6(1):58-76. https://doi.org/10.33902/jpsp.202425242
In-text citation: (Mpuangnan et al., 2024)
Reference: Mpuangnan, Kofi Nkonkonya, Blankson Kwaku Adjei, and Samantha Nkonkonya Govender. "Impact of multiple representations-based instruction on teaching and learning of linear equations". Journal of Pedagogical Sociology and Psychology 2024 6 no. 1 (2024): 58-76. https://doi.org/10.33902/jpsp.202425242
In-text citation: (Mpuangnan et al., 2024)
Reference: Mpuangnan, K. N., Adjei, B. K., and Govender, S. N. (2024). Impact of multiple representations-based instruction on teaching and learning of linear equations. Journal of Pedagogical Sociology and Psychology, 6(1), pp. 58-76. https://doi.org/10.33902/jpsp.202425242
In-text citation: (Mpuangnan et al., 2024)
Reference: Mpuangnan, Kofi Nkonkonya et al. "Impact of multiple representations-based instruction on teaching and learning of linear equations". Journal of Pedagogical Sociology and Psychology, vol. 6, no. 1, 2024, pp. 58-76. https://doi.org/10.33902/jpsp.202425242
REFERENCES
  • Anamuah-Mensah, J., & Mereku, D. (2005). Ghanaian JSS 2 students' absymal mathematics achievement in Timss-2003: A consequence of the basic school mathematics curriculum [Paper presentation]. West African Examination Council (WAEC) Monthly Seminar at WAEC Conference Hall, Accra. https://doi.org/10.4314/mc.v5i1.21489
  • Bal, A. P. (2014). The examination of representations used by classroom teacher candidates in solving mathematical problems. Educational Sciences: Theory & Practice, 14(6), 1-17.
  • Beatty, R. A. (2010). Pattern rules, patterns, and graphs: Analyzing grade 6 students' learning of linear functions through the processes of webbing, situated abstractions, and convergent conceptual change [Unpublished doctoral dissertation). Canada, University of Toronto.
  • Birgin, O., Gurbug, A. O., & Catlioglu, H. (2012). Determining eighth grade students understanding and difficulties of linear functions. International Journal of Education in Mathematics, Science and Technology, 1(4), 253-264.
  • Bittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2013). Introductory and intermediate algebra. Pearson.
  • Boaler, J. (2016). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. John Wiley & Sons.
  • Cai, J. (2005). U.S and Chinese teachers' constructing, knowing,and evaluating representations to teach mathematics. Mathematical Thinking Learning, 7(2), 135-169. https://doi.org/10.1207/s15327833mtl0702_3
  • Canterbury, S. A. (2007). An investigation of conceptual knowledge: Urban African American Middle School students' use of fraction representations and computations in performance-based tasks [Unpublished doctoral dissertation]. University of Georgia.
  • Celik, D., & Baki, A. (2007, May). A study on pre-service teachers' use of multiple representations in algebra [Paper presentation]. 7th International Educational Technology Conference, Near East University.
  • Cikla, O. A. (2004). The effects of multiple representations-based instruction on seventh grade students' algebra performance, attitude toward mathematics, and representation preference (Publication no. 153723) [Doctoral dissertation, Anadolu University]. Council of Higher Education Thesis Center.
  • Cohen, L., Maniom, L., & Morrison, K. (2008). Research methods in education. Routledge.
  • Cortes, A., & Pfaff, N. (2000). Solving equations and inequations: Operational invariants and methods constructed by students [Paper presentation]. 24th Conference of the International Group for the Psychology of Mathematics Education, Hiroshima, Japan.
  • Creswell, J. W. (1994). Research design: quantitative and qualitative approaches. Sage.
  • DeJarnette, A. F., Oehrtman, M., & Carlson, M. P. (2020). A synthesis of research on the use of multiple representations in mathematics education. Educational Psychology Review, 32(4), 819-853. https://doi.org/10.1007/s10648-020-09533-6
  • Delice, A., & Sevimli, E. (2010). Educational Sciences. Theory & Practice, 10, 111-149.
  • de Lima, R. N. & Tall, D. (2008). Procedural embodiment and magic in linear equations. Educational Studies in Mathematics, 67(1), 3-18. https://doi.org/10.1007/s10649-007-9086-0
  • Doktoroglu, R. (2013). The effects of teaching linear equations with Dynamic Mathematic Software on seventh grade students' achievement (Publication no. 345127) [Master’s thesis, Middle East Technical University]. Council of Higher Education Thesis Center.
  • Gado, A. K. A., & Adonteng-Kissi, E. (2016). An investigation into pre-service teachers’ knowledge and understanding of mathematical language. Journal of Education and Practice, 7(6), 109-118.
  • Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645-657 https://doi.org/10.1080/0144341042000262953
  • George, D., & Mallery, P. (2003). SPSS for Windows step by step: A simple guide and reference. Allyn & Bacon.
  • Hitt, F., & Trinterud, T. (2019). The role of multiple representations in improving students' mathematical understanding. Journal of Mathematics Education, 42(3), 315-330.
  • Huntley, M. A., & Terrel, M. S. (2014). One-step and multi-step linear equations: A content analysis of five textbook series. ZDM Mathematics Education, 46, 751-766. https://doi.org/10.1007/s11858-014-0627-6
  • Huntley, M. A., Marcus, R., Kahan, J., & Miller, J. L. (2007). Investigating high-school students' reasoning strategies when they solve linear equations. Journal of Mathematical Behavior, 26, 115-139. https://doi.org/10.1016/j.jmathb.2007.05.005
  • Kaur, B., & Drijvers, P. (2021). Graphical representations in mathematics education: A review of current research and future directions. Educational Studies in Mathematics, 107(1), 1-18. https://doi.org/10.1007/s10649-021-10049-w
  • Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). Macmillan Publishing Company.
  • Larbi, E., & Okyere, M. (2014). Algebra tiles manipulative and gender differences in learning and achievement in mathematics: A case of Sunyani West. Journal of Education and Practice, 5(38), 1-8.
  • Larson, R., Boswell, L., Kanold, T. D., & Stiff, L. (2022). Algebra 1: Common Core. Great Source Education Group.
  • Leung, F. K., Clarke, D., Holton, D., & Park, K. (2014). Algebra teaching around the world. Sense Publishers. https://doi.org/10.1007/978-94-6209-707-0
  • Li, K. (2007). An investigation of secondary school algebra teachers' mathematical knowledge for teaching algebraic equations solving [Unpublished doctoral dissertation]. University of Texas, Austin.
  • Lima, R. N., & Tall, D. (2008). Procedural embodiment and magic in linear equations. Educational Studies in Mathematics, 67, 3-18. https://doi.org/10.1007/s10649-007-9086-0
  • Linge, S., Langtangen, H.P. (2016). Solving nonlinear algebraic equations. In T. J. Barth, M. Griebei, D. E. Keyes, R. M. Nieminen, D. Roose, T. Schlick (Eds.), Programming for computations - MATLAB/Octave (pp. 177-201). Springer. https://doi.org/10.1007/978-3-319-32452-4_6
  • Llinares, S., Fernández, C., & Valls, J. (2021). Using multiple representations to promote mathematical understanding: A case study on the concept of function. Journal of Mathematical Behavior, 60, 100840. https://doi.org/10.1016/j.jmathb.2021.100840
  • Matz, M. (1981). Building Metaphoric Theory of Mathematical Thought. Journal of Mathematical Behavior, 3(1), 93-166.
  • Mpuangnan, N. K., Amegbanu V.A. and Padhan S. (2021). Analysing the methods and approaches for transacting diploma in basic education curriculum in Ghana. International Journal of Curriculum and Instruction, 13(2), 1006-1023.
  • Mpuangnan, K.N & Adusei Opoku (2021). Implementation of standard‑based curriculum in Ghana: concerns of basic school teachers. International Journal of Education and Research, 9(3), 53‑66.
  • Mpuangnan, N.K. (2020). Issues in Ghanaian basic education curriculum development. Third Concept Journal, 34(399), 35‑37.
  • NCTM. (2020). Principles to actions: Ensuring mathematical success for all. Author.
  • Osula, E. (2001). Introduction to research methodology. African-Fep Publishers.
  • Poon, K., & Leung, C. (2010). Pilot study on algebra learning among junior secondary students. International Journal of Mathematics Education in Science and Technology, 41, 49-62. https://doi.org/10.1080/00207390903236434
  • Ronda, E., & Dzoba, N. (2022). Enhancing student success in algebraic problem solving through the use of graphing technology. Journal of Technology and Teacher Education, 30(1), 5-33.
  • Sidney, L. R. (1993). Algebra I: A Process Approach. University of Hawaii Press.
  • Smith, R., & Thompson, A. (2020). Enhancing mathematical problem-solving through multiple representations-based instructions. Mathematics Teaching Techniques, 18(2), 145-160.
  • Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal of Research of Mathematics Education, 36, 404-411.
  • Van Dooren, W., De Bock, D., Janssens, D., & Verschaffel, L. (2020). The effectiveness of visual representations in mathematics problem solving: A meta-analysis. Educational Psychology Review, 32(4), 829-869.
  • West African Examination Council [WAEC]. (2017). Chief examiners' report. Author.
  • World Bank. (2021). Ghana: Improving education outcomes through learning materials. Author.
LICENSE
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.