DEVELOPING MATHEMATICAL LITERACY THROUGH AN INSTRUCTIONAL PROCESS: A GRADE 9 CASE STUDYON SOLVING SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES
DOI:
https://doi.org/10.18173/2354-1075.2026-0030Keywords:
mathematical literacy, instructional process, RME, DAPIC, systems of linear equationsAbstract
This research develops and illustrates an instructional process integrating Realistic Mathematics Education (RME) principles with the DAPIC problem-solving cycle (Define, Assess, Plan, Implement, Communicate) to enhance mathematical literacy among Grade 9students. Addressing gaps in existing frameworks, the model, grounded in the PISA framework, emphasizes mathematical reasoning across all phases while embedding critical21st-century skills. The process begins with the realistic problems to engage students, progresses through collaborative solution exploration and discussion of diverse strategies, and culminates in formalizing mathematics and applying knowledge to new contexts. A Vietnamese classroom case study on solving systems of linear equations in two variables demonstrates how students transition from informal methods to structured algebraic techniques. Guided by targeted teacher prompts and collaborative discussions, students deepen both conceptual understanding and procedural fluency. The findings suggest that this integrated RME–DAPIC approach not only aligns with international literacy goals but also effectively cultivates the core dimensions of mathematical literacy within realistic contexts and supports students’ development as reflective and adept problem-solvers in secondary mathematics education.
Downloads
References
[1] Dudley U, (2010). What is mathematics for? Notices of the AMS, 57(5), 608-613.
[2] UNESCO, (1990). World declaration on education for all and framework for action to meet basic learning needs. https://unesdoc.unesco.org/ark:/48223/pf0000127583.
[3] Genc M & Erbas AK, (2019). Secondary mathematics teachers’ conceptions of mathematical literacy. International Journal of Education in Mathematics, Science andTechnology (IJEMST), 7(3), 222-237.
[4] McCrone SS & Dossey JA, (2007). Mathematical literacy - It’s become fundamental. Principal Leadership, 7(5), 32-37.
[5] Umbara U & Nuraeni Z, (2019). Implementation of realistic mathematics education based on adobe flash professional CS6 to improve mathematical literacy. Infinity Journal, 8(2),167-178. https://doi: 10.22460/infinity.v8i2.p167-178.
[6] Umbara U & Suryadi D, (2019). Re-interpretation of mathematical literacy based on the teacher’s perspective. International Journal of Instruction, 12(4), 789-806. https://doi:10.29333/iji.2019.12450a.
[7] Novita R & Putra M, (2016). Using task like PISA’s problem to support student’s creativity in mathematics. Journal on Mathematics Education, 7(1), 31-42.
[8] Pradana LN, Sholikhah OH, Maharani S & Kholid MN, (2020). Virtual mathematics kits (VMK): Connecting digital media to mathematical literacy. International Journal of Emerging Technologies in Learning, 15(3), 234-241. https://doi: 10.3991/ijet.v15i03.11674.
[9] Freudenthal H, (1968). Why teach mathematics so as to be useful? Educational Studies in Mathematics, 1, 3-8. https://doi: 10.1007/BF00426224.
[10] Anderson J, (2009). Mathematics curriculum development and the role of problem solving. Proceedings of 2009 Australian Curriculum Studies Association National Biennial Conference. Curriculum: A National Conversation. ASCA, 1-8.
[11] Polya G, (1962). Mathematical discovery. On understanding, learning, and teaching problem solving. Wiley.
[12] Genc M & Erbas AK, (2020). Exploring secondary mathematics teachers’ conceptions of the barriers to mathematical literacy development. International Journal for Mathematics Teaching and Learning, 21(2), 143-173. https://doi: 10.4256/ijmtl.v21i2.181.
[13] Sumirattana S, Makanong A & Thipkong S, (2017). Using realistic mathematics education and the DAPIC problem-solving process to enhance secondary school students’ mathematical literacy. Kasetsart Journal of Social Sciences, 38(3), 307-315. https://doi:10.1016/j.kjss.2016.06.001.
[14] Çakıroğlu Ü, Güler M, Dündar M & Coşkun F, (2024). Virtual Reality in RealisticMathematics Education to Develop Mathematical Literacy Skills. International Journal of Human–Computer Interaction, 40(17), 4661-4673. https://doi:10.1080/10447318.2023.2219960.
[15] OECD, (2023). PISA 2022 Assessment and Analytical Framework. OECD Publishing. https://doi: 10.1787/dfe0bf9c-en.
[16] Huntley MA, Marcus R, Kahan J & Miller JL, (2007). Investigating high-school students’ reasoning strategies when they solve linear equations. The Journal of Mathematical Behavior, 26(2), 115-139. https://doi: 10.1016/j.jmathb.2007.05.005.
[17] Bosque JS, (2025). Common challenges students face when learning linear equation. International Journal of Multidisciplinary Research and Analysis, 8(4), 2100–2115.https://doi: 10.47191/ijmra/v8-i04-65.
[18] Van Reeuwijk M, (1995). The role of realistic situations in developing tools for solving systems of equations. Annual conference of the American Educational Research Association. AERA, 1-11.
[19] ND Hoang & TNM Dang, (2023). Pedagogical measures to develop mathematical modeling competency for students in teaching problem-solving (Mathematics 9). Vietnam Journal of Education, 23(14), 18-22 (in Vietnamese).
[20] PH Trang, NA Quoc, NN Giang & NTT Thuy, (2025). Developing mathematical thinking and reasoning competency in teaching practical problems on the topic of linear equations and systems of linear equations in two variables (Mathematics 9). Vietnam Journal of Education, 25(13), 36-41.
[21] The Quantitative Literacy Design Team, (2001). The case for quantitative literacy. In: Steen L(ed.), “Mathematics and Democracy: The Case for Quantitative Literacy”, p. 1-22. TheWoodrow Wilson National Fellowship Foundation.
[22] Goos M, Dole S & Geiger V, (2012). Numeracy across the curriculum. Australian Mathematics Teacher, 68(1), 3-7.
[23] Niss M & Jablonka E, (2020). Mathematical Literacy. In: Lerman S (ed.), “Encyclopedia of Mathematics Education”, p. 548–553. Springer. https://doi: 10.1007/978-3-030-15789-0_100.
[24] Cockcroft W, (1982). Mathematics counts. https://education-uk.org/documents/cockcroft/cockcroft1982.html#03.
[25] Coben D, Colwell D, Macrae S, Boaler J, Brown M & Rhodes V, (2003). Adult numeracy: review of research and related literature. National Research and Development Centre for Adult Literacy and Numeracy.
[26] Geiger V, Forgasz H & Goos M. (2015). A critical orientation to numeracy across the curriculum. ZDM, 47(4), 611-624. https://doi: 10.1007/s11858-014-0648-1.
[27] Cranfield C, (2012). The Implementation of Mathematical Literacy as a New Subject in the South African Curriculum. In: Tatto MT (ed.), “Learning and Doing Policy Analysis in Education. Comparative and International Education”, p. 207-232. SensePublishers.https://doi: 10.1007/978-94-6091-933-6_8.
[28] OECD, (n.d.). PISA 2022 Mathematics Framework. https://pisa2022-maths.oecd.org/ca/index.html#Overview.
[29] Stacey K, (2015). The real world and the mathematical world. In: Stacey K & Turner R (eds.),“Assessing Mathematical Literacy”, p. 57-84. Springer. https://doi: 10.1007/978-3-319-10121-7_3.
[30] Gravemeijer K & Doorman M, (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39, 111-129. https://doi:10.1023/A:1003749919816.
[31] Suparatulatorn R, Jun-On N, Hong YY, Intaros P & Suwannaut S, (2023). Exploring problem-solving through the intervention of technology and Realistic Mathematics Education in the Calculus content course. Journal on Mathematics Education, 14(1), 103-128. https://doi:10.22342/JME.V14I1.PP103-128.
[32] Van den Heuvel-Panhuizen M, (2000). Mathematics education in the Netherlands: A guided tour. Freudenthal Institute CD-rom for ICME9, Utrecht University, p. 1-32.
[33] Van den Heuvel-Panhuizen M & Drijvers P, (2020). Realistic Mathematics Education. In: Lerman S (ed.), “Encyclopedia of Mathematics Education,” p. 713-717. Springer.https://: 10.1007/978-3-030-15789-0_170.
[34] Yusmi AN, Halimah A & Nur F, (2024). The effectiveness of a realistic mathematics approach application to improve students’ mathematical literacy. Journal Tadris Matematika, 5(1), 11-18.https://doi: 10.47435/jtmt.v5i1.2314.
[35] Gravemeijer K & Terwel J, (2000). Hans Freudenthal: A mathematician on didactics and curriculum theory. Journal of Curriculum Studies, 32(6), 777-796. https://doi:10.1080/00220270050167170.
[36] Meier SL, Hovde RL & Meier RL, (1996). Problem solving: teachers’ perceptions, content area models, and interdisciplinary connections. School Science and Mathematics, 96(5), 230-237. https://doi: 10.1111/j.1949-8594.1996.tb10234.x.
[37] Van den Heuvel-Panhuizen M, (2005). The role of contexts in assessment problems in Mathematics. For the Learning of Mathematics, 25(2), 2-9, 23.
[38] Steinberg RN, (2000). Computers in teaching science: To simulate or not to simulate? American Journal of Physics, 68(1), 37-41. https://doi: 10.1119/1.19517.
