Relationship Between Prerequisite Mathematical Competencies and Trigonometric Learning Proficiency Among Grade 9 Students
DOI:
https://doi.org/10.5281/zenodo.21392924Keywords:
Prerequisite mathematical competencies, trigonometry learning proficiency, algebraic expressions, rational expressions, geometric propertiesAbstract
This study explores the relationship between prerequisite mathematical competencies and trigonometry learning proficiency among Grade 9 students at Bernardo Lirio National High School. It focuses on students’ mastery of basic algebraic expressions, rational expressions, and geometric properties of triangles, and their impact on proficiency in right triangle trigonometry, the Pythagorean theorem, special angles, and solving angles of elevation and depression. Using a descriptive-correlational design, data were collected from 216 students through a validated questionnaire. Results show strong mastery in algebraic and rational expressions and moderate mastery in geometric properties. Students demonstrated high proficiency in trigonometry, with significant positive correlations between foundational skills and trigonometric proficiency, especially in applied problem-solving. The study recommends reinforcing foundational skills, integrating real-world applications, providing targeted support, and monitoring progress to improve trigonometry learning outcomes. These findings offer valuable guidance for educators and curriculum developers to enhance mathematics education.
References
Accelerate Learning. (2023). Constructivist approaches in mathematics education. https://www.acceleratelearning.com
Alreshidi, N. M. (2023). The impact of foundational skills on mathematics achievement. Journal of Educational Research, 45(2), 123–135.
Angeles, R., Cruz, M., & Santos, L. (2019). Strengthening procedural fluency in algebra among Filipino students. Philippine Journal of Mathematics Education, 12(1), 45–60.
Ausubel, D. P. (1968). Educational psychology: A cognitive view. Holt, Rinehart & Winston.
Balandra, R. F. (2022). Students’ proficiency and attitudes toward trigonometry in a Philippine higher education institution. Asian Journal of Mathematics Education, 8(3), 78–92.
Bruner, J. S. (1960). The process of education. Harvard University Press.
Casanova, J., Cantoria, M., & Lapinid, R. (2021). Geometric thinking and problem-solving among secondary students. Philippine Journal of Educational Research, 15(2), 101–115.
Clements, D. H. (2018). The role of geometric understanding in mathematics achievement. Mathematics Education Review, 30(4), 210–225.
Díaz, M. (2017). Constructivist learning theory in mathematics education. International Journal of Educational Research, 82, 1–10. https://doi.org/10.1016/j.ijer.2017.01.005
Ellis, A. (2017). Contextualized trigonometry problems and student learning. Journal of Mathematics Teaching, 22(1), 45–59.
Garcia, L., & Martinez, P. (2021). Trigonometry proficiency and conceptual understanding. International Journal of Math Education, 9(2), 134–150.
Garcia, R., & Santos, M. (2025). The ANGLE instructional approach for angles of elevation and depression. Philippine Journal of Science Education, 18(1), 67–80.
Garinganao, J., & Bearneza, L. (2021). Algebraic skills and mathematics performance of Filipino students. Philippine Educational Journal, 14(3), 89–104.
Gupta, S. (2020). Cognitive load theory and mathematics learning. Educational Psychology Review, 32(3), 567–589. https://doi.org/10.1007/s10648-019-09507-2
Hattie, J. (2017). Visible learning for mathematics. Routledge.
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Information Age Publishing.
Jorda, M., & De los Santos, F. (2016). Game-based learning strategies in trigonometry. Philippine Journal of Educational Technology, 10(2), 23–38.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press. https://doi.org/10.17226/9822
Lee, S., & Kim, H. (2020). Prerequisite competencies and mathematics achievement. Journal of Educational Psychology, 112(5), 987–1002. https://doi.org/10.1037/edu0000407
Moore, K. C., Smith, J. R., & McGee, A. W. (2017). Conceptual understanding of trigonometric ratios. Mathematics Education Quarterly, 29(1), 55–70.
Moore, T. (2018). Learning difficulties in introductory trigonometry. Journal of Mathematics Education Research, 11(4), 210–225.
Murtianto, A. (2022). Cognitive load and mathematics learning. International Journal of Cognitive Education, 7(1), 45–60.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM.
National Council of Teachers of Mathematics. (2018). Principles to actions: Ensuring mathematical success for all. NCTM.
Nguyen, T., et al. (2019). Foundational skills and mathematics success. Educational Research Review, 25, 100–115. https://doi.org/10.1016/j.edurev.2018.10.001
Orale, R., & Uy, M. (2018). Geometric knowledge and trigonometric problem-solving. Philippine Journal of Mathematics, 16(2), 78–92.
Orbe, M., & Espinosa, J. (2020). Conceptual understanding of geometric principles. Philippine Journal of Science Education, 19(1), 34–50.
Organisation for Economic Co-operation and Development. (2019). PISA 2018 results (Volume I): What students know and can do. OECD Publishing. https://doi.org/10.1787/5f07c754-en
Piaget, J. (1972). The psychology of the child. Basic Books.
Quebec Education Program. (2021). Geometric properties of triangles. Quebec Ministry of Education.
Reinhold, S., et al. (2020). Prior knowledge and mathematics achievement. Journal of Educational Psychology, 112(3), 456–470. https://doi.org/10.1037/edu0000375
Reyes, M., & Cruz, J. (2022). Impact of mastery of basic algebraic operations on secondary mathematics performance. Philippine Journal of Science Education, 18(1), 67–80.
Rianto, A. (2022). Cognitive theories in mathematics learning. International Journal of Educational Psychology, 8(2), 120–135.
Ritchie, F. B. (2022). Level of proficiency and attitudes toward trigonometry: A Philippine study. Philippine Journal of Mathematics Education, 13(1), 45–60.
Rittle-Johnson, B., et al. (2017). Procedural fluency and conceptual understanding. Educational Psychology Review, 29(3), 405–418. https://doi.org/10.1007/s10648-016-9383-5
Samaco, R., Cabanes, J., & Minoza, L. (2023). Mastery of mathematical operations and expressions among secondary students. Philippine Journal of Mathematics Education, 14(2), 56–70.
Santos, M., & Villanueva, R. (2023). Rational expressions and mathematics performance. Philippine Journal of Mathematics Education, 13(1), 67–81.
Santoso, A., & Lee, J. (2024). The impact of prerequisite mathematical competencies on trigonometry learning: A cross-national study. Journal of Mathematics Education Research, 15(2), 112–130.
Small, M. (2018). The role of the Pythagorean theorem in mathematics learning. Mathematics Education Review, 31(2), 112–125.
Toledo-Nieto, M. (2024). Challenges in learning trigonometric ratios. International Journal of Math Education, 10(1), 45–60.
Tugas, R. C. (2023). Mathematical background and performance in geometry and trigonometry. Philippine Journal of Science Education, 20(2), 90–105.
Uy, J., & Limbaco, R. (2017). Rational expressions and student misconceptions. Philippine Journal of Mathematics Education, 11(3), 56–70.
Weber, K. (2016). Students’ reasoning in trigonometry. Journal of Mathematics Education Research, 9(2), 78–95.
Zazkis, R. (2019). Rational expressions and mathematical reasoning. Educational Studies in Mathematics, 100(1), 45–60. https://doi.org/10.1007/s10649-018-9861-7
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 International Journal of Research on Multidisciplinary Studies
This work is licensed under a Creative Commons Attribution 4.0 International License.
