From Formula to Problem Solving: Teaching Trigonometry in  Preparation for University Admission

Kevin Santiago Mullo Cóndor

doi:10.56200/mentor.v5i15.13612

Authors

Kevin Santiago Mullo Cóndor Universidad Central del Ecuador. Quito-Ecuador

DOI:

https://doi.org/10.56200/mentor.v5i15.13612

Keywords:

trigonometry, problem solving, mathematics teaching, pre-university education, teachers

Abstract

Pre-university preparation in trigonometry often focuses on mastering formulas and procedures, although admission to higher education requires students to solve problems involving interpretation, modeling, and strategy selection. The objective was to understand how teachers in pre-university courses in Quito taught trigonometry and what difficulties they identified in the transition from applying formulas to solving problems. A qualitative, descriptive-interpretive study was conducted with 23 teachers selected through purposive sampling. Semi-structured interviews were conducted, and the information was examined through thematic analysis. The results revealed three main trends: the predominance of procedural teaching focused on trigonometric identities and ratios; students’ difficulties in interpreting problem statements, representing situations, and deciding which trigonometric relationship to use; and better responses when contextualized problems, graphical representations, error analysis, and progressively challenging sequences were used. It was also found that pressure to cover content and prepare students for examinations favored practices focused on procedural speed. It was concluded that pre-university preparation should integrate procedural knowledge with strategies for interpretation, representation, and problem solving.

Downloads

Download data is not yet available.

Author Biography

Kevin Santiago Mullo Cóndor , Universidad Central del Ecuador. Quito-Ecuador

Universidad Central del Ecuador. Quito-Ecuador

References

Adhikari, T. N., & Subedi, A. (2021). Difficulties of Grade X students in learning Trigonometry. Siddhajyoti Interdisciplinary Journal, 2(01), 90–99. https://doi.org/10.3126/sij.v2i01.39243

Braithwaite, D. W., & Sprague, L. (2021). Conceptual Knowledge, Procedural Knowledge, and Metacognition in Routine and Nonroutine Problem Solving. Cognitive Science, 45(10), e13048. https://doi.org/10.1111/cogs.13048

Creswell, J., & Creswell, D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.

Fererde, A., Mihrka, A., Ayele, M., & Arara, A. (2024). Enhancing Students’ Conceptual Understanding and Problem-Solving Skills in Learning Trigonometry Through Contextual-Based Mathematical Modeling Instruction. International Journal of Secondary Education, 12(4), 108–119. https://doi.org/10.11648/j.ijsedu.20241204.15

Gradini, E., Yustinaningrum, B., & Safitri, D. (2022). Kesalahan Siswa Dalam Memecahkan Masalah Trigonometri Ditinjau dari Indikator Polya. Mosharafa: Jurnal Pendidikan Matematika, 11(1), 49–60. https://doi.org/10.31980/mosharafa.v11i1.686

Güner, N., & Çermik, H. (2022). CHALLENGES OF BEING A SECONDARY SCHOOL MATHEMATICS TEACHER. European Journal of Education Studies, 9(11). https://doi.org/10.46827/ejes.v9i11.4534

Guo, W. (2022). Exploratory Case Study on Solving Word Problems Involving Triangles by Pre-Service Mathematics Teachers in a Regional University in Australia. Mathematics, 10(20), 3786. https://doi.org/10.3390/math10203786

Melissa, M. M., Anindito Wisnu Susanto, L., Nindya Puspita, A., & Vandam Sigalingging, S. (2023). MATHEMATICAL REPRESENTATION ABILITY OF PROSPECTIVE MATHEMATICS TEACHERS IN SOLVING TRIGONOMETRIC PROBLEMS. Kalamatika: Jurnal Pendidikan Matematika, 8(1), 11–26. https://doi.org/10.22236/KALAMATIKA.vol8no1.2023pp11-26

Ngu, B. H., & Phan, H. P. (2023). Differential instructional effectiveness: Overcoming the challenge of learning to solve trigonometry problems that involved algebraic transformation skills. European Journal of Psychology of Education, 38(4), 1505–1525. https://doi.org/10.1007/s10212-022-00670-5

Piñeiro, J. L., & Castro-Rodríguez, E. (2024). Primary teachers’ knowledge for teaching mathematical problem solving. In B. Doig, J. Novotná, B. Kaur, & D. Pugalee (Eds.), Elementary Mathematics Teaching (1st ed., pp. 23–38). Oxford University PressOxford. https://doi.org/10.1093/oso/9780192869647.003.0002

Roorda, G., De Vries, S., & Smale-Jacobse, A. E. (2024). Using lesson study to help mathematics teachers enhance students’ problem-solving skills with teaching through problem solving. Frontiers in Education, 9, 1331674. https://doi.org/10.3389/feduc.2024.1331674

Santos-Trigo, M. (2024). Problem solving in mathematics education: Tracing its foundations and current research-practice trends. ZDM – Mathematics Education, 56(2), 211–222. https://doi.org/10.1007/s11858-024-01578-8

Setiawan, Y. E. (2022). PROSPECTIVE TEACHERS REPRESENTATIONS IN PROBLEM SOLVING OF SPECIAL ANGLE TRIGONOMETRY FUNCTIONS BASED ON THE LEVEL OF ABILITY. Infinity Journal, 11(1), 55. https://doi.org/10.22460/infinity.v11i1.p55-76

Spangenberg, E. D. (2021). Manifesting of pedagogical content knowledge on trigonometry in teachers practice. Journal of Pedagogical Research, 5(3), 135–163. https://doi.org/10.33902/JPR.2021371325

Sulistyaningsih, D., Purnomo, E. A., & Purnomo, P. (2021). Polya’s Problem Solving Strategy in Trigonometry: An Analysis of Students’ Difficulties in Problem Solving. Mathematics and Statistics, 9(2), 127–134. https://doi.org/10.13189/ms.2021.090206