Effectiveness of Cross-Age Tutoring on Problem-Solving Skills in Trigonometry Among Grade 9 Students
Justine Ace Guanga | Eloise Barañao | Rhumer S. Lañojan | Jean Bergante | Esmaida Andang-alaiden
Discipline: Education
Abstract:
A known area of academic difficulty is problem-solving in trigonometry. The complexity of trigonometric concepts and the need for strong problem-solving skills often contribute to difficulties in student comprehension and application. This study addresses these challenges by exploring the potential of cross-age tutoring as a remedial strategy to improve trigonometry problem-solving skills. A quasi-experimental, non-equivalent group design was employed with 60 Grade 9 students from a public high school in General Santos City. The sample was divided into an experimental group comprising 30 respondents who received cross-age tutoring and a control group comprising 30 respondents who received only traditional instruction. A 25-item multiple-choice assessment, specifically aligned with the Department of Education's learning competencies, was administered as a pretest and post-test to measure changes in performance. The results revealed a statistically significant improvement in post-test scores for both groups (p = 0.000). However, the experimental group demonstrated a substantially greater increase in mean scores, rising from a pretest mean of 5.37 to a post-test mean of 19.00, compared to the control group's increase from 5.57 to 17.53. An analysis of the mean gain scores confirmed a significant difference between the two groups (p = 0.010), establishing the superior efficacy of the cross-age tutoring intervention. These findings directly support Vygotsky's Zone of Proximal Development (ZPD) theory, showing that peer-led guidance effectively scaffolds learning. The study provides strong empirical evidence for implementing cross-age tutoring as a practical, low-cost strategy to support struggling learners. This aligns with national educational recovery initiatives, such as the Philippines' ARAL Program Act of 2024, by offering a scalable model to address learning gaps and improve academic outcomes in challenging subjects, ensuring that no students are left behind. Future research may investigate the applicability of this intervention across other subjects.
References:
- Ahmad, H., Febryanti, N., Muthmainnah, N., Yakin, A. A., & Sarbi, S. (2018). The analysis of student error in Solve the Problem of Spherical Trigonometry Application. Journal of Physics Conference Series, 1114, 012114. https://doi.org/10.1088/1742-6596/1114/1/012114
- Albert, J. R., Basillote, L., Alinsunurin, J., Vizmanos, J. F., Muñoz, M., & Hernandez, A. (2023). Sustainable Development Goal 4 on Quality Education for all: How does the Philippines fare and what needs to be done?. Philippine Institute for Development Studies, Discussion Paper Series No. 2023-16. https://doi.org/10.62986/dp2023.16
- Alegre, F., Moliner, L., Maroto, A., & Lorenzo-Valentin, G. (2020). Academic Achievement and peer tutoring in mathematics: A comparison between primary and secondary education. SAGE Open, 10(2). https://doi.org/10.1177/2158244020929295
- Alwi, S. K. K., Rauf, M. B., & Soomro, S. (2016). Effects of cross and same age peer tutoring on reading attitudes of primary school students. The Sindh University Journal of Education, 45(1), 161–182. https://sujo.usindh.edu.pk/index.php/SUJE/article/view/1410/1187
- Amalina, I. K., & Vidákovich, T. (2023). Cognitive and socioeconomic factors that influence the mathematical problem-solving skills of students. Heliyon, 9(9), e19539. https://doi.org/10.1016/j.heliyon.2023.e19539
- Amirova, N. (2025). Traditional vs. Non-Traditional Teaching in Secondary Education: A Comparative Analysis. Porta Universorum, 1(3), 101–109. https://doi.org/10.69760/portuni.010309
- An Act Establishing an Academic Recovery and Accessible Learning (ARAL) Program and Appropriating Funds Therefor, Republic Act No. 12028, (2024, October 16). https://lawphil.net/statutes/repacts/ra2024/ra_12028_2024.html
- Asamoah, B. (2025). Examining the Factors Afffecting Students' Performance in Trigonometry Word Problems. International Journal of Research and Innovation in Social Science, 9(02), 2279-2321. https://doi.org/https://dx.doi.org/10.47772/IJRISS.2025.9020181
- Arhin, J., & Hokor, E. K. (2021). Analysis of high school students' errors in solving trigonometry problems. Journal of Mathematics and Science Teacher, 1(1), em003. https://doi.org/10.29333/mathsciteacher/11076
- Arivina, A. N., & Jailani, J. (2020). Development of trigonometry learning kit with a STEM approach to improve problem solving skills and learning achievement. Jurnal Riset Pendidikan Matematika, 7(2), 178-194. https://doi.org/10.21831/jrpm.v7i2.35063
- Asparin, A. A. & Tan, D. A. (2018). Students' Problem Solving Skills in Enhanced Gradual Release of Responsibility Instruction Model. Asian Academic Research Journal of Multidisciplinary, 5(3), 121-128. https://www.researchgate.net/publication/326654219_STUDENTS'_PROBLEM_SOLVING_SKILLS_IN_ENHANCED_GRADUAL_RELEASE_OF_RESPONSIBILITY_INSTRUCTIONAL_MODEL
- Barahona, E., Padrón, Y. N., & Waxman, H. C. (2023). Classroom observations of a cross-age peer tutoring mathematics program in elementary and middle schools. European Journal of Science and Mathematics Education, 11(3), 515–532. https://doi.org/10.30935/scimath/12983
- Boz Yaman, B. (2019). A multiple case study: What happens in peer tutoring of calculus studies? International Journal of Education in Mathematics, Science and Technology, 7(1), 53–72. https://eric.ed.gov/?id=EJ1204149
- Byiringiro, E. (2024). Effect of remedial teaching on mathematics achievement among secondary school students in Sweden: evidence from high Secondary school. International Journal of Recent Research in Mathematics Computer Science and Information Technology, 10(2), 37–44. https://doi.org/10.5281/zenodo.1051245
- Cambaya, Edenly Jane & Tan, Denis. (2022). Enhancing Students' Problem-Solving Skills and Engagement in Mathematics Learning through Contextualized Instruction. Science International. 34(2). 101-109. https://www.sci-int.com/pdf/637837170468018431.edited.pdf
- Capili, B., & Anastasi, J. K. (2024). An introduction to types of Quasi-Experimental Designs. AJN American Journal of Nursing, 124(11), 50–52. https://doi.org/10.1097/01.naj.0001081740.74815.20
- Caraan, D.C., Dinglasan, J.L. & Ching, D.A. (2022). Realistic Mathematics Education Approach on Improving Problem-Solving Skills of Students. The Research Probe, 2(2), 88-96. https://iiari.org/conference_article/realistic-mathematics-education-approach-on-improving-problem-solving-skills-of-students/
- Dada, O., Ekim, R. E. D., Olusegun Olujıde, F., Mbakwe, N., et al. (2023). Effect of Peer and Cross-age tutoring on Mathematics Achievement and Interest of Underachieving Gifted Students. Journal for the Mathematics Education and Teaching Practices, 4(1), 11-19. https://dergipark.org.tr/en/download/article-file/3144083
- Davis, L. L., Spooner, F., & Saunders, A. (2022). Efficacy of Peer-Delivered mathematical Problem-Solving instruction to students with extensive support needs. Council for Exceptional Children, 89(1), 101–118. https://doi.org/10.1177/00144029221098764
- Dhungana, S., Pant, B. P., & Dahal, N. (2023). Students' experience in learning trigonometry in high school mathematics: A phenomenological study. Mathematics Teaching Research Journal, 15(4), 184–201. https://mtrj.commons.gc.cuny.edu/wp-content/blogs.dir/34462/files/2024/06/9th-MTRJ-48-15-4-GFA2023.pdf
- Epol, L. (2025). Fostering Numeracy Skills And Interest Among Grade 7 Students Through Cross-Age Peer Tutoring. International Multidisciplinary Journal of Research for Innovation, Sustainability, and Excellence, 2(7), 102-121. https://doi.org/10.5281/zenodo.15809368
- Fauziyah, N., Asari, S., Ma'rifah, U., Uchtiawati, S., & Husniati, A. (2021). Improving students' creativity through sharing and jumping task in mathematics lesson study activity. Journal of Physics Conference Series, 1764(1), 012100. https://doi.org/10.1088/1742-6596/1764/1/012100
- Fernández-Barros, A., Duran, D., & Viladot, L. (2022). Peer tutoring in music education: A literature review. International Journal of Music Education, 41(1), 129–140. https://doi.org/10.1177/02557614221087761
- Greene, I., Tiernan, A. M., & Holloway, J. (2018). Cross-Age Peer Tutoring and Fluency-Based Instruction to Achieve Fluency with Mathematics Computation Skills: A Randomized Controlled Trial. Journal of Behavioral Education, 27(2), 145–171. https://doi.org/10.1007/s10864-018-9291-1
- Guban, M.T., & Revilla, N. (2022). The Impact of Remedial Program in the Filipino subject of Grade 10 Students. International Journal of Arts, Sciences and Education, 3(4), 131–14. https://ijase.org/index.php/ijase/article/view/189
- Haynes, K., & Brendle, J. (2019). Cross-Age math tutoring of kindergarten and first grade students by middle school tutors. International Journal of Education in Mathematics Science and Technology, 7(3), 238–250. https://files.eric.ed.gov/fulltext/EJ1223881.pdf
- Hernane, N. J. L., Licomes, N. S. M. A., & Rebusora, N. R. I. (2025). ANGLE (Analyze, Note, Get, Logic, Evaluate) Approach in Improving Solving Skills in Angle of Elevation and Depression Among Grade 9 Students. EPRA International Journal of Multidisciplinary Research (IJMR), 11(6), 1688–1699. https://doi.org/10.36713/epra22609
- Hidayat, R., & Saad, M. R. M. (2025). A Meta-analysis of the effect of peer tutoring in Science, Technology, Engineering and Mathematics (STEM) subjects. International Journal of Educational Research Open, 8, 100446. https://doi.org/10.1016/j.ijedro.2025.100446
- Hidayat, R., Nasir, N., Fadzli, S. a. M., Rusli, N. S., Kamaruzzaman, N. N., Sheng, V. Y. Z., Mohammad, N. H. H., & Shukeri, A. S. (2023). Peer Tutoring Learning Strategies in Mathematics Subjects: Systematic Literature review. European Journal of Educational Research, 12(3), 1407–1423. https://doi.org/10.12973/eu-jer.12.3.1409
- Hsieh, H., Gormley, D., Robinson, C.D., & Loeb, S. (2025). The Power of Personalized Attention: Comparing Pedagogical Approaches in Small Group and One-on-One Early Literacy Tutoring. EdWorkingPaper: 25-1289. https://doi.org/10.26300/ykhg-zr64
- Ismayanti, S., & Jatisunda, N. M. G. (2025). An analysis of students' difficulties and problem-solving strategies in trigonometry instruction. Jurnal Inovasi Pembelajaran Matematika PowerMathEdu, 4(1). https://doi.org/10.31980/pme.v4i1.2647
- Jitpranee, S., Chookhampaeng, S., & Chaya, J. (2022). Enhancing scientific literacy through inquiry-based learning: A quasi-experimental study among secondary school students. Asia-Pacific Journal of Science Education, 8(1), 45–61. https://doi.org/10.1163/23641177-bja10030
- Khatimah, H., & Sugiman, S. (2019). The effect of problem solving approach to mathematics problem solving ability in fifth grade. Journal of Physics: Conference Series, 1157(4), 042104. https://doi.org/10.1088/1742-6596/1157/4/042104
- Klein, K., Calabrese, J., Aguiar, A., Mathew, S., Ajani, K., Almajid, R., & Aarons, J. (2023). Evaluating Active Lecture and Traditional Lecture in Higher Education. Journal on Empowering Teaching Excellence, 7(2), 40-51. https://doi.org/10.26077/ba42-a5cc
- Kour, S. J., & Rafaqi, M. Z. U. (2024). Factors influencing problem-solving ability in mathematics: A systematic review of literature. Education India: A Quarterly Refereed Journal of Dialogues on Education, 13(1), EIJ20110000906. https://www.researchgate.net/publication/379055616_Factors_Influencing_Problem_Solving_Ability_in_Mathematics_A_Systematic_Review_of_Literature
- Leung, K. C. (2019). An updated meta-analysis on the effect of peer tutoring on tutors' achievement. School Psychology International, 40(2), 200-214. https://doi.org/10.1177/0143034318808832
- Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem Solving in Mathematics Education. In: Problem Solving in Mathematics Education (ICME-13 Topical Surveys). Springer, Cham. 1-39. https://doi.org/10.1007/978-3-319-40730-2_1
- Ma’ruf, A., Triyono, A., & Ismail, M. (2023). Improving students' mathematical problem-solving ability in trigonometry material using the flipped classroom model. Journal of Instructional Mathematics, 4(2), 106–118. https://doi.org/10.37640/jim.v4i2.1896
- Macapayad, G. L., Lapinid, E. L., Valmoria, G. P., Colis, K. V., & Bacalso, L. (2024). Efficacy of One-On-One Peer Tutoring in Improving the Problem-Solving Performance Among The Grade 10 Learners. European Journal of Education Studies, 11(11), 818-829. https://doi.org/10.46827/ejes.v11i11.5692
- Makilan, N. C. (2020). Problem-based learning approach: Its effect on the problem-solving skills and attitude of the students towards trigonometry. International Journal of Management Studies and Social Science Research, 2(2), 138–144. https://www.ijmsssr.org/paper/IJMSSSR00128.pdf
- Martin-Beltrán M., Daniel S., Peercy M., Silverman R. (2017). Developing a zone of relevance: Emergent bilinguals' use of social, linguistic, and cognitive support in peer-led literacy discussions. International Multilingual Research Journal, 11(3), 152–166. https://doi.org/10.1080/19313152.2017.1330061
- Mauer, E., & Swanson, E. (2024). Cross-Age peer tutoring to improve literacy outcomes for students with disabilities. TEACHING Exceptional Children, 57(4), 286-293 https://doi.org/10.1177/00400599241231229
- Miller, C. J., Smith, S. N., & Pugatch, M. (2019). Experimental and quasi-experimental designs in implementation research. Psychiatry Research, 283, 112452. https://doi.org/10.1016/j.psychres.2019.06.027
- Moliner L., Alegre F. (2020). Effects of peer tutoring on middle school students' mathematics self-concepts. PLOS ONE, 15(4), Article e0231410. https://doi.org/10.1371/journal.pone.0231410
- Moliner, L., & Alegre, F. (2020). Peer tutoring effects on Students' mathematics anxiety: A middle school experience. Frontiers in Psychology, 11. https://doi.org/10.3389/fpsyg.2020.01610
- Mukuka, A., & Tatira, B. (2025). Analysis of pre-service teachers' understanding of solving trigonometric equations: A perspective through actions, processes, objects, and schemas theory. Pythagoras, 46(1), a830. https://doi.org/10.4102/pythagoras.v46i1.830
- Ngu, B. H., & Phan, H. P. (2020). Learning to solve trigonometry problems that involve algebraic transformation skills via learning by analogy and learning by comparison. Frontiers in Psychology, 11. https://doi.org/10.3389/fpsyg.2020.558773
- Nurmeidina, R., & Rafidiyah, D. (2019). Analysis of Students' Difficulties in Solving Trigonometry Problems. European Union Digital Library. https://doi.org/10.4108/eai.7-8-2019.2288422
- Ouma, O. B., Okello, M. O., & Odongo, J. A. (2018). Cross-age peer tutoring as a pedagogical strategy: A remedy for enhancing academic achievement in secondary schools. International Journal of Novel Research in Interdisciplinary Studies, 5(4), 43–51. https://www.noveltyjournals.com/upload/paper/Cross%20Age%20Peer-1462.pdf
- Pagtulon-an, E. & Tan D. (2018). Students' Mathematics Performance and Self-efficacy Beliefs in a Rich Assessment Tasks Environment. Asian Academic Research Journal of Multidisciplinary. 5(2), 54-64. https://www.researchgate.net/publication/326653311_STUDENTS'_MATHEMATICS_PERFORMANCE_AND_SELF-EFFICACY_BELIEFS_IN_A_RICH_ASSESSMENT_TASKS_ENVIRONMENT
- Passion, O. V., & Marcelo, P. (2024). Benefits of Peer Tutoring in Enhancing Students' Academic Performance in Mathematics. International Journal of Advanced Multidisciplinary Studies. 4(5), 754-765. https://www.ijams-bbp.net/wp-content/uploads/2024/06/5-IJAMS-MAY-2024-754-765.pdf
- Policy Guidelines on Classroom Assessment for the K to 12 Basic Education Program, DepEd Order No. 8 s. 2015, (2015, April 01). https://www.deped.gov.ph/wpcontent/uploads/2015/04/DO_s2015_08.pdf
- Rohimah, S., & Prabawanto, S. (2020). Students' difficulties in solving trigonometric equations and identities. Journal of Physics: Conference Series, 1521, 032002. https://doi.org/10.1088/1742-6596/1521/3/032002
- Romero, M., Chen, L., & Magari, N. (2021). Cross-Age Tutoring: Experimental Evidence from Kenya. Economic Development and Cultural Change, 70(3), 1133–1157. https://doi.org/10.1086/713940
- Simms, V. (2016). Mathematical mindsets: unleashing students' potential through creative math, inspiring messages and innovative teaching. Research in Mathematics Education, 18(3), 317–320. https://doi.org/10.1080/14794802.2016.1237374
- Soroño-Gagani, F., Olvido, M. M., & Bonotan, A. M. (2019). Hitting two birds with one stone: A phenomenological inquiry of junior high math buddies in a university. European Scientific Journal, 15(24), 187–203. https://doi.org/10.19044/esj.2019.v15n24p187
- Suendarti, M., & Liberna, H. (2021). Analisis pemahaman konsep perbandingan trigonometri pada siswa SMA. Jurnal Nasional Pendidikan Matematika, 5(2), 326-339. https://doi.org/10.33603/jnpm.v5i2.4917
- Tajik, O., Golzar, J. and Noor, S. (2025). Purposive Sampling. International Journal of Education & Language Studies, 2(2), 1-9. https://doi.org/10.22034/ijels.2025.490681.1029
- Thurston, A., Cockerill, M., & Chiang, T. (2021). Assessing the differential effects of peer tutoring for tutors and tutees. Education Sciences, 11(3), 97. https://doi.org/10.3390/educsci11030097
- Wardhani, T. a. W., & Argaswari, D. P. a. D. (2022). High School Students' Error in Solving Word Problem of Trigonometry Based on Newman Error Hierarchical Model. Infinity Journal, 11(1), 87. https://doi.org/10.22460/infinity.v11i1.p87-102
- Watts, G. W., Bryant, D. P., & Roberts, G. J. (2020). Effects of cross-age tutors with EBD for kindergarteners at risk of mathematics difficulties. Journal of Emotional and Behavioral Disorders, 28(4), 244-256. https://doi.org/10.1177/1063426619884271
- Wood, T., Mazzocco, M. M. M., Calhoon, M. B., Crowe, E. C., & Connor, C. M. (2020). The effect of Peer-Assisted mathematics learning opportunities in first grade classrooms: What works for whom? Journal of Research on Educational Effectiveness, 13(4), 601–624. https://doi.org/10.1080/19345747.2020.1772422
- Yolak, B. B., Kiziltepe, Z., & Seggie, F. N. (2019). The contribution of remedial courses on the academic and social lives of secondary school students. Journal of Education, 199(1), 24-34. https://doi.org/10.1177/0022057419836434
- Zhang, J., Zhao, N., & Kong, Q. P. (2019). The Relationship between math anxiety and math Performance: A Meta-Analytic Investigation. Frontiers in Psychology, 10. https://doi.org/10.3389/fpsyg.2019.01613
- Zeneli, M., Tymms, P., & Bolden, D. (2018). Interdependent Cross-Age peer tutoring in mathematics. International Journal of Psychology and Educational Studies, 5(3), 33–50. https://doi.org/10.17220/ijpes.2018.03.004.