Level of Mastery in Fraction Computation Among Grade 10 Students at Dimasalang National High School: Basis for Intervention Program
DOI:
https://doi.org/10.65339/ijsair.V2.I2.374Keywords:
Cognitive Load Theory, Constructivist Learning Theory, Fraction Computation, Mathematics Education, Mastery Learning Theory, Problem-Solving Strategies, Quality Education, Sustainable Education, School InterventionAbstract
This study assessed the mastery level of fraction computation among Grade 10 students at Dimasalang National High School as basis for a school intervention program. Anchored on Constructivist Learning Theory, Mastery Learning Theory, Cognitive Load Theory, and an Input-Process-Output framework, the study used a descriptive-quantitative research design. Data were gathered from 58 Grade 10 students through a structured questionnaire and diagnostic tool covering addition and subtraction, multiplication and division, mixed number and improper fraction conversion, application in word problems, fraction-solving strategies, common difficulties, and suggested improvement measures. The data were analyzed using frequency count, percentage, weighted mean, and Pearson correlation. Findings showed that students had satisfactory mastery in addition and subtraction and word problem application, moderate mastery in multiplication and division, and acceptable mastery in mixed number and improper fraction conversion. Students commonly used step-by-step procedures, while mental computation, visual representations, conversion strategies, and problem-solving methods were used only occasionally. The main difficulties involved lack of confidence in independent problem-solving, finding correct denominators, converting mixed numbers and improper fractions, and identifying operations in word problems. A strong and significant positive relationship was found between students’ fraction-solving strategies and mastery level. The study concludes that while learners possess basic fraction computation skills, targeted interventions are needed to strengthen independence, conceptual understanding, and problem-solving confidence. The study aligns with SDG 4 – Quality Education and supports sustainable educational improvement by providing localized evidence for mathematics remediation, instructional planning, and learner-centered intervention.
References
Abdulaziz. (2024). The effects of using video-based instruction in solving fraction computations of students with autism spectrum disorder.
Agustin, et al. (2023). Elementary students’ difficulties in adding fractions.
Apelo, & Arcenas. (2023). Learner-centered and context-based strategies in mathematics instruction.
Asril, & Purwanta. (2024). Enhancing the ability to recognize fraction numbers through context-based concrete media in Grade V slow learners at a public elementary school.
Ballenas, G. J. (2023). Improving the computational skills in integers, fractions, and decimals through technology-enhanced mathematics instruction (TEMI). American Journal of Educational Research, 11(9), 603–613. https://doi.org/10.12691/education-11-9-9
Batucan, et al. (n.d.). Profile-based analysis and performance in science high school mathematics test of fundamental academic skills.
Bhatia, P., Le Diagon, S., Langlois, E., William, M., Prado, J., & Gardes, M.-L. (2023). Impact of a game-based intervention on fraction learning for fifth-grade students: A pre-registered randomized controlled study. Journal of Computer Assisted Learning, 39(1), 49–62. https://doi.org/10.1111/jcal.12726
Bloom, B. S. (1968). Learning for mastery. Evaluation Comment, 1(2), 1–12.
Camarines. (2024). Experiential and contextual learning strategies in enhancing students’ numeracy outcomes.
Catacutan, & Cajandig. (2024). Math Basics Pro with 5Is learning path integration in mastering algebra prerequisites.
Ching, & De Guzman. (2024). Simulation tools toward mastery of the most essential learning competencies in Mathematics 8.
Cinense. (2024). Mastery levels and experiences in learning addition and subtraction of fractions through flipped classroom model approach among Grade 5 learners.
De Las Peñas, et al. (2023). Bridging the mathematics gap through the use of mathematical apps.
Deri, & Ebio. (n.d.). Formative assessments in teaching and learning combinatorics concepts of Grade 10 Mathematics in Sorsogon City, Philippines.
Dictado, M., & Dagdag, J. (2025). Barriers to achieving mathematics proficiency: Synthesis of research. Journal of Interdisciplinary Perspectives, 3(9), 242–250. https://doi.org/10.69569/jip.2025.254
Domanais. (2023). Improving the least mastered competencies on number and number sense of Grade 7 learners.
Doni, & Probawanto. (2024). The challenges of junior high school students in solving fraction problems based on Newman’s error analysis.
Dube, & Maseko. (2024). Error analysis in fraction addition and subtraction using Structured Observed Learning Outcomes.
Espiritu, & Vendicacion. (2024). Sequential learning activity: Effect on the performance of Grade 5 pupils in dividing fractions.
Fabros, B. G., & Ibañez, E. D. (2023). Effectiveness of utilizing graphic organizers in improving conceptual understanding towards operations of fractions among teachers. International Journal of Instruction, 16(1), 507–526. https://doi.org/10.29333/iji.2023.16128a
Govender, & Machingura. (2023). Ascertaining Grade 10 learners’ levels of mathematical modelling competency through solving simultaneous equations word problems.
Hafiz, et al. (2022). Mastery of basic mathematics for high school students in solving mathematics problems.
Han, & Lin. (2024). Investigating the features of mathematics writing among Chinese students.
Harun, et al. (2023). Assessing students’ mastery and misconceptions in the fundamental operations on integers.
Hibi. (2024). Written calculation ability and numerical sense in Grades 6 and 7 among the Arab sector in Israel.
Hwang, W.-Y., Luthfi, M. I., Hariyanti, U., & Wardani, R. (2023). Evaluation of fraction learning in authentic context using Ubiquitous Fraction App. Education and Information Technologies, 28, 6755–6779. https://doi.org/10.1007/s10639-022-11453-2
Ismaiel, et al. (2024). The effectiveness of game-based learning in improving fractions mastery among 5th-grade students, comparing it with traditional teaching methods.
Jarrah, et al. (2022). Assessing the impact of digital games-based learning on students’ performance in learning fractions using ABACUS software application.
Joutsenlahti, & Perkkilä. (2024). Mastery of the concept of percentage and its representations in Finnish comprehensive school Grades 7–9.
Laranang, et al. (2024). Math SCRABBLE: Strengthening critical thinking and problem-solving, reinforcing rational numbers and integers, applying basic operations for building learner’s excellence in mathematics.
Latif, & Sharill. (2024). Mastering fractions and innovating with the station rotation model in blended learning.
Legal. (2024). Effectiveness of the Mathematics Enhancement Tool: A strategic intervention material to teaching fractions among Grade 4 students of Osmeña Colleges.
Li. (2024). Examining procedural proficiency in fraction addition: Comparative insights from England and Taiwan.
Llona, & Tonga. (2020). Lessons in Grade 10 Mathematics for use in a flipped classroom.
Loriente, Á. P., González-Calero, J. A., Tirado-Olivares, S., & del Olmo-Muñoz, J. (2025). Enhancing mathematics performance in primary education: The impact of personalized learning on fractions and decimal numbers. Education and Information Technologies, 30, 15961–15991. https://doi.org/10.1007/s10639-025-13428-5
Lucy, et al. (2024). Enhancing higher-order thinking skills among elementary students: A classroom action research on teaching fractions.
Magbag, & Tayag. (n.d.). A narrative review on the common errors of students when solving fractions.
Mageed. (2024). A fraction geometric approach to teaching fractions for mastery in Key Stages Two and Three: Open problems and a combined theoretical framework with intelligent practice.
Marr. (2024). The effect of learning environment and student groupings on math skill mastery.
Millamena. (n.d.). Instructional material for teaching fractions.
Moeller, K., & Spitzer, M. W. H. (2022). Predicting fraction and algebra achievements online: A large-scale longitudinal study using data from an online learning environment. Journal of Computer Assisted Learning, 38(6), 1797–1806. https://doi.org/10.1111/jcal.12721
Morata. (2024). Readiness of Grade 10 students on the prerequisite skills in STEM Mathematics: A basis for strategic intervention material.
Nasayao, et al. (2024). Singaporean Mathematics as a tool towards mastery of the four basic operations on fractions.
Noor. (2024). Development of cognitive diagnostic assessment to measure the mastery level of factorisation of algebraic fractions among Form Two students.
Nqabeni. (2023). Assessing Grade 3 learners’ current level of conceptual understanding of common fraction subtraction.
Odekeye, & Jita. (2024). Bridging learning gaps: Testing the efficacy of simulation-based instruction on the mastery of fractions.
Palculict. (2022). The effects of computer-assisted instruction on student learning of fractions in middle school mathematics.
Pedersen, et al. (2023). Differences in high- and low-performing students’ fraction learning in the fourth grade.
Pereda Loriente, Á., González-Calero, J. A., Tirado-Olivares, S., & del Olmo-Muñoz, J. (2025). Enhancing mathematics performance in primary education: The impact of personalized learning on fractions and decimal numbers. Education and Information Technologies, 30, 15961–15991. https://doi.org/10.1007/s10639-025-13428-5
Piaget, J. (1952). The origins of intelligence in children. International Universities Press.
Powell, S. R., Mao, J., Lariviere, D. O., & MacLean, K. B. (2026). A research synthesis of fraction interventions for middle-school students with a disability or mathematics difficulty. The Journal of Special Education, 59(4), 207–216. https://doi.org/10.1177/00224669251405854
Pradinar, et al. (2023). Analysis of learning difficulties of Grade IV elementary school students on fractal materials reviewed from numeracy ability and self-efficacy.
Prihandini, et al. (2023). Developing smart fractions as a learning media assisted by iSpring Suite 9 and GeoGebra for escalating students’ computational thinking skills.
Raza. (n.d.). Role of arithmetic principles and operations in understanding students’ mathematics performance.
Rosales, et al. (2024). Effectiveness of the Summer Arithmetic Enhancement Initiative: A pretest-posttest study among Grade 7–10 students.
Rosli, et al. (2024). Assessment of fraction concept among lower secondary students.
Salazar, & Magto. (2024). Tangible mathematics for Grade 7 learners: Design and validation of manipulatives for rational number concepts.
Salim, N. A. A. B., Singh, P., Hoon, T. S., & Nasir, N. A. M. (2024). Exploring the relationship between students’ attitudes and fraction sense proficiency across lower secondary grades. Indonesian Journal of Science and Mathematics Education, 7(2), 210–222. https://doi.org/10.24042/ijsme.v7i2.21776
Sanchez, J. S., & Pasia, A. E. (2023). Reality pedagogy and the numeracy skills among Grade 10 students.
Satsangi, R., & Raines, A. R. (2023). Examining virtual manipulatives for teaching computations with fractions to children with mathematics difficulty. Journal of Learning Disabilities, 56(4). https://doi.org/10.1177/00222194221097710
Satsangi, R., Park, S., & Raines, A. R. (2025). Teaching fraction computations to children with mathematics difficulties using a virtual number line intervention. Learning Disabilities Research & Practice, 40(4). https://doi.org/10.1177/09388982251358399
Schulz. (2023). Assessing student teachers’ procedural fluency and strategic competence in operating and mathematizing with natural and rational numbers.
Shalonda. (2024). The effect of using models to enhance Grade 7 learners’ understanding of fractions: A case of a primary school in Onankali Circuit, Oshikoto Region.
Sibiya, & Essien. (2024). Affordances for developing mathematical proficiency in fraction word problems in South African textbooks.
Silva, & Aldover. (2024). Exploring the level of numeracy and mathematics achievement of Grade 10 students. International Journal of Open-Access, Interdisciplinary & New Educational Discoveries of ETCOR Educational Research Center (iJOINED ETCOR).
Singh, P., Hoon, T. S., Nasir, N. A. M., Han, C. T., Rasid, S. M., & Hoong, J. B. Z. (2021). Obstacles faced by students in making sense of fractions. The European Journal of Social & Behavioural Sciences, 30(1), 34–51. https://doi.org/10.15405/ejsbs.287
Siregar, et al. (2023). Students’ procedural fluency in fraction addition through Built-in Definition Fraction Media. Supremum Journal of Mathematics Education.
Spitzer, M. W. H., & Moeller, K. (2022). Predicting fraction and algebra achievements online: A large-scale longitudinal study using data from an online learning environment. Journal of Computer Assisted Learning, 38(6), 1797–1806. https://doi.org/10.1111/jcal.12721
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285. https://doi.org/10.1207/s15516709cog1202_4
Tadeu. (2024). A synopsis of the importance of teaching fractions to children until K–10.
Tian, P., Fan, Y., Sun, D., & Li, Y. (2024). Evaluating students’ computation skills in learning amount of substance based on SOLO taxonomy in secondary schools. International Journal of Science Education, 46(15), 1578–1600. https://doi.org/10.1080/09500693.2023.2291691
Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5–13. https://doi.org/10.1016/j.learninstruc.2014.03.002
Viernes, M. D. D., & Seeping, A. V. (2024). Preservice teachers’ proficiency in fraction subconstructs as predictors of conceptual understanding in fraction arithmetic. The Palawan Scientist, 16(2), 82–94. https://doi.org/10.69721/TPS.J.2024.16.2.08
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.
Wilkins, J. L. M., & Norton, A. (2018). Learning progression toward a measurement concept of fractions. International Journal of STEM Education, 5, Article 27. https://doi.org/10.1186/s40594-018-0119-2
Winanda, et al. (2024). Project-based learning based on mastery learning to improve continuous numeracy literacy in high school students: Literature review.
Wolff, et al. (2024). Students’ self-assessment in the field of fractions: How accurate are they?
Yuniara, et al. (2020). The students’ mastery of fraction and its relation to the students’ abilities on its prerequisites.
Zhang, et al. (2024). How much mastery is enough mastery? The relationship between mastery in a lesson and the performance on the subsequent lesson.
