Elementary learners’ struggles with fractions pose a major obstacle to building a strong mathematical foundation. Unlike whole numbers, fractions often lack immediate real-world referents, making their abstract nature especially challenging for young learners (Barmby, 2018). The shift from using concrete tools, such as fraction strips, to engaging with abstract computational tasks intensifies these difficulties, requiring students to develop a deeper conceptual grasp of number relationships (Clarke & Roche, 2020). Individual learner differences, including limitations in working memory or spatial reasoning, further exacerbate comprehension challenges (Fuchs et al., 2013). In addition, widespread misconceptions such as misinterpreting the fraction bar as a subtraction sign frequently result in calculation errors (Bailey et al., 2018).

Research consistently shows that solving fraction-based word problems is particularly problematic for learners (Kenney & Ntow, 2024; López-Martín et al., 2022; Bhatia et al., 2023; Copur-Gencturk & Doleck, 2021). These challenges often stem from difficulties in problem interpretation, translating situations into mathematical expressions, and selecting appropriate operations. Learners also tend to omit units in their answers, lowering accuracy (Istiqomah & Prabawanto, 2019). Moreover, gaps persist in understanding fundamental fraction concepts, including arithmetic operations and problem-solving strategies (Hariyani et al., 2022).

National and regional assessments mirror these struggles. The Philippines ranked low in mathematics proficiency in PISA 2018 (DepEd – National Report, 2019). While the National Achievement Test (NAT) scores showed modest gains between 2005 and 2013, results still fell short of the 75 percent benchmark. More recently, a district-level assessment in San Jose revealed that 15.8% of Grade 3 learners lacked basic numeracy skills, with fractions identified as a key area of weakness.

These persistent gaps underscore the need to design supplementary instructional materials tailored to fraction learning. Such resources can scaffold conceptual understanding, bridge knowledge gaps, and provide guided practice in solving and creating fraction-based problems. Addressing these challenges not only aligns with the Department of Education’s thrust to strengthen numeracy but also highlights the potential of design-based research in producing responsive, evidence-based solutions.

 

Bibliography

Anives, J.B. & Ching, D.A. (2022). Application of task-based learning module in mathematics V. International Journal of Educational Management and Development Studies, 3(1), 97-113. https://doi.org/10.53378/352865

Bailey, M. H., Armstrong, B. J., & Wessman, A. E. (2018). Misconceptions in fractions: An examination of preservice teachers’ understanding of part-whole relationships and fraction operations. International Journal of Early Childhood, 20(2), 3–18.

Barmby, P. (2019). Developing fraction understanding: A research-based guide for preservice and inservice teachers (2nd ed.). Routledge.

Bhatia, P., Léone, J., Gardes, M.-L., & Prado, J. (2024). Fraction knowledge in adults with persistent mathematics difficulties. Learning Disability Quarterly, 47(1), 30–43. https://doi.org/10.1177/07319487231171380

Borko, H., & Whitin, P. (2021). Inquiry-based instruction for teaching and learning mathematics. Routledge.

Cai, J., & Jitendra, A. K. (2022). Developing fraction proficiency in struggling learners: A meta-analysis. Educational Psychology, 37(1), 154–174.

Clarke, D. M., & Roche, A. (2020). Fractions and decimals: A learning trajectory. Mathematics Teaching in the Middle School, 25(8), 484–491.

Copur-Gencturk, Y., & Doleck, T. (2021). Strategic competence for multistep fraction word problems: An overlooked aspect of mathematical knowledge for teaching. Educational Studies in Mathematics, 107(1), 49–70. https://doi.org/10.1007/s10649-021-10028-1

Department of Education. (2019). Programme for International Student Assessment (PISA) 2018: National report of the Philippines. https://www.deped.gov.ph/wp-content/uploads/2019/12/PISA-2018-Philippine-National-Report.pdf

Fennell, F., & Karp, K. (2017). Fraction sense: Foundational understandings. Journal of Learning Disabilities, 50(6), 648–650. https://doi.org/10.1177/0022219416662030

Fuchs, L. S., Fuchs, D., & Vaughn, S. (2013). Fractions: Important concepts and misconceptions. Routledge.

Hariyani, M., Herman, T., Suryadi, D., & Prabawanto, S. (2022). Exploration of student learning obstacles in solving fraction problems in elementary school. International Journal of Educational Methodology, 8(3), 505–515. https://doi.org/10.12973/ijem.8.3.505

Hofer, S. I., & Reinhold, F. (2025). Scaffolding of learning activities: Aptitude-treatment-interaction effects in math? Learning and Instruction, 99, 102177. https://doi.org/10.1016/j.learninstruc.2025.102177

Hsu, Y. C., & Lee, R. C. (2022). Using fraction dice to enhance fifth-grade students’ learning of fractions. Mathematics Teaching in the Middle School, 28(5), 336–347.

Hunting, R. (2019). Developing proportional reasoning: A teacher’s guide for grades K–6. Corwin.

Istiqomah, M. N., & Prabawanto, S. (2019). The difficulties of fifth-grade students in solving mathematic fractions word problems. Al-Asasiyya: Journal Basic of Education, 3(2), 152–160.

Jitendra, A. K., & Griffin, C. C. (2020). Fraction intervention for students with mathematics difficulties: A meta-analysis and implications for instruction. Review of Educational Research, 90(3), 407–446.

Kenney, S., & Ntow, F. D. (2024). Unveiling the errors learners make when solving word problems involving algebraic task. SAGE Open, 14(4). https://doi.org/10.1177/21582440241299245

Khoo, K. S., & Wong, F. Y. (2021). Learning fractions with a board game: An action research in a Singapore primary school. Journal of Educational Research and Innovation, 14(1), 55–70.

Kurniawan, H., Sutawidjaja, A., As’ari, A. R., & Muksar, M. (2018, October 9–10). The thinking process of students in representing images to symbols in fractions. Journal of Physics: Conference Series, 1028(012138), 1–7.

Loc, T. N., Tong, V. M., & Chau, T. M. (2017). Learners who have limited foundational knowledge concerning solving problems involving concepts of fractions. South African Journal of Childhood Education, 8(2), 1–12.

López-Martín, M. d. M., Aguayo-Arriagada, C. G., & García López, M. d. M. (2022). Preservice elementary teachers’ mathematical knowledge on fractions as operator in word problems. Mathematics, 10(3), 423. https://doi.org/10.3390/math10030423

Moschkovich, J. N. (2019). Multilingual practices in math classrooms: Leveraging students’ abilities for equity and learning. Guilford Publications.

Mpiladeri, M., Palaigeorgiou, G., & Lemonidis, C. (2016). FRACTANGI: A tangible learning environment for learning about fractions with an interactive number line. In Proceedings of the 13th International Conference on Cognition and Exploratory Learning in Digital Age (CELDA 2016) (pp. 175–182). IADIS Press.

Nemirovsky, R., & Ferrara, F. (2018). Embodied design: Shaping mathematics instruction and teacher education. Routledge.

Nnachi, R. O. (2009). Advanced psychology of learning and scientific enquiries. Totan Publishers.

Onasanwa, M. O., & Omosewo, E. O. (2011). Instructional materials as a key component in teaching and learning process that can disseminate information, data, idea, and messages. International Journal of Research in Education, 8(1), 139–148.

Ozimek, D., & Jitendra, A. K. (2021). Using interactive computer manipulatives to improve fraction skills of sixth-grade students with mathematics difficulties. Journal of Learning Disabilities, 54(4), 335–347.

Pearn, C., & Stephens, M. (2015). Deep understanding of fractions is important for the successful transition to algebra. Mathematics Teaching in the Middle School, 21(3), 132–138.

Rivera, F. G., & Barroso, C. R. (2022). Culturally responsive fraction instruction with Mayan fraction bars. Mathematics Teaching in the Middle School, 28(5), 348–355.

Shin, M., Bryant, D. P., Bryant, B. R., McKenna, J. W., Hou, F., & Ok, M. W. (2017). Virtual manipulatives: Tools for teaching mathematics to students with learning disabilities. Intervention in School and Clinic, 52(3), 148–153. https://doi.org/10.1177/1053451216644830

Siegler, R. S., & Lortie-Forgues, H. (2017). Hard lessons: Why rational number arithmetic is so difficult for so many people. Current Directions in Psychological Science, 26(4), 346–351. https://doi.org/10.1177/0963721417700129

Simon, M. A., Placa, N., Avitzur, A., & Kara, M. (2018). Promoting a concept of fraction-as-measure: A study of the learning through activity research programme. The Journal of Mathematical Behaviour, 52(1), 122–133. https://doi.org/10.1016/j.jmathb.2018.03.004

Staub, F. L., & Stein, M. K. (2018). Essential components of a connected curriculum for teaching fraction concepts and operations. Mathematics Teaching in the Middle School, 23(8), 484–493.

Ubah, J. A. I., & Bansilal, S. (2018). Pre-service primary mathematics teachers’ understanding of fractions: An action-process-object-schema perspective. South African Journal of Childhood Education, 8(2), 1–12.

Yeo, J., & Park, Y. (2023). Enhancing proportional reasoning and explanation skills through dynamic visual representations in a virtual manipulative app. Research in Mathematics Education, 25(1), 43–65.