Effects of the Concrete–Representational–Abstract (CRA) Approach on Grade 6 Students’ Fraction Achievement and Attitudes
Keywords:
Concrete-Representational-Abstract, Elementary mathematics instruction, Fractions, Mathematics achievement, Student attitudesAbstract
This study addressed the persistent difficulty elementary learners experience with fractions and the limited classroom-based evidence on short Concrete–Representational–Abstract (CRA) interventions in Philippine public schools. This study aimed to determine the effects of a five-week CRA intervention on Grade 6 students’ achievement in fractions and attitudes toward learning fractions. Using a quasi-experimental one-group pretest posttest design, the study involved one intact Grade 6 class (N = 45). Matched pretest–posttest data were available for 39 students on the researcher assembled fraction achievement test based on released TIMSS-style items (35 points) and for 40 students on the adapted Mathematics Attitude Scale. Lessons progressed from hands-on fraction models to drawings and then to symbols and procedures, with explicit bridging across stages. Achievement scores increased from M = 5.92 (SD = 4.03) to M = 13.18 (SD = 6.05), t(38) = 12.63, p < .001, dz = 2.02. Attitude ratings improved from M = 3.52 (SD = 0.62) to M = 3.88 (SD = 0.40), t(39) = 5.49, p < .001, dz = 0.87. The CRA approach was effective in improving both fraction achievement and class attitudes, indicating that sequenced and connected representations can support conceptual understanding and learner confidence. These findings highlight CRA as a practical, classroom-feasible instructional strategy for elementary mathematics instruction.
Downloads
References
Bernardo, A., Cordel, M., II., Lapinid, M.R., Teves, J.M., Yap, S., & Chua, U. (2022). Contrasting profiles of low-performing mathematics students in public and private schools in the Philippines: Insights from machine learning. Journal of Intelligence, 10(3), Article 61. https://doi.org/10.3390/jintelligence10030061
Bruner, J. (1966). Toward a theory of instruction. Harvard University Press. https://www.hup.harvard.edu/books/9780674897014
Ching, B.H.-H., & Li, X.Y. (2024). Early fraction relational reasoning uniquely predicts later algebraic thinking in children: A longitudinal study. Contemporary Educational Psychology, 79, 102300. https://doi.org/10.1016/j.cedpsych.2024.102300
Department of Education. (2020a). Most Essential Learning Competencies (MELCs). https://www.deped.gov.ph/2020/07/13/melcs/
Department of Education. (2020b). DepEd Order No. 018, s. 2020: Policy guidelines for the provision of learning resources in the implementation of the Basic Education Learning Continuity Plan. https://tinyurl.com/3tj6kaek
Ennis, R., & Losinski, M. (2019). Interventions to improve fraction skills for students with disabilities: A meta-analysis. Exceptional Children, 85(3), 367–386. https://doi.org/10.1177/0014402918817504
Flores, M., & Hinton, V. (2021). The effects of a CRA-I intervention on students’ number sense and understanding of addition. Remedial and Special Education, 43, 183–194. https://doi.org/10.1177/07419325211038009
Flores, M., Hinton, V., & Schweck, K. (2024). Using CRA-I to teach fraction and decimal concepts to students with learning disabilities. Learning Disability Quarterly, 47(1), 44–58. https://doi.org/10.1177/07319487231176545
Hwang, S., & Son, T. (2021). Students’ attitude toward mathematics and its relationship with mathematics achievement. Journal of Education and e-Learning Research, 8(3), 272–280. https://doi.org/10.20448/journal.509.2021.83.272.280
Iyamuremye, E., & Burns, D. (2025). Concrete-Pictorial-Abstract instruction: Enhancing students' learning motivation and achievement in mathematics. Cogent Education, 12(1), 2558303. https://doi.org/10.1080/2331186X.2025.2558303
Jordan, N., Dyson, N., Guba, T.-P., Botello, M., Suchanec-Cooper, H., & May, H. (2024). Exploring the impact of a fraction sense intervention in authentic school environments: An initial investigation. Journal of Experimental Child Psychology, 244, 105954. https://doi.org/10.1016/j.jecp.2024.105954
Lim, S.Y., & Chapman, E. (2013). Development of a short form of the attitudes toward mathematics inventory. Educational Studies in Mathematics, 82(1), 145–164. https://doi.org/10.1007/s10649-012-9414-x
Morano, S., Flores, M., Hinton, V., & Meyer, J. (2020). The effects of a CRA fraction intervention in an inclusive setting. Exceptionality, 28(2), 77–91. https://doi.org/10.1080/09362835.2020.1727328
Mullis, I., & Martin, M. (Eds.). (2020). TIMSS 2019 Assessment Frameworks. Boston College, TIMSS & PIRLS International Study Center. https://timssandpirls.bc.edu/timss2019/frameworks/
Post, M., & Prediger, S. (2024). Teaching practices for unfolding information and connecting multiple representations: The case of conditional probability information. Mathematics Education Research Journal, 36, 97–129. https://doi.org/10.1007/s13394-022-00431-z
Prosser, S., & Bismarck, S. (2023). Concrete–Representational–Abstract (CRA) instructional approach in an Algebra I inclusion class: Knowledge retention versus students’ perception. Education Sciences, 13(10), 1061. https://doi.org/10.3390/educsci13101061
Schwarzmeier, S., Obersteiner, A., Alibali, M., & Marupudi, V. (2024). How do people compare visualizations of fraction magnitudes? Evidence from adults’ and children’s eye movements with continuous and discretized tape diagrams. The Journal of Mathematical Behavior, 75, 101160. https://doi.org/10.1016/j.jmathb.2024.101160
Syed Ismail, S.A., Maat, S.M., & Khalid, F. (2024). 35 years of fraction learning: Integrating systematic review and bibliometric analysis on a global scale. Eurasia Journal of Mathematics, Science and Technology Education, 20(12), em2543. https://doi.org/10.29333/ejmste/15657
Vessonen, T., Hakkarainen, A., Väisänen, E., Laine, A., Aunio, P., & Gagnon, J.C. (2021). Differential effects of virtual and concrete manipulatives in a fraction intervention on fourth and fifth grade students’ fraction skills. Investigations in Mathematics Learning, 13(4), 323–337. https://doi.org/10.1080/19477503.2021.1982586
Wen, R., & Dubé, A. (2022). A systematic review of secondary students’ attitudes towards mathematics and its relations with mathematics achievement. Journal of Numerical Cognition, 8(2), 295–325. https://doi.org/10.5964/jnc.7937
Wilkie, K., & Roche, A. (2023). Primary teachers’ preferred fraction models and manipulatives for solving fraction tasks and for teaching. Journal of Mathematics Teacher Education, 26, 703–733. https://doi.org/10.1007/s10857-022-09542-7
Witzel, B. (2005). Using CRA to teach algebra to students with math difficulties in inclusive settings. Learning Disabilities: A Contemporary Journal, 3(2), 49–60. https://eric.ed.gov/?id=EJ797683
Xu, C., Di Lonardo Burr, S., Li, H., Liu, C., & Si, J. (2024). From whole numbers to fractions to word problems: Hierarchical relations in mathematics knowledge for Chinese Grade 6 students. Journal of Experimental Child Psychology, 242, 105884. https://doi.org/10.1016/j.jecp.2024.105884
Zhang, Y., Yu, J., Xiao, R., Liu, H., & Jiang, Y. (2022). The effects of Concrete-Representational-Abstract sequence instruction on fractions for Chinese elementary students with mathematics learning disabilities. International Journal of Science and Mathematics Education, 20(7), 1481–1498. https://doi.org/10.1007/s10763-021-10215-9
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Journal of Interdisciplinary Perspectives
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
