EFFECT OF CONCRETE-REPRESENTATIONAL-ABSTRACT AS TEACHING APPROACH ON LEARNERS’ NUMERACY SKILL
Keywords:
Concrete, Representational, Abstract, Math InstructionAbstract
This study aimed to determine the effectiveness of the Concrete–Representational–Abstract (CRA) approach in enhancing the numeracy skills of Grade 11 TVL (Electrical Installation and Maintenance) learners at Major Manuel A. Aaron Memorial National High School for the school year 2024–2025. Utilizing a quasi-experimental design with a non-equivalent control group, the study involved two groups: the experimental group, which received instruction using the CRA method, and the control group, which was taught using traditional methods. Both groups underwent a pre-test and post-test using the researcher-made questionnaire to assess their numeracy performance. The pre-test results showed that both the experimental and control groups were at a Moderate level of performance, indicating comparable baseline numeracy skills. After the intervention, the experimental group’s performance improved to a High level, while the control group remained in the Moderate range. A paired sample t-test revealed a statistically significant difference in the experimental group’s pre-test and post-test scores (t = -2.863, p = .010), while the control group showed no significant improvement (t = 1.261, p = .223). Moreover, an independent t-test confirmed a significant difference in post-test performance between the two groups, favoring the experimental group. These findings suggest that the CRA approach significantly enhances learners’ numeracy skills by providing a scaffolded learning structure that transitions from concrete manipulatives to abstract symbols. The study concludes that the CRA method is more effective than traditional instruction in developing mathematical understanding among senior high school learners. Integrating CRA into mathematics instruction is therefore recommended to address persistent numeracy gaps and promote higher-level mathematical thinking in technical-vocational education contexts.
References
Camañan, C. T. (2019). Employing concrete-representation-abstract approach in enhancing mathematics performance. Slongan | Volume 4, 64-88. https://rpo.cjc.edu.ph/index.php/slongan/article/view/21
Dewhirst, C. B. (2023). Exploring the cognitive apprenticeship approach in teacher education: a case study of an early childhood practicum experience. Early Child Development and Care, 193(8), 965–978. https://doi.org/10.1080/03004430.2023.2187326
Flores, M. M., Hinton, V. M., & Meyer, J. M. (2018). Teaching Fraction Concepts Using the Concrete-Representational-Abstract Sequence. Remedial and Special Education, 41(3), 165-175. https://doi.org/10.1177/0741932518795477 (Original work published 2020)
Gallo-Toong, N. (2020). The extent of use of Concrete-Representational-Abstract (CRA) model in mathematics. International Journal for Research in Mathematics and Statistics, 6(5). https://www.studocu.com/ph/document/foundation-university-philippines/research-outputs/the-extent-of-use-of-concrete-representational-abstract-cra-model-in-mathematics/8601817
Gilead, M., Trope, Y., & Liberman, N. (2020). Above and beyond the concrete: The diverse representational substrates of the predictive brain. Behavioral and Brain Sciences, 43, e121. https://doi.org/10.1017/S0140525X19002000
Goya, D. (2023). Effects of the concrete-representational-abstract instructional sequence on solving algebraic equations for middle school students with autism spectrum disorder (Doctoral dissertation). University of Hawai'i at Manoa. ProQuest Dissertations Publishing. https://eric.ed.gov/?id=ED636393
Huan, C., et al (2022). Mathematics Learning from Concrete to Abstract (1968-2021): A Bibliometric Analysis. Participatory Educational Research (PER) Vol.9(4). 445-468. https://www.researchgate.net/publication/361184372_Mathematics_Learning_from_Concrete_to_Abstract_1968-2021_A_Bibliometric_Analysis
Libo-on, J. T., & Casite, M. L. (2025). Application of the Concrete–Representational–Abstract (CRA) framework in teaching integer operations: Evidence from a rural senior high school. Journal Name, 18(11), 333–342. https://doi.org/12.163022.Gj.2025.v18.11.024
Mathematics Hub (2024). Concrete, representational, abstract (CRA). https://www.mathematicshub.edu.au/plan-teach-and-assess/teaching/teaching-strategies/concrete-representational-abstract-cra/
Medical College of Wisconsin (2022). Cognitive apprenticeship theory: A guide to Collins and Brown’s theory of learning. https://www.mcw.edu/-/media/MCW/Education/Academic-Affairs/OEI/Faculty-Quick-Guides/Cognitive-Apprenticeship-Theory.pdf
Morata, D. E., Estores, R. C., Famentera, A. R., Ignacio, R. M. M., Labajo, V. J., & Arado, Sr. M. M. (2024). The Use Concrete-Representational-Abstract Approach (CRA) in Improving the Adding Skills in Kindergarten. International Research Journal of Modernization in Engineering Technology and Science, 6(10). https://doi.org/10.56726/IRJMETS62957
Nugroho, S.A. & Jailani (2019). The Effectiveness of Concrete Representational Abstract Approach (CRA)Approach and Problem-Solving Approach on Mathematical Representation Ability at Elementary School. International Conference on Meaningful Education Volume 2019, 27-36. https://knepublishing.com/index.php/Kne-Social/article/view/4620/9312
Prosser, S. K., & Bismarck, S. F. (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
Reyes, J. A. (2021). Effectiveness of Concrete-Representational-Abstract sequence of instruction in probability on select groups of eight graders. ResearchGate. https://www.researchgate.net/publication/349476959
Sterner, G., Wolff, U., & Helenius, O. (2019). Reasoning about Representations: Effects of an Early Math Intervention. Scandinavian Journal of Educational Research, 64(5), 782–800. https://doi.org/10.1080/00313831.2019.1600579
Shen, Z. (2023). The effectiveness of concrete-representational-abstract integration framework within word-problem solving for students experiencing mathematics difficulty. University of Texas at Austin Repository. https://repositories.lib.utexas.edu/server/api/core/bitstreams/67ece62d-574e-42ff-9225-243f8d3effd6/content
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