Concrete&ndash;Pictorial&ndash;Abstract Approach in Developing Students&#039; Understanding of Surface Area of Solids

Emerlyn  Abrenica,

Concrete–Pictorial–Abstract Approach in Developing Students' Understanding of Surface Area of Solids

Discipline: Education

Abstract:

Learning geometry, particularly the surface area of solids, is challenging for many Grade 8 students due to its abstract nature and reliance on spatial visualization. The Concrete–Pictorial–Abstract (CPA) approach, grounded in Bruner's theory of enactive, iconic, and symbolic representation, has been shown to enhance conceptual understanding in mathematics, yet its application in geometry remains limited. This study investigated the effectiveness of CPA in improving students' understanding of the surface area of solids. Using a single-group pre-experimental design, 30 Grade 8 students participated in a 4-week CPA intervention covering rectangular and triangular prisms and pyramids. A researcher-made 40-item achievement test measured conceptual and procedural knowledge before and after the intervention. Descriptive statistics and paired-sample t-tests were employed to analyze the data. Results indicated that students' mean pre-test score of 52.40 (SD = 8.12) increased to a post-test mean of 78.65 (SD = 6.54), with a statistically significant improvement, t(29) = 14.32, p < 0.05. These findings suggest that the CPA approach effectively scaffolds learning by guiding students from concrete manipulation to pictorial representation and abstract reasoning, reducing cognitive load and enhancing comprehension. The study concludes that CPA is a practical and evidence-based instructional framework that enhances conceptual understanding, procedural skills, and engagement in geometry, providing educators with a structured method to address persistent challenges in teaching the surface area of solids.

References:

Arslan, A., & Ramazan, O. (2018). Effects of the Concrete-Pictorial-Abstract (CPA) approach on students' achievement and retention in mathematics. Journal of Education and Practice, 7(2), 112–120. https://doi.org/10.5539/jel.v7n2p112
Battista, M. T. (2007). The Development of Geometric and Spatial Thinking. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 843-908). Charlotte, NC: Information Age. https://www.scirp.org/reference/referencespapers?referenceid=1503337
Bruner, J. S. (1966). Toward a Theory of Instruction. Cambridge: Harvard University Press. https://www.scirp.org/reference/referencespapers?referenceid=1457921
Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. https://doi.org/10.1037/a0031084
Clements, D. H., & Samara, J. (2007). Early Childhood Mathematics Learning. In F. K. Lester Jr. (Ed.), Second Handbook on Mathematics Teaching and Learning (pp. 461-555). Charlotte, NC: Information Age. https://www.scirp.org/reference/referencespapers?referenceid=2164588
Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4th ed.). SAGE Publications. https://www.scirp.org/reference/ReferencesPapers?ReferenceID=1964849
Etikan, I., Musa, S. A., & Alkassim, R. S. (2016). Comparison of convenience sampling and purposive sampling. American Journal of Theoretical and Applied Statistics, 5(1), 1–4. https://doi.org/10.11648/j.ajtas.20160501.11
Jones, K. (2000). Teacher knowledge and professional development in geometry. Proceedings of the British Society for Research into Learning Mathematics, 20(3), 109–114. https://files.eric.ed.gov/fulltext/EJ1227350.pdf
Miller, S. P., & Hudson, P. J. (2007). Using evidence–based practices to build mathematics competence related to conceptual, procedural, and declarative knowledge. Learning Disabilities Research & Practice, 22(1), 58–68. https://doi.org/10.1111/j.1540-5826.2007.0023
Moyer-Packenham, P. S., & Westenskow, A. (2013). Effects of virtual manipulatives on student achievement and mathematics learning. International Journal of Science and Mathematics Education, 11, 133–154. https://doi.org/10.1007/s10763-012-9365-5 .
Purwadi, I. M. A., Sudiarta, I. G. P., & Suparta, I. N. (2019). The effect of concrete-pictorial-abstract strategy toward students' mathematical conceptual understanding and mathematical representation on fractions. International Journal of Instruction, 12(1), 1113–1126. https://doi.org/10.29333/iji.2019.12171a