Home⇛Journal of Interdisciplinary Perspectives⇛vol. 4 no. 9 (2026)

Concrete-Pictorial-Abstract (CPA) and Traditional Methods of Instruction in Enhancing Mathematical Proficiency Among Grade 7 Learners

Michael H. Dejaño | Kirt Anthony Diaz

Discipline: Education

 

Abstract:

(CPA) and Traditional Methods of Instruction in Enhancing Mathematical Proficiency Among Grade 7 Learners Michael H. Dejaño, Kirt Anthony R. Diaz Author Information: Abstract. The desire to enhance students' mathematical proficiency has encouraged many teachers to adopt innovative teaching approaches, such as the Concrete-Pictorial-Abstract (CPA) method, and to provide alternatives to traditional instructional methods. This study aimed to determine which method is more effective in improving students' mathematical proficiency. A quasi-experimental research design was used, specifically a pretest-posttest design, and data were analyzed using an independent-samples t-test. Using purposive and universal sampling techniques, a total of 100 students from the Department of Education, Division of Davao City, served as respondents in the study. Data were gathered through a researcher-made mathematical proficiency test, which underwent content validation and reliability testing. The results revealed that students taught using the Concrete-Pictorial- Abstract (CPA) method obtained higher mathematical proficiency scores (M = 55.78) than those taught using the traditional method (M = 47.84), and the independent samples t-test showed a statistically significant difference between the two groups (t = 2.88, p = .005). The study concluded that while both the CPA method and the traditional method improved Grade 7 students' mathematical proficiency, the CPA method produced significantly greater learning gains and was more effective in enhancing students' conceptual understanding, problem-solving skills, and overall mathematical performance.



References:

  1. Agusta, E.S. (2025). Enhancing students' understanding of mathematical concepts through the concrete-pictorial-abstract (CPA) approach in learning fractions. ALGORITMA: Journal of Mathematics Education, 7(1), 55-65.
  2. Agustin, G. (2023). Concrete pictorial abstract (CPA) approach in mathematics problem solving. International Advanced Research Journal in Science, Engineering and Technology (IARJSET), 10(7), 658-662. https://doi.org/10.17148/IARJSET.2023.107109
  3. Ahmad, S., & Siller, H.-S. (2024). Investigating the effect of manipulatives on mathematics achievement: The role of concrete and virtual manipulatives for diverse achievement level groups. Journal on Mathematics Education, 15(3), 979-1002. https://doi.org/10.22342/jme.v15i3.pp979-1002
  4. Akinoso, S.O. (2015). Teaching mathematics in a volatile, uncertain, complex and ambiguous (VUCA) world: The use of concrete-representational-abstract instructional strategy. Journal of Education and Practice, 19(1), 97-107. https://files.eric.ed.gov/fulltext/EJ1177074.pdf
  5. Angco, R.J., & Angco, L. (2024). A meta-synthesis of effective practices and outcomes in the use of manipulatives for teaching mathematics. Human Behavior, Development & Society, 25(2). https://doi.org/10.62370/hbds.v25i2.274848
  6. Azzumar, F., & Juandi, D. (2023). Concrete-pictorial-abstract approaches to mathematics education: A systematic literature review. Journal of Mathematics and Mathematics Education,13(1), 1-11.
  7. Binatlao, H., & Cordova, C. (2025). Assessing students' problem-solving skills in concrete-representational-abstract approach. Journal of Education and Sociology, 4(6), 28-34. https://doi.org/10.5281/zenodo.15579215
  8. Bruner, J. (1974). Toward a theory of instruction. Harvard University Press. https://tinyurl.com/dpyj789z
  9. Camañan, C.T. (2019). Employing concrete-representation-abstract approach in enhancing mathematics performance. SLONGAN, 4(1), 25. https://rpo.cjc.edu.ph/index.php/slongan/article/view/21
  10. Camilleri, M.A. (2024). Artificial intelligence governance: Ethical considerations and implications for social responsibility. Expert Systems, 41(7), e13406. https://doi.org/10.1111/exsy.13406
  11. Canto López, M.D.C., Manchado Porras, M., Piñero Charlo, J.C., Mera Cantillo, C., Delgado Casas, C., Aragón Mendizábal, E., & García Sedeño, M.A. (2022). Description of main innovative and alternative methodologies for mathematical learning of written algorithms in primary education. Frontiers in Psychology, 13, 913536. https://doi.org/10.3389/fpsyg.2022.913536
  12. Chasanah, U., Wibowo, W.C., Supriatna, U., & Riyandi, W.B. (2024). Improving students' numeracy skills using the CPA (concrete, pictorial, abstract) approach in number material for 2nd grade at MIN 1 Batam. Jurnal Profesionalisme Guru, 1(4), 577-582.
  13. Chen, X. (2025). A comparative study on the effectiveness of traditional and modern teaching methods. Lecture Notes in Education Psychology and Public Media, 85, 13-18.
  14. https://doi.org/10.54254/2753-7048/2025.20824
  15. Corrêa, P.D., & Haslam, D. (2021). Mathematical proficiency as the basis for assessment: A literature review and its potentialities. Mathematics Teaching Research Journal, 12(4), 3-20.
  16. Czarnota-Bojarska, J. (2021). The ethics of organizational research: Methodological considerations for ensuring respondents' anonymity and confidentiality. EWOP in Practice, 15(1). https://doi.org/10.21825/ewopinpractice.87141
  17. Dairo, N.O.M., Okonkwo, N.C.A., & Orakwe, N.C.U. (2024). A review of primary school teachers' insight into traditional instruction and activity-based learning in mathematics education. International Journal of Applied Research in Social Sciences, 6(11), 2778-2790. https://doi.org/10.51594/ijarss.v6i11.1725
  18. Dela Peña, R.M.J., & Doronio, R. (2025). An experimental study on mathematics teaching strategies and academic performance of students. International Journal of Research and Innovation in Social Science. https://dx.doi.org/10.47772/IJRISS.2025.90700097
  19. Estrada, E., Ferrer, E., & Pardo, A. (2019). Statistics for evaluating pre-post change: Relation between change in the distribution center and change in the individual scores. Frontiers in Psychology, 9, 2696. https://doi.org/10.3389/fpsyg.2018.02696
  20. 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
  21. Evans, B.J., Bettinger, E.P., & Antonio, A.L. (2025). Data collection and monitoring in an educational RCT of a postsecondary access program: Assessing internal and external validity. Education Sciences, 15(3), 363. https://doi.org/10.3390/educsci15030363
  22. Gabina, S., Jagri, B., Mohammed, A.A., Anass, A.A., Abdul-Mumin, A.H., Agyei, E., & Domonaamwin, C.B. (2021). Factors affecting efficient teaching and learning of mathematics in senior high schools in Wa. Teacher Education and Curriculum Studies, 6(3), 81-88. https://doi.org/10.11648/j.tecs.20210603.11
  23. Galope, G., & Gumanoy, R. (2025). Mathematics mastery through innovative pedagogical approaches. International Journal of Research and Innovation in Applied Science, 10(2), 442-452. https://doi.org/10.51584/IJRIAS.2025.10020040
  24. Garrett, R., & Hong, G. (2016). Impacts of grouping and time on the math learning of language minority kindergartners. Educational Evaluation and Policy Analysis, 38(2), 222-244. https://doi.org/10.3102/0162373715611484
  25. Ines, J. (2023, December 5). PH still among lowest in math, science, reading in global student assessment. Rappler. https://tinyurl.com/bddbb4mk
  26. 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
  27. Kang, E., & Hwang, H.-J. (2023). The importance of anonymity and confidentiality for conducting survey research. Journal of Research and Publication Ethics, 4(1), 1-7. https://doi.org/10.15722/JRPE.4.1.202303.1
  28. Kaur, P., Stoltzfus, J., & Yellapu, V. (2018). Descriptive statistics. International Journal of Academic Medicine, 4(1), 60-63. https://doi.org/10.4103/IJAM.IJAM_7_18
  29. Khasawneh, E., Hodge-Zickerman, A., York, C., Smith, T., & Mayall, H. (2023). Examining the effect of inquiry-based learning versus traditional lecture-based learning on students' achievement in college algebra. International Electronic Journal of Mathematics Education, 18(1), em0724. https://doi.org/10.29333/iejme/12715
  30. Kim, H.-Y. (2019). Statistical notes for clinical researchers: The independent samples t-test. Restorative Dentistry & Endodontics, 44(3), e26. https://doi.org/10.5395/rde.2019.44.e26
  31. Kocdar, S., Karadag, N., & Sahin, M.D. (2016). Analysis of the difficulty and discrimination indices of multiple-choice questions according to cognitive levels in an open and distance learning context. Turkish Online Journal of Educational Technology-TOJET, 15(4), 16-24. https://www.tojet.net/articles/v15i4/1542.pdf
  32. Kozanitis, A., & Nenciovici, L. (2023). Effect of active learning versus traditional lecturing on the learning achievement of college students in humanities and social sciences: A meta-analysis. Higher Education, 86(6), 1377-1394. https://doi.org/10.1007/s10734-022-00977-8
  33. Larbi, E., & Mavis, O. (2016). The use of manipulatives in mathematics education. Journal of Education and Practice, 7(36), 53-61. https://tinyurl.com/ymndzmbv
  34. Latumbo, I.L. (2024). Differentiated instruction in teaching fourth grade mathematics: Basis for an instructional module. Psychology and Education: A Multidisciplinary Journal, 17(6), 1-1. https://scimatic.org/storage/journals/11/pdfs/2603.pdf
  35. Lee, J., & Paul, N. (2023). A review of pedagogical approaches for improved engagement and learning outcomes in mathematics. Journal of Student Research, 12(3), 1-9.
  36. Leong, Y.H., Ho, W.K., & Cheng, L.P. (2015). Concrete-pictorial-abstract: Surveying its origins and charting its future. https://tinyurl.com/3bnmc4pn
  37. Leyson, J., & Andrino, V. (2025). Enhancing pupils' performance in mathematics through the use of concrete-pictorial-abstract approach. International Journal of Research and Innovation in Social Science, 8(12), 1937-1951. https://doi.org/10.47772/ijriss.2024.8120165
  38. Libo-on, J., & Perez, J. (2021). Effects of four teaching strategies on the academic performance of senior high school students. Romblon State University Research Journal, 3(2), 22-30. https://doi.org/10.58780/rsurj.v3i2.60
  39. Lutfi, J.S., & Dasari, D. (2024). Research trends on learning mathematics with the CPA (Concrete-Pictorial-Abstract) approach. Prisma, 13(1), 103-112.
  40. Manota, A.C. (2025). Acceptability of the developed spreadsheet-based item analysis tool. https://tinyurl.com/b58pa8uz
  41. Mas'udah, S., & Utaminingsih, S. (2024). Development of mathematics textbook based on the concrete, pictorial, abstract (CPA) number approach for MI students in Sedan District, Rembang City. Uniglobal Journal of Social Sciences and Humanities, 3(1), 107-111. https://doi.org/10.53797/ujssh.v3i1.16.2024
  42. Mizzi, D., & Calleja, J. (2024). Using lesson study to implement the CPA approach in a mathematics primary classroom. https://www.um.edu.mt/library/oar/handle/123456789/129978
  43. Mohajan, H.K. (2017). Two criteria for good measurements in research: Validity and reliability. Annals of Spiru Haret University: Economic Series, 17(4), 59-82. https://doi.org/10.26458/1746
  44. Mudaly, V., & Naidoo, J. (2015). The concrete-representational-abstract sequence of instruction in mathematics classrooms. Perspectives in Education, 33(1), 42-56. https://doi.org/10.38140/pie.v33i1.1895
  45. Nida, N.K., Usodo, B., & Saputro, D.R.S. (2020, May). Effectiveness of the flipped classroom model on the students' mathematical creative thinking skills. In International Conference on
  46. Online and Blended Learning 2019 (ICOBL 2019) (pp. 107-110). Atlantis Press. https://doi.org/10.2991/assehr.k.200521.022
  47. Nugroho, S.A., & Jailani, J. (2019). The effectiveness of concrete representational abstract (CRA) approach and problem solving approach on mathematical representation ability at elementary school. https://doi.org/10.18502/KSS.V3I17.4620
  48. OECD. (2023). PISA 2022 results (Volume I): The state of learning and equity in education. PISA, OECD Publishing. https://doi.org/10.1787/53f23881-en
  49. Ouyang, B. (2023). Efficacy of problem-based learning over traditional pedagogy on US CPA practice exam performance among Chinese accounting university students (Doctoral dissertation, Walden University).
  50. Palomares, N., & Gonzalvo, I. (2025). Learning gaps in Mathematics 7 and teachers' instructional strategies in selected public secondary schools in the second congressional district of Quezon. Psychology and Education: A Multidisciplinary Journal, 48(3), 327-341. https://doi.org/10.70838/pemj.480303
  51. Pelayo, E.O. (2024). The effect of social based-trends instruction to students' conceptual understanding in mathematics. Indonesian Journal of Education Research (IJoER), 5(6), 324-330. https://doi.org/10.37251/ijoer.v5i6.1303
  52. Pham, H.T.H., Pham, Q.D., Bui, C.K., & Le, H.T. (2025). Factors affecting the effectiveness of math teachers' integrated teaching in secondary schools: The case of Vietnam. Journal of Pedagogical Research, 9(1), 235-253. https://doi.org/10.33902/jpr.202532448
  53. 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
  54. Putri, H.E., Suwangsih, E., Rahayu, P., Nikawanti, G., Enzelina, E., & Wahyudy, M.A. (2020, April). Influence of concrete-pictorial-abstract (CPA) approach on the enhancement of primary school students' mathematical reasoning ability. Mimbar Sekolah Dasar, 7(1), 119-132. https://doi.org/10.17509/mimbar-sd.v7i1.22574
  55. Reyes, J.D. (2021). Effectiveness of concrete-representational-abstract sequence of instruction in probability on select-groups of eight graders. International Journal of Multidisciplinary Research and Growth Evaluation, 2(1), 438-443.
  56. ROBERT, P. (2020). A study to foster proactive learning in mathematics at primary schools in the Republic of the Marshall Islands through concrete-pictorial-abstract (CPA) approach. International Cooperation Center for the Teacher Education and Training, Naruto University of Education. https://doi.org/10.24727/00028532
  57. Rozata, U., & Theoneste, H. (2024). Concrete pictorial abstract approach use in teaching mathematics on secondary students' participation in six selected schools in Kicukiro District,
  58. Rwanda. African Journal of Empirical Research, 5(4), 1243-1251. https://doi.org/10.51867/ajernet.5.4.102
  59. Salingay, N., & Tan, D. (2018). Concrete-pictorial-abstract approach on students' attitude and performance in mathematics. International Journal of Scientific & Technology Research, 7(5), 90-111.
  60. Salkind, N. (2017). Statistics for people who (think they) hate statistics (6th ed.). SAGE Publications. https://tinyurl.com/yjpdbaw6
  61. Shafiee, M.S., & Meng, C.C. (2023). Impact of concrete-pictorial-abstract approach with collaborative lesson research on year four pupils' proficiency in volume. Asia Pacific Journal of Educators and Education, 38(1), 119-140. https://doi.org/10.21315/apjee2023.38.1.7
  62. Shuxratovna, R.N. (2024). Pedagogical possibilities of implementing the CPA (concrete-pictorial-abstract) approach. International Journal of Pedagogics, 4(2), 68-76. https://doi.org/10.37547/ijp/Volume04Issue02-13
  63. Suryaningsih, T., Nisa, K., Widiyanto, R., Latip, A.E., & Siron, Y. (2025). Enhancing elementary students' numeracy skills through the concrete pictorial abstract (CPA) approach. Journal of Integrated Elementary Education, 5(1), 224-236. https://doi.org/10.21580/jieed.v5i1.25383
  64. Tabuena, A.C., Hilario, Y.M., & Buenaflor, M. (2021). Overview and exemplar components of the research methodology on the research writing process for senior high school students. International Journal of Trend in Scientific Research and Development, 5(3), 117-126. https://doi.org/10.2139/ssrn.3802722
  65. Tenzin, S. (2024). The implementation of the concrete-pictorial-abstract (CPA) instructional model in teaching primary mathematics in Thimphu Dzongkhag. RABSEL, 25(1). https://doi.org/10.5281/zenodo.14524332
  66. Tjandra, C. (2023). Effectiveness of using manipulatives in mathematics teaching in inclusive education programs in an elementary school. Dharmas Education Journal (DE_Journal), 4(1), 168-178. https://tinyurl.com/4csbspah
  67. Vygotsky, L.S., & Cole, M. (1978). Mind in society: Development of higher psychological processes. Harvard University Press.
  68. Wu, C., Wang, N., Wang, Q., Wang, C., Wei, Z., Wu, Z., Yu, S., & Jiang, X. (2024). Participants' understanding of informed consent in clinical trials: A systematic review and updated meta- analysis. PLoS ONE, 19(1), e0295784. https://doi.org/10.1371/journal.pone.0295784

Tools


Copyright © 2026  KITE Digital Educational Solutions |  Exclusively distributed by CE-Logic