Current Language EN
English English Türkçe Türkçe Español Español Português Português Pусский Pусский Filipino Filipino Tiếng Việt Tiếng Việt हिन्दी हिन्दी العربية العربية বাংলা বাংলা Deutsch Deutsch 中文 中文
Research Article

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

763 reads
Emerlyn Abrenica
Psych Educ Multidisc J, 2025, 47 (9), 1071-1075, DOI: https://doi.org/10.70838/pemj.470903, ISSN 2822-4353
Verified on SciChain · token #6512 of SciMatic Articles (ERC-1155, 1,000,000 tokens)
Contract 0x0E596B4b…F05eF8 · mint transaction · verify the record
Proof of record · recorded 2026-10-17 · anchored on SciChain · Verify (opens in a new tab) · record

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.

Keywords surface area instructional strategy geometry education concrete–pictorial–abstract mathematical understanding
Author 1
View Publication Certificate View PDF Cite This Article Back to Archives

The team behind this paper

1 author, 1 institution.

This paper Manor Independent School District — United States Manor Independent Schoo… 1 author Emerlyn Abrenica — corresponding author EA Emerlyn Abrenica ✉

Readership

765 reads over 14 months.

October 2025 November 2026

Related work on SciMatic

Closest of 4 articles sharing keywords with this one. A rarer shared keyword counts for more than a common one.

On SciChain

This article is token #6512 of SciMatic Articles (ERC-1155): 1,000,000 tokens, minted once, never more. The chain also stores a fingerprint (SHA-256) of the article's record, so anyone can check that it has not been altered.

HolderWalletTokens
SciMatic 0xc35709…277732 100,000 (10%)
Emerlyn Abrenica 0x0edF6D…02e6f9 900,000 (90%)
Content hash 0x9729e901997793643d3d8a9eacad94f79822ebed72477c4173db2e8b6aa7bbfc
View on the explorer Verify the record Mint transaction

Bibliographic Information

Emerlyn Abrenica (2025). Concrete–Pictorial–Abstract Approach in Developing Students' Understanding of Surface Area of Solids, Psychology and Education: A Multidisciplinary Journal, 47(9): 1071-1075
Bibtex Citation
@article{emerlyn_abrenica2025pemj,
author = {Emerlyn Abrenica},
title = {Concrete–Pictorial–Abstract Approach in Developing Students' Understanding of Surface Area of Solids},
journal = {Psychology and Education: A Multidisciplinary Journal},
year = {2025},
volume = {47},
number = {9},
pages = {1071-1075},
doi = {10.70838/pemj.470903},
url = {https://scimatic.org/show_manuscript/6512}
}
APA Citation
Abrenica, E., (2025). Concrete–Pictorial–Abstract Approach in Developing Students' Understanding of Surface Area of Solids. Psychology and Education: A Multidisciplinary Journal, 47(9), 1071-1075. https://doi.org/10.70838/pemj.470903

Author Information

  • To change your profile photo, login to scimatic.org, go to your profile and change the photo.
  • Any photo that shows your face will do: we crop it to your head and shoulders and give it a plain background automatically.
  • To sign in, go to Sign in and enter the e-mail address registered with the article: we e-mail you a one-time sign-in link (there is no password).
  • In case of any other problem, contact your editor directly or write to us at info @ scimatic.org