Prisma Sains: Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram
Vol. 14 No. 3: July 2026

Cognitive Barriers in the Transition from Graphical to Symbolic Representation of Integral Concepts: A Systematic Literature Review

Marthinus Yohanes Ruamba (Cenderawasih University)
Rian Efendi (Cenderawasih University)
Elsi Sirampun (Cenderawasih University)
Natalia M. I. Weya (Cenderawasih University)



Article Info

Publish Date
08 Jun 2026

Abstract

Integral calculus requires students to coordinate graphical, symbolic, and verbal representations rather than rely only on procedural manipulation. However, many students experience cognitive difficulty when converting graphical information, such as shaded regions or curves, into formal integral notation. This study synthesizes empirical evidence on cognitive barriers in the graphical-to-symbolic transition of integral concepts through a Systematic Literature Review (SLR). The review followed PRISMA 2020 guidance and examined empirical journal articles and conference proceedings published from 2016 to 2025 at the university or pre-university transition level. Records were searched in Google Scholar, Garuda, ERIC, and ScienceDirect; after screening and eligibility assessment, eleven studies were included. The selected studies were analyzed through descriptive synthesis and thematic coding to identify literature distribution, theoretical tendencies, and recurring barrier types. The synthesis indicates that representation-oriented and cognitive frameworks, including Duval's Semiotic Register Theory, APOS theory, mental models, and accumulation perspectives, are frequently used to interpret students' difficulties. Three central barriers were identified: (1) visual attribute disorientation, in which students misread visually salient features such as intercepts as integration limits; (2) cognitive conflict in signed area, in which students struggle to reconcile positive area images with negative symbolic accumulation; and (3) multicurve decomposition barriers, in which students have difficulty determining boundaries, intersections, and upper-lower function relationships. These findings suggest that graphical-to-symbolic transition is not merely a procedural issue but a representational coordination challenge. The review recommends barrier-specific learning designs that combine graphical tasks, dynamic visualization, accumulation-based reasoning, and structured error reflection.

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Journal Info

Abbrev

prismasains

Publisher

Subject

Biochemistry, Genetics & Molecular Biology Earth & Planetary Sciences Education Electrical & Electronics Engineering Energy Engineering Environmental Science Mathematics Physics Other

Description

J-PS (Prisma Sains: Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram) was published by the Faculty of Science, Engineering, and Applied Science Universitas Pendidikan Mandalika. J-PS containing scientific articles in the form of research and ...