Cognitive Barriers in the Transition from Graphical to Symbolic Representation of Integral Concepts: A Systematic Literature Review
DOI:
https://doi.org/10.33394/j-ps.v14i3.20660Keywords:
Integral calculus, Cognitive barriers, Multimodal representation, Semiotic transition, Systematic Literature ReviewAbstract
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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