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All Journal Prisma Sains: Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram Journal of Research in Science and Mathematics Education
Marthinus Yohanes Ruamba
Cenderawasih University
Biochemistry, Genetics & Molecular Biology Chemistry Earth & Planetary Sciences Education Electrical & Electronics Engineering Energy Engineering Environmental Science Mathematics Physics Other

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Cognitive Barriers in the Transition from Graphical to Symbolic Representation of Integral Concepts: A Systematic Literature Review Marthinus Yohanes Ruamba; Rian Efendi; Elsi Sirampun; Natalia M. I. Weya
Prisma Sains : Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram Vol. 14 No. 3: July 2026
Publisher : Universitas Pendidikan Mandalika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33394/j-ps.v14i3.20660

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.
Penerapan Model Pembelajaran Kooperatif Tipe Jigsaw pada Materi Hubungan Antar Sudut di Kelas VII SMP Pricilia Claudia Ardani; Raoda Ismail; Marthinus Yohanes Ruamba; Mayor M. H Manurung; Rina Ananta Sumawardani Sitepu
Journal of Research in Science and Mathematics Education Vol. 5 No. 2 (2026): August
Publisher : EDUPEDIA PUBLISHER

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56855/jrsme.v5i2.2177

Abstract

Purpose: Angle relationships remain a challenging topic in junior high school mathematics, as many students struggle to understand abstract geometric concepts through conventional, teacher-centered instruction. This study aims to describe the implementation of the Jigsaw cooperative learning model in teaching angle relationships to seventh-grade students, examining instructional implementation, student attitudes, and conceptual understanding throughout the learning process. Methodology: A descriptive qualitative approach was employed, involving 28 seventh-grade junior high school students in Jayapura, Papua, Indonesia, with data collected through observation, interviews, individual tests, and documentation, then analyzed using data reduction, data display, and conclusion drawing. Findings: Findings show that the Jigsaw cooperative learning model was implemented very effectively, with students actively engaging in expert-group and home-group discussions to exchange ideas and complete collaborative tasks. Students demonstrated good levels of cooperation, responsibility, curiosity, accuracy, and self-confidence, while most achieved very good to good understanding of angle relationships, supported by peer teaching, multiple representations, and meaningful social interaction consistent with constructivist learning theory. Significance: These results indicate that the Jigsaw cooperative learning model effectively enhances student engagement, positive attitudes, and conceptual understanding in mathematics learning, offering teachers a practical, collaborative instructional alternative for teaching geometry topics such as angle relationships in junior high school classrooms.
Co-Authors Elsi Sirampun Ismail, Raoda Mayor M. H Manurung Natalia M. I. Weya Pricilia Claudia Ardani Rian Efendi Rina Ananta Sumawardani Sitepu