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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
Elsi Sirampun
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 TERHADAP PEMAHAMAN PESERTA DIDIK PADA MATERI PENYAJIAN DATA DALAM BENTUK DIAGRAM Gabriela Hariati Darin; Raoda Ismail; Elsi Sirampun; Bettisari Napitupulu; Pitriana Tandililing
Journal of Research in Science and Mathematics Education Vol. 5 No. 2 (2026): Current Issue - In Progress
Publisher : EDUPEDIA PUBLISHER

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56855/jrsme.v5i2.2186

Abstract

Purpose: Conceptual understanding is fundamental to mathematics learning because it enables students to interpret and apply mathematical concepts meaningfully. In learning data presentation, students are expected to construct and interpret statistical diagrams. However, preliminary observations at YPK Hedam Abepura Junior High School revealed that many students experienced difficulties in these tasks, while teacher-centered instruction limited active participation. This study explored the implementation of the Jigsaw cooperative learning model and its contribution to students’ conceptual understanding of data presentation in diagram form. Methodology: A descriptive qualitative design was employed involving one mathematics teacher and 23 seventh-grade students. Data were collected through classroom observations, interviews, individual tests, and documentation. Trustworthiness was established through data source and method triangulation, and data were analyzed using the interactive model of Miles, Huberman, and Saldaña. Findings: The findings indicate that the Jigsaw cooperative learning model was implemented systematically in accordance with its instructional procedures. The use of home and expert groups promoted active participation, collaboration, responsibility, self-confidence, curiosity, and careful data interpretation. Individual test results showed that 18 of the 23 students achieved the minimum mastery criterion, whereas five students encountered difficulties, particularly in constructing pie charts. Significance: Overall, the findings suggest that the Jigsaw cooperative learning model enhances students’ conceptual understanding by facilitating collaborative knowledge construction through peer discussion and shared learning responsibilities. Nevertheless, because the study involved a single class and was conducted over only two instructional sessions, the findings should be interpreted cautiously when considering their transferability to other educational contexts.
Penerepan Model Pembelajaran Kooperatif Tipe Student Teams Achievement Division (STAD) pada Materi Kekongruenan Bangun Datar Halimatussa’diah; Raoda Ismail; Pitriana Tandililing; Dewi Kristika Findia Ning Tyas; Elsi Sirampun
Journal of Research in Science and Mathematics Education Vol. 5 No. 2 (2026): Current Issue - In Progress
Publisher : EDUPEDIA PUBLISHER

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56855/jrsme.v5i2.2189

Abstract

Purpose: This study aimed to describe the implementation of the Student Teams Achievement Division (STAD) cooperative learning model, students’ responses and engagement during the learning process, and students’ conceptual understanding of plane figure congruence. Methodology: This study employed a descriptive method with a qualitative approach and was conducted in Grade 7 of Muhammadiyah Junior High School Jayapura during the 2025/2026 academic year, involving 30 students as research participants. Data were collected through observations, interviews, tests, and documentation. Data validity was ensured through source triangulation and technique triangulation, while data analysis was carried out using the Miles and Huberman interactive model, which consists of data reduction, data display, and conclusion drawing. Findings: The findings revealed that the STAD cooperative learning model was implemented in accordance with the planned instructional stages: class presentation, team study, quizzes, individual improvement scores, and team recognition. During the learning process, students demonstrated positive responses through active participation in group discussions, confidence in expressing their opinions, and collaboration in completing assigned tasks. Significance: Interactions among students within heterogeneous groups provided opportunities for peer support in understanding the concept of plane figure congruence. Students’ conceptual understanding was reflected in their ability to identify corresponding elements of congruent figures, explain concepts in their own words, and solve problems related to the material being studied. Overall, the findings indicate that STAD supports active student engagement and the development of conceptual understanding of plane figure congruence.
Co-Authors Bettisari Napitupulu Dewi Kristika Findia Ning Tyas Gabriela Hariati Darin Halimatussa’diah Ismail, Raoda Marthinus Yohanes Ruamba Natalia M. I. Weya Pitriana Tandililing Rian Efendi