KAJIAN KONSEPTUAL TENTANG LIMIT FUNGSI SEBAGAI FONDASI PEMBELAJARAN KALKULUS

Aferbina Br Barus, Fasya Maharani Umri, Nur Hidayah Aini, Tiur Malasari Siregar

Abstract


This study aims to examine the basic concept of function limits in calculus and analyze their vital role as the main foundation in learning calculus. The research method employed is a literature review, analyzing various sources such as textbooks and scientific journal articles related to limit concepts, student misconceptions, and relevant pedagogical strategies. Data analysis was conducted qualitatively and descriptively to synthesize the relationship between the concept of limits, derivatives, and integrals. The results indicate that the limit is a fundamental concept that explains functional behavior and serves as the formal basis for defining derivatives as rates of change and integrals as area accumulation (Riemann sums). The study concludes that a strong conceptual understanding of limits is essential to avoid the dominance of mechanistic procedures and to help students master advanced calculus concepts systematically. It is suggested that calculus instruction should emphasize visual representation and mathematical interpretation, although this study is limited to a literature approach without empirical field data.

Keywords


Fondasi matematika; kalkulus; konsep limit; pembelajaran matematika

Full Text:

PDF

References


Andiani, D., Rahayu, S. D., & Suwanda, C. (2025). Geogebra-Assisted Teaching Experiment on Students’ Conceptual Change in Multivariable Calculus. Koordinat Jurnal Pembelajaran Matematika dan Sains, 6(2), 125–139. https://doi.org/https://doi.org/10.24239/koordinat.v6i2.181

Azizah, U. N., Sumiaty, E., & Ulfa, N. (2025). Analyzing Epistemological Learning Obstacles on Limit Concept Using AVAE Framework in Prospective Mathematics Teacher. Ar-Riyadhiyyat: Jurnal Pendidikan Matematika, 6(1), 1–10. https://doi.org/https://doi.org/10.47766/arriyadhiyyat.v6i1.6243

Cahyani, A., Rahayu, W., & Hidajat, F. A. (2024). Studi Literatur: Pemilihan Media Pembelajaran Matematika untuk Siswa Sekolah Menengah Atas. Jurnal Riset Pendidikan Matematika Jakarta, 6(1), 70–80. https://doi.org/https://doi.org/10.21009/jrpmj.v6i1.290238

Fernández, C., Moreno, M., & Sánchez-Metamoros, G. (2024). Prospective secondary teachers’ noticing of students’ thinking about the limit concept: pathways of development. ZDM – Mathematics Education, 56, 1137–1151. https://doi.org/10.1007/s11858-024-01573-z

Hajerina, Rochaminah, S., & Suciati, I. (2025). Analyzing Mathematics Education Students’ Misconceptions on Limit Functions: A Case Study at Alkhairaat University. Jurnal Pendidikan MIPA, 26(1), 51–61. http://jurnal.fkip.unila.ac.id/index.php/jpmipa/

Herianto, R., Harahap, M. I., & Amir, A. (2025). Studi Literatur: Perkembangan Penelitian Graf Plana dan Aplikasinya dalam Matematika dan Komputasi. SIGMA : JURNAL PENDIDIKAN MATEMATIKA, 17(2), 884–893. https://journal.unismuh.ac.id/index.php/sigma%0ASTUDI

Hughes-Hallett, D., Gleason, A. M., & McCallum, W. G. (2020). Calculus Single & Multivariable. Calculus: Single and multivariable. John Wiley & Sons.

Jufri. (2022). Miskonsepsi Mahasiswa STKIP Rokania pada Materi Limit Fungsi. Jurnal Cendekia: Jurnal Pendidikan Matematika, 06(01), 414–422.

Julaihi, N. H. (2025). Exploring Common Errors, Challenges, and Strategies of Solving Limits in Calculus. International Journal of Service Management and Sustainability (IJSMSust), 10(1), 19–38. https://doi.org/10.24191/ijsms.v10i1.24214

Kurudirek, A., Karin, B., Sarhang, D., & Machisi, E. (2025). Challenges faced by first-year university students in learning calculus. Contemporary Mathematics and Science Education, 6(2), 1–14.

Laja, Y. P. W. (2022). Analisis Kesulitan Mahasiswa Pendidikan Matematika dalam Menyelesaikan Soal Limit Trigonometri. Mosharafa: Jurnal Pendidikan Matematika, 11(1), 37–48. http://journal.institutpendidikan.ac.id/index.php/mosharafa%0AI.

Mishra, A. K. (2023). An Introduction to Calculus: Fundamental Concepts and Apllications. International Journal of Creative Research Thoughts (IJCRT), 11(2), 536–541. www.ijcrt.org

Neldiana, R., & Harisman, Y. (2025). Peranan Integral dan Diferensial Terhadap Kalkulus. Jurnal Cendekia: Jurnal Pendidikan Matematika, 09(01), 273–283. https://doi.org/https://doi.org/10.31004/cendekia.v9i1.3853

Nurdin, Assagaf, S. F., & Arwadi, F. (2019). Students’ Understanding on Formal Definition of Limit. Journal of Physics: Conference Series, 1–4. https://doi.org/10.1088/1742-6596/1752/1/012082

Nurpadila, Meridina, R., Sinaga, V. R., & Simanullang, M. C. (2025). Analisis Kemampuan Penalaran Mahasiswa dalam Memahami Konsep Limit Fungsi. Jurnal Pendidikan MIPA, 15(1), 339–348. https://doi.org/https://doi.org/10.37630/jpm.v15i1.2606 Analisis

Prihandhika, A., & Sopiany, H. N. (2025). Procedural Dominance in Students’ Reasoning on the Limit Definition: Insights from a Ways of Thinking Framework. Journal of Mathematics Instruction, Social Research and Opinion, 4(4), 1313–1324. https://doi.org/https://doi.org/10.58421/misro.v4i4.776

Saifudin, M. N., Cahyaningrum, Z. F., Habiba, D. H. I., Ulayya, S. D., & Susilo, B. E. (2024). Studi Literatur: Tantangan dan Peluang: Inovasi Pembelajaran Matematika di Era Revolusi Industri 4.0. PRISMA, Prosiding Seminar Nasional Matematika, 7, 906–913. https://proceeding.unnes.ac.id/prisma

Septiani, R. D., & Harisman, Y. (2025). Studi Pemahaman Kalkulus: Uji Kemampuan Mahasiswa Pendidikan Matematika dalam Perhitungan Integral dan Diferensial. JRPMS (Jurnal Riset Pembelajaran Matematika Sekolah), 9(1), 28–42.

Simanjuntak, J., Simangunsong, M. I., Tiofanny, & Naibaho, T. (2021). Perkembangan Matematika Dan Pendidikan Matematika Di Indonesia Berdasarkan Filosofi. SEPREN: Journal of Mathematics Education and Applied, 02(02), 32–39.

Simin, T, A. Y., & Bistari. (2022). Literasi Matematis Siswa Sekolah Menengah Atas dari Struktur Kognitif pada Konsep Limit Fungsi. Jurnal Cendekia : Jurnal Pendidikan Matematika, 06(01), 48–57.

Sinaga, B., Sitorus, J., & Situmeang, T. (2023). The Influence of Students’ Problem-Solving Understanding and Results of Students’ Mathematics Learning. Frontiers in Education, 8(1088556), 1–9. https://doi.org/10.3389/feduc.2023.1088556

Solijonovna, K. H. (2024). The Concept of Limit, Limit of a Function, and Continuity of a Function. Western European Journal of Modern Experiments and Scientific Methods, 2(5), 35–37. https://westerneuropeanstudies.com/index.php/1

Sulastri, R. (2023). Studi didactic transposition: Eksplorasi knowledge to be taught pada limit fungsi. Journal of Didactic Mathematics, 4(2), 106–117. https://doi.org/10.34007/jdm.v4i2.1903

Susiswo, Parameswari, P., Putri, O. R. U., Lanya, H., Utami, A. D., & Mrniasih, T. R. (2023). The Growth of Students’ Function Limit Concepts Understanding in Solving Controversial Problems Based on Pirie Kieren’s Theory. JTAM (Jurnal Teori dan Aplikasi Matematika), 7(4), 1204–1220. http://journal.ummat.ac.id/index.php/jtam

Suwanto, Sagala, Y. N., Syahputri, A., Silalahi, H. F., Limbong, I. R. U., Harianja, S. S., & Mukhtar. (2025). Studi Analitis Miskonsepsi dalam Buku Ajar Kalkulus Peubah Banyak Karya Sumadji serta Strategi Pedagogis untuk Meningkatkan Pemahaman Konseptual Mahasiswa. Pendas : Jurnal Ilmiah Pendidikan Dasar, 10(05), 1–19.

Tanjung, J. Y., Simanjuntak, R. A. P., Manullang, J. C., Turnip, L., & Simanullang, M. C. (2025). Analisis Kesalahan Mahasiswa dalam Menyelesaikan Soal Limit Fungsi Berdasarkan Teori Kastolan. Mandalika Mathematics and Education Journal, 5(2), 391–400. https://doi.org/http://dx.doi.org/10.29303/jm.v3i1.9014

Usman, Aiyub, & Hasbi, M. (2025). Students’ conceptual understanding of limit of functions reviewed from mathematical beliefs. Jurnal Elemen, 11(3), 515–532. https://doi.org/https:/doi.org/10.29408/jel.v11i3.29144

Wijaya, Y. S., Puspaningtyas, N. D., & Dewi, P. S. (2024). Analisis Kemampuan Pemahaman Konsep Matematika pada Mahasiswa dalam Menyelesaikan Soal Materi Limit Fungsi. Prismatika: Jurnal Pendidikan dan Riset Matematika, 6(2), 260–274. https://doi.org/https://doi.org/10.33503/prismatika.v6i2.3806




DOI: http://dx.doi.org/10.33087/phi.v10i1.627

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

PHI: Jurnal Pendidikan Matematika
published by Program Studi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan Universitas Batanghari
Adress: FKIP Universitas Batanghari, Jl.Slamet Ryadi, Broni-Jambi, Kec.Telanaipura, Kodepos: 36122, email: phi.unbari@gmail.com

Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.