Analyzing Students’ Thinking Processes in Solving Exponential Problems Based on APOS Theory: A Qualitative Study at SMA Negeri 7 Tanjung Jabung Timur

Authors

  • Liawati Universitas Jambi, Jl. Jambi-Muara Bulian KM 15, Kab. Muaro Jambi, Indonesia
  • Nizlel Huda
  • Jefri Marzal

DOI:

https://doi.org/10.33541/edumatsains.v10i4.8076

Keywords:

The APOS Theory, Student Thinking Processes, Exponents, Mathematics Education

Abstract

This study aims to describe students’ thinking processes in solving exponential problems based on the APOS theory (action, process, object, and schema). This research employed a descriptive qualitative approach conducted in class X Phase E3 at SMA Negeri 7 Tanjung Jabung Timur. The subjects consisted of three students selected through purposive sampling, representing high, moderate, and low ability levels. Data were collected using written tests in the form of open-ended questions and semi-structured interviews to explore students’ thinking processes in depth. The results indicate that students with high ability were able to achieve all stages of APOS, demonstrating a comprehensive understanding and integration of concepts. Students with moderate ability reached the action and process stages adequately but showed limited understanding at the object and schema stages. Meanwhile, students with low ability were only able to perform at the action and partial process stages, relying on procedural steps without deep conceptual understanding. These findings highlight differences in students’ conceptual construction across ability levels.

References

Anderha, R. R., & Maskar, S. (2021). Pengaruh Kemampuan Numerasi Dalam menyelesaikan Masalah Matematika Terhadap Prestasi Belajar Mahasiswa Pendidikan Matematika. Jurnal Ilmiah Matematika Realistik (JI-MR, 2(1).

Antasari, M., Hanifah, H., Susanta, A., & Andriani, I. (2023). PENERAPAN PENDEKATAN REALISTIC MATHEMATICS EDUCATION MELALUI MODEL APOS BERBANTUAN GEOGEBRA UNTUK MENINGKATKAN HASIL BELAJAR MATEMATIKA. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(2), 2468. https://doi.org/10.24127/ajpm.v12i2.6928

Borji, V., Martínez-Planell, R., & Trigueros, M. (2024). Students’ Understanding of Riemann Sums and Double Integrals: The Case of Task Design in APOS Theory. International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-024-00250-6

Creswell, J. W., & David Creswell, J. (2018). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches.

EK Ajeng Rahmi Pinahayu. (2015). Problematika Pembelajaran Matematika Pada Pokok Bahasan Eksponen dan Alternatif Pemecahannya. Jurnal Formatif , 5(3), 182–191.

Fauziyah, N., & Wahyunita, E. N. (2025). Constructing the Concept of Geometric Transformation through APOS Theory: A Perspective on Learning Readiness. Edumatica: Jurnal Pendidikan …, 15(2). https://online-journal.unja.ac.id/edumatica/article/view/43166

Febrila, L. G., Hanifah, H., Sumardi, H., & Utari, T. (2023). IMPROVE STUDENT LEARNING OUTCOMES USING STUDENT WORKSHEETS BASED ON THE APOS MODEL ASSISTED BY GEOGEBRA. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(1), 1322. https://doi.org/10.24127/ajpm.v12i1.6876

Fitra, G. &, Gunawan, M. S., Fitra, D., Keguruan, F., Pendidikan, I., Adiwangsa, U., Jalan, J., Muslim, S., 24, R. T., Thehok, J., Selatan, K., & Jambi, I. (2021). Kesulitan Siswa dalam Mengerjakan Soal-soal Eksponen dan Logaritma. Mosharafa: Jurnal Pendidikan Matematika , 10(2). http://journal.institutpendidikan.ac.id/index.php/mosharafa

Herdian, F., Widada, W., Herawaty, D., Kandang, J. W. S., & Bengkulu, L. (2019). Level Berpikir Siswa dalam Memahami Konsep dan Prinsip Bangun Ruang dengan Pendekatan Pembelajaran Etnomatematika Beradasarkan Teori APOS. In JPMR (Vol. 04, Number 02). https://ejournal.unib.ac.id/index.php/jpmr

Khamidah, K. S. (2016). Proses Berpikir Matematis Siswa dalam Menyelesaikan Masalah Matematika Ditinjau dari Tipe Kepribadian Keirsey. Jurnal Pendidikan Matematika, 7(2), 231–248.

Longe, I. O., & Maharaj, A. (2023). Applying APOS Theory to Enhance Algebraic Logic Skills: Comparing Traditional Teaching and Computer-Assisted Instruction. Indonesian Journal of Science and Mathematics Education, 6(3), 378. https://doi.org/10.24042/ijsme.v6i3.16298

Muhammad Sabirin. (2014). Representasi Dalam Pembelajaran Matematika. JPM IAIN Antasari, 01(2), 33–44.

Mulyani, S., Rahman, A., Fajar Arwadi, dan, Kunci, K., Matematika, S., Siswa, K., Menyelesaikan Soal, K., & Belajar, G. (2022). Analisis Kesulitan Siswa dalam Menyelesaikan Soal Eksponen Ditinjau dari Gaya Belajar Siswa. In Issues in Mathematics Education (Vol. 6, Number 2). http://www.ojs.unm.ac.id/imed

Nurajijah, M., Khaerunnisa, E., & Hadi FS, C. A. (2023). Kemampuan Pemahaman Konsep Matematis Siswa Berdasarkan Teori Apos Pada Materi Program Linear. Jurnal Educatio FKIP UNMA, 9(2), 785–797. https://doi.org/10.31949/educatio.v9i2.4800

Rahma, A. F., & Khabibah, S. (2022). Analisis Kesalahan Siswa Dalam Menyelesaikan Soal Eksponen. Jurnal Ilmiah Pendidikan Matematika, 11(2).

Robiah Nofikusumawati Peni, N. (2025). Miskonsepsi dalam Pembelajaran Matematika: Tinjauan Literatur Pada Materi Eksponen. Jurnal Pendidikan Matematika, 4, 902–912.

Rosyidi, A. H., & Hasanah, K. (2022). THE CONSTRUCTION PROCESS OF NEW CONCEPT BASED ON APOS THEORY: MALE VS FEMALE IN DIRECT PROPORTION. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 3360. https://doi.org/10.24127/ajpm.v11i4.5706

Soku, F. A., Okyere, G. A., & Awuah, F. K. (2025). APOS Theory-based research in Mathematics Education: A systematic literature review. East African Journal of Education Studies, 8(2), 549–561. https://doi.org/10.37284/eajes.8.2.3070

Tatira, B. (2021). Mathematics Education Students’ Understanding of Binomial Series Expansion Based on the APOS Theory. Eurasia Journal of Mathematics, Science and Technology Education, 17(12), 1–13. https://doi.org/10.29333/EJMSTE/11287

Trigueros, M., Badillo, E., Sánchez-Matamoros, G., & Hernández-Rebollar, L. A. (2024). Contributions to the characterization of the Schema using APOS theory: Graphing with derivative. ZDM - Mathematics Education, 56(6), 1093–1108. https://doi.org/10.1007/s11858-024-01615-6

Umam, K., & Susandi, D. (2022). Critical thinking skills: Error identifications on students’ with APOS theory. International Journal of Evaluation and Research in Education, 11(1), 182–192. https://doi.org/10.11591/ijere.v11i1.21171

Widya Pratama, F. (2022). Tingkat Pemahaman Konsep Siswa pada Materi Pola Bilangan Berdasarkan Teori APOS. Mosharafa: Jurnal Pendidikan Matematika, 11(2). http://journal.institutpendidikan.ac.id/index.php/mosharafa

Winarsih, M., Helti, D., & Mampouw, L. (2019). Profil Pemahaman Himpunan oleh Siswa Berdasarkan Perbedaan Kemampuan Matematika Ditinjau dari Teori APOS. 8(2). http://journal.institutpendidikan.ac.id/index.php/mosharafa

Yarman, Dwina, F., Murni, D., Yerizon, & Hevardani, K. A. (2024a). Analysis of Concept Construction and Student Errors on the Topic of Double Integral Based on APOS Theory. Mathematics Education Journal, 18(3), 367–386. https://doi.org/10.22342/jpm.v18i3.pp367-386

Yarman, Dwina, F., Murni, D., Yerizon, & Hevardani, K. A. (2024b). Analysis of Concept Construction and Student Errors on the Topic of Double Integral Based on APOS Theory. Mathematics Education Journal, 18(3), 367–386. https://doi.org/10.22342/jpm.v18i3.pp367-386

Yuliana, D., & Ratu, N. (2018). Deskripsi Kemampuan Pemahaman Konsep Eksponen Berbasis Teori Apos pada Siswa SMA Theresiana Salatiga. Maju, 5(1), 51–65. https://repository.uksw.edu//handle/123456789/16792

Downloads

Published

2026-04-30

How to Cite

Liawati, Nizlel Huda, & Jefri Marzal. (2026). Analyzing Students’ Thinking Processes in Solving Exponential Problems Based on APOS Theory: A Qualitative Study at SMA Negeri 7 Tanjung Jabung Timur. EduMatSains : Jurnal Pendidikan, Matematika Dan Sains, 10(4), 69–81. https://doi.org/10.33541/edumatsains.v10i4.8076

Issue

Section

Articles