Analysis of the Understanding of Straight-Line Equation Concepts Based on Action, Process, Object, Schema Theory
DOI:
https://doi.org/10.59211/mjpjetl.v4i2.478Keywords:
APOS; straight-line; Conceptual understanding.Abstract
Understanding the concept of straight-line equations is essential as a prerequisite for advanced mathematics. Observations at SMP Negeri 5 Jayapura indicated that eighth-grade students still encountered difficulties, particularly in determining the gradients of parallel and perpendicular lines. This study aimed to describe students' conceptual understanding profiles of straight-line equations based on APOS Theory (Action, Process, Object, and Schema) across high-, medium-, and low-ability categories. The research employed a descriptive qualitative method. Subjects were purposively selected from 27 students based on their MID scores, categorized as high (≥90), medium (80–89), and low (<80), with one student representing each category. The instruments consisted of two essay-type test questions incorporating Papuan cultural contexts and a semi-structured interview guide. The findings revealed that the high-ability student achieved all four APOS stages, the medium-ability student achieved the Action, Process, and Object stages, whereas the low-ability student achieved only the Action stage. Although performance across the Action to Object stages varied, the collective failure of all three subjects in graphical representation indicated cognitive obstacles during the encapsulation process at the Schema stage. These findings recommend the implementation of the APOS-based ACE cycle and special attention to graphical aspects in learning straight-line equations.
Downloads
References
[1] NCTM, “Principles and standards for school mathematics,” National Academies Press, Reston, VA, Jan. 2000. doi: 10.17226/9870.
[2] F. Rihi and L. M. Saija, “Analisis kemampuan pemahaman matematis peserta didik smp pada materi persamaan garis lurus ditinjau berdasarkan gender,” Jurnal Pendidikan Matematika dan Sains, vol. 9, no. 2, pp. 69–76, 2021, doi: 10.21831/jpms.v9i1.44944.
[3] V. P. Setyaningsih and D. Firmansyah, “Analisis kemampuan pemecahan masalah matematis siswa smp pada materi persamaan garis lurus,” PRISMA, vol. 11, no. 1, p. 10, Jun. 2022, doi: 10.35194/jp.v11i1.2048.
[4] Y. H. Bohalima, “Analisis Kemampuan Pemahaman Konsep Siswa Pada Materi Persamaan Garis Lurus,” Educativo: Jurnal Pendidikan, vol. 1, no. 1, pp. 22–28, Apr. 2022, doi: 10.56248/educativo.v1i1.4.
[5] R. N. Laili, A. D. Utami, and N. Rohman, “Pelevelan Model Mental Siswa Dalam Memahami Konsep Persamaan Garis Lurus Di Era Pandemi COVID-19,” Kognitif: Jurnal Riset HOTS Pendidikan Matematika, vol. 1, no. 2, pp. 89–103, Dec. 2021, doi: 10.51574/kognitif.v1i2.86.
[6] A. S. Lestari, U. Aripin, and H. Hendriana, “Identifikasi kesalahan siswa smp dalam menyelesaikan soal kemampuan penalaran matematik pada materi bangun ruang sisi datar dengan analisis kesalahan newman,” JURING (Journal for Research in Mathematics Learning), vol. 1, no. 4, pp. 493–504, 2018, doi: 10.24014/juring.v1i1.4912.
[7] G. A. Manihuruk and K. N. S. Effendi, “Kemampuan pemahaman konsep matematika siswa smp kelas viii pada materi persamaan garis lurus,” Laplace : Jurnal Pendidikan Matematika, vol. 7, no. 2, pp. 424–436, Oct. 2024, doi: 10.31537/laplace.v7i2.2047.
[8] Suswigi and L. S. Zanthy, “Kemampuan pemahaman matematik siswa mts di cimahi pada materi persamaan garis lurus,” Jurnal Cendekia: Jurnal Pendidikan Matematika, vol. 3, no. 1, pp. 40–46, 2019, doi: 10.31004/cendekia.v3i1.77.
[9] E. Dubinsky and M. A. McDonald, Apos: a constructivist theory of learning in undergraduate mathematics education research. Dordrecht: Springer, 2001.
[10] R. Cisilia, L. Ariyanto, and R. D. Setyawati, “Imajiner: Jurnal Matematika dan Pendidikan Matematika Analisis Kemampuan Pemahaman Konsep Matematis dalam Menyelesaikan Soal Hots Materi Persamaan Garis Lurus Ditinjau dari Gaya Belajar Peserta Didik,” vol. 6, no. 1, pp. 1–5, 2024.
[11] R. Priatna, L. Roesdiana, and Hanifah, “Analisis pemahaman konsep matematis ditinjau dari kemandirian belajar siswa materi persamaan garis lurus,” Jurnal Pendidikan Matematika, vol. 7, pp. 62–72, 2023, doi: 10.33087/phi.v7i1.178.
[12] N. Agustina, Darmawijoyo, and N. Aisyah, “Kemampuan pemahaman konsep siswa smp pada materi persamaan garis lurus berbasis apos,” Histogram: Jurnal Pendidikan Matematika, vol. 2, pp. 12–21, 2018, doi: 10.31100/histogram.v2i1.34.
[13] F. F. Kadafuk, K. D. Djong, and I. V. Uskono, “Kemampuan pemahaman konsep pada materi sistem persamaan linear dua variabel berdasarkan teori apos bagi siswa smp,” ANARGYA: Jurnal Ilmiah Pendidikan Matematika, vol. 3, no. 2, 2020, doi: 10.24176/anargya.v3i2.4901.
[14] R. Cisilia, L. Ariyanto, and R. D. Setyawati, “Analisis kemampuan pemahaman konsep matematis dalam menyelesaikan soal hots materi persamaan garis lurus ditinjau dari gaya belajar peserta didik,” Imajiner: Jurnal Matematika dan Pendidikan Matematika, vol. 6, no. 1, pp. 1–5, 2024, doi: 10.26877/imajiner.v6i1.16826.
[15] Sugiyono, Metode penelitian kuantitatif, kualitatif, dan r&d, Cetakan ke-19. Bandung: Alfabeta, 2013.
[16] J. W. Creswell and J. D. Creswell, Research design: qualitative, quantitative, and mixed methods approaches, 6th ed. Thousand Oaks: SAGE Publications, 2023.
[17] F. Lestari, A. Syaifuddin, and A. H. Wati, “MATH LOCUS: Jurnal Riset dan Inovasi Pendidikan Matematika Analisis Kemampuan Pemahaman Konsep Matematis Siswa SMP Negeri 1 Bandongan pada Materi Persamaan Garis Lurus,” vol. 4, no. 1, pp. 46–56, 2023.
[18] J. W. Creswell and J. D. Creswell, Research design: qualitative, quantitative, and mixed methods approaches, 6th ed. Thousand Oaks: SAGE Publications, 2023.
[19] F. Rihi and L. M. Saija, “Analisis kemampuan pemahaman matematis peserta didik smp pada materi persamaan garis lurus ditinjau berdasarkan gender,” Jurnal Pendidikan Matematika dan Sains, vol. 9, no. 2, pp. 69–76, 2021, doi: 10.21831/jpms.v9i1.44944.
[20] S. Maulina, Muchtadi, and Hartono, “Analisis kesulitan pemahaman konseptual siswa dalam materi aljabar berdasarkan teori apos,” Indo-MathEdu Intellectuals Journal, vol. 6, no. 1, pp. 1337–1353, 2025.
[21] R. L. Yunita, P. Pathuddin, A. Alfisyahra, and R. Lefrida, “Profil penyelesaian soal spldv berdasarkan teori apos ditinjau dari kemampuan matematika siswa,” Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah di Bidang Pendidikan Matematika, vol. 10, no. 1, pp. 124–139, May 2024, doi: 10.29407/jmen.v10i1.22260.
[22] P. Alicia Ozika, E. S. Maruti, and V. Rulviana, “Analisis penyelesaian masalah numerasi matematika berdasarkan teori apos di kelas v sd,” TRILOGI: Jurnal Ilmu Teknologi, Kesehatan, dan Humaniora, vol. 6, no. 1, pp. 63–73, 2025, doi: 10.33650/trilogi.v6i1.10744.
[23] V. P. Setyaningsih and D. Firmansyah, “Analisis Kemampuan Pemecahan masalah matematis siswa smp pada materi persamaan garis lurus,” PRISMA, vol. 11, no. 1, p. 10, Jun. 2022, doi: 10.35194/jp.v11i1.2048.
[24] A. Restianingsih, Y. Yuhana, and N. Anriani, “Kemampuan Pemecahan Masalah Matematis Berdasarkan Teori APOS Ditinjau Dari Self Confidence Siswa (Mathematical Problem Solving Ability Based on APOS Theory in View of Students’ Self Confidence),” Jurnal Pendidikan Matematika, vol. 14, no. 1, pp. 66–79, 2023, doi: 10.36709/jpm.v14i1.43.
[25] A. Firmansyah, J. Sabandar, and M. Bernard, “Analisis kesulitan siswa smp kelas viii dalam menyelesaikan soal pada materi persamaan garis lurus berdasarkan teori newman,” Jurnal Pembelajaran Matematika Inovatif, vol. 6, no. 6, 2023, doi: 10.22460/jpmi.v6i6.19757.
[26] N. Agustina, Darmawijoyo, and N. Aisyah, “Kemampuan pemahaman konsep siswa smp pada materi persamaan garis lurus berbasis apos,” Histogram: Jurnal Pendidikan Matematika, vol. 2, pp. 12–21, 2018, doi: 10.31100/histogram.v2i1.34.
[27] F. F. Kadafuk, K. D. Djong, and I. V. Uskono, “Kemampuan pemahaman konsep pada materi sistem persamaan linear dua variabel berdasarkan teori apos bagi siswa smp,” ANARGYA: Jurnal Ilmiah Pendidikan Matematika, vol. 3, no. 2, 2020, doi: 10.24176/anargya.v3i2.4901.
[28] R. Ismail and M. M. H. Manurung, “Analisis kemampuan pemecahan masalah matematika siswa smp yppk teruna mulia kota jayapura,” Jurnal Pendidikan Mandala, vol. 8, no. 1, 2023, doi: 10.58258/jupe.v8i1.4807.
[29] E. Dubinsky and M. A. McDonald, Apos: a constructivist theory of learning in undergraduate mathematics education research. Dordrecht: Springer, 2001.
[30] S. Maulina, Muchtadi, and Hartono, “Analisis kesulitan pemahaman konseptual siswa dalam materi aljabar berdasarkan teori apos,” Indo-MathEdu Intellectuals Journal, vol. 6, no. 1, pp. 1337–1353, 2025.
Downloads
Published
Issue
Section
URN
License
Copyright (c) 2026 Melkisedhek Rudy Selfianus Mofu
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors grant the journal the right of first publication. which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited. Authors are responsible for ensuring that any third-party materials included in their work have proper permissions.
