Analyzing conceptual and procedural errors in solving routine problems on gradients and straight-line equation among prospective mathematics teachers

DOI: https://doi.org/10.34007/jdm.v6i2.2722
David Pratama(1), Nur Azizah(2),


(1) Universitas Singaperbangsa Karawang, Karawang, West Java, Indonesia, 41331
(2) Universitas Singaperbangsa Karawang, Karawang, West Java, Indonesia, 41331

Abstract


This study examines the types of errors made by prospective mathematics teachers in solving routine problems involving gradients and linear equations, which are fundamental to Analytic Geometry. Employing a qualitative descriptive methodology, the research involved 35 mathematics education students who completed a semi-structured written test designed to assess both conceptual comprehension and procedural proficiency. Eleven responses containing incomplete or incorrect solutions were purposively selected for detailed analysis. Data were analyzed using Miles and Huberman’s interactive model, encompassing stages of data reduction, presentation, and conclusion derivation. Errors were systematically categorized into conceptual, procedural, and other types, with further refinement into 18 specific misconception subtypes. The findings revealed persistent misconceptions in gradient interpretation, improper application of linear equation forms, and frequent procedural errors in algebraic simplification and negative sign operations. Several students exhibited overlapping error types, indicating a strong correlation between conceptual gaps and procedural breakdowns. These results emphasize the significance of designing instructional interventions that simultaneously enhance conceptual and procedural proficiency.

Keywords


Analytic geometry; conceptual and procedural errors; error analysis; mathematics education; prospective mathematics teacher

Full Text:

PDF
DOI: https://doi.org/10.34007/jdm.v6i2.2722

References


Busrah, Z., & Buhaerah. (2021). Geometri analitik bidang. (A. Wahab & Gusniwati, Eds.). IAIN Parepare Nusantara Press.

Dahlia, D., Rizal, M., & Baharuddin, B. (2024). Analisis kesalahan siswa dalam menyelesaikan soal ujian akhir semester matematika kelas VIII C SMP Negeri 9 Palu tahun pelajaran 2022/2023. Jurnal Kajian Riset Multisiplin, 8(5), 161–170. https://sejurnal.com/pub/index.php/jkrm/article/view/1567/1812

Fadilah, R., & Bernard, M. (2021). Analisis kesalahan siswa dalam menyelesaikan masalah matematika kontekstual materi kekongruenan dan kesebangunan. Jurnal Pendidikan Matematika Inovatif (JPMI), 4(4), 817–826. https://doi.org/10.22460/jpmi.v4i4.817-826

Halidin. (2022). Geometri analitik bidang dan ruang. Eureka Media Aksara.

Harahap, R. (2022). Analisis kemampuan pemecahan masalah soal rutin dan non-rutin pada mata kuliah kapita selekta matematika sekolah. Edukatif: Jurnal Ilmu Pendidikan, 4(3), 3470–3478. https://doi.org/10.31004/edukatif.v4i3.2602

Ismail, I., & Ismail, A. M. (2024). Analisis kesulitan belajar matematika di Mts Hidayatul Fallah dalam persamaan garis lurus. Al Bannani: Journal of Islamic Education Guidance and Counseling, 1(1), 66–73. https://ejournal.staikhbadruzzaman.ac.id/index.php/alBannani/article/view/34/31

Lingga, D. R. M., Rustam, R., & Siregar, L. N. K. (2024). Peran guru dalam prestasi belajar matematika siswa kelas IV MIN 1 Kota Sidikalang Kabupaten Dairi. Lencana: Jurnal Inovasi Ilmu Pendidikan, 2(2). https://doi.org/10.55606/lencana.v2i2.3554

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). SAGE Publications.

Novitasari, Z. D., & Fitriani, N. (2021). Analisis kesalahan siswa pada persamaan garis lurus berdasarkan tahapan kastolan. Jurnal Pendidikan Matematika Inovatif, 4(4), 957–964. https://journal.ikipsiliwangi.ac.id/index.php/jpmi/article/view/7374

Polya, G. (2014). How to solve it: A new aspect of mathematical method. Princeton University Press.

Rezkia, P., Baharuddin, & Hadjar, I. (2025). Analisis kesalahan siswa dalam menyelesaikan soal penjumlahan dan pengurangan bilangan bulat di kelas VII C SMP Negeri 6 Palu. Jurnal Elektronik Pendidikan Matematika Tadulako (JEPMT), 12. https://jurnalfkipuntad.com/index.php/jpmt/article/view/3474/2383

Saygili, S. (2017). Examining the problem solving skills and the strategies used by high school students in solving non-routine problems. E-International Journal of Educational Research, 8(2), 91–114. https://dergipark.org.tr/en/download/article-file/338828

Sehole, L., Sekao, D., & Mokotjo, L. (2023). Mathematics conceptual errors in the learning of a linear function- a case of a Technical and Vocational Education and Training college in South Africa. International Journal of Teaching and Learning, 18(1), 81–97. https://journals.assaf.org.za/index.php/ijtl/article/view/17173/20561

Setyaningsih, V. P., & Firmansyah, D. (2022). Analisis kemampuan pemecahan masalah matematis siswa SMP pada materi persamaan garis lurus. PRISMA, 11(1), 10–20. https://doi.org/10.35194/jp.v11i1.2048

Stovner, R. B., & Klette, K. (2022). Teacher feedback on procedural skills, conceptual understanding, and mathematical practices: A video study in lower secondary mathematics classrooms. Teaching and Teacher Education, 110, 103593. https://doi.org/10.1016/j.tate.2021.103593

Sudjanta, R. D., Fahri A, M. A., Sasmita, R. F. P., & Abdullayev, R. (2024). Analisis kesalahan siswa SMK dalam menyelesaikan soal aljabar berbasis teori Kastolan. Jurnal Riset Rumpun Matematika dan Ilmu Pengetahuan Alam, 3(1), 129–137. https://doi.org/10.55606/jurrimipa.v3i1.2289

Sukirman, S. (2016). Geometri analitik bidang dan ruang (4th ed.). Universitas Terbuka.

Susilawati, S., Wardono, W., & Waluya, B. (2024). Analisis kesalahan siswa dalam menyelesaikan soal polinomial berdasarkan teori kastolan. In PRISMA, Prosiding Seminar Nasional Matematika (Vol. 7, pp. 578–586). https://proceeding.unnes.ac.id/prisma/article/download/3007/2471

Susilo, D. A., & Hariyani, S. (2019). Geometri analitika datar dan ruang (I). Kanjuruhan Press.

Sehajun, P., & Tambunan, N. (2021). Analisis kesulitan matematika siswa kelas VIII SMP Santo Paulus pada materi persamaan garis lurus. Prosiding Diskusi Panel Nasional Pendidikan Matematika, 7(1), 177–188. https://proceeding.unindra.ac.id/index.php/DPNPMunindra/article/view/5600

Wahyuni, I., & Alfiana, E. (2022). Analisis kemampuan eksplorasi matematis siswa kelas x pada materi fungsi komposisi. Inspiramatika: Jurnal Inovasi Pendidikan Dan Pembelajaran Matematika, 8(1), 39–47. https://e-jurnal.unisda.ac.id/index.php/Inspiramatika/article/view/3074/2148

Wati, R., & Darmawan, P. (2024). Analisis kesalahan siswa dalam menyelesaikan soal persamaan kuadrat berdasarkan klasifikasi kastolan. Populer: Jurnal Penelitian Mahasiswa, 3(4), 56–72. https://doi.org/10.58192/populer.v3i4.2713

Yunita, A. (2017). Geometri analitik (Y. Sri, Ed.). Rumahkayu Pustaka Utama.

Yuwono, M. R., & Widyawati, S. (2022). An analysis of the difficulty of prospective mathematics teachers on algebraic materials. Al-Jabar: Jurnal Pendidikan Matematika, 13(1), 67–79. https://doi.org/10.24042/ajpm.v13i1.11378




DOI: https://doi.org/10.34007/jdm.v6i2.2722

Refbacks

  • There are currently no refbacks.


Journal of Didactic Mathematics

Mahesa Research Center