Dampak Pemahaman Konsep Perkalian Bilangan Bulat pada Peserta Didik

Authors

  • Mohamad Ikbal Universitas Islam Negeri Datokarama Palu
  • Nursupiamin Nursupiamin Universitas Islam Negeri Datokarama Palu
  • Yulia Yulia Universitas Islam Negeri Datokarama Palu

DOI:

https://doi.org/10.31539/7m3hms43

Keywords:

conceptual understanding; integers; multiplication; misconception; mathematical representation; pembelajaran matematika

Abstract

This study aims to describe the level of conceptual understanding of integer multiplication among students at MTs Nida’ul Khairaat Pombewe and to analyze its impact on their ability to solve mathematical problems. The research employed a descriptive qualitative approach using diagnostic tests, semi-structured interviews, observations, and documentation as data collection techniques. A total of 31 students participated in a test measuring four indicators of conceptual understanding: classification, concept connection, algorithm, and representation. The results showed that 80% of students were in the low understanding category, 15% in the moderate category, and only 5% in the high category. In-depth analysis of three representative subjects revealed that students in the high category demonstrated strong relational understanding, those in the moderate category showed partial understanding, while students in the low category experienced fundamental misconceptions, particularly regarding sign rules and mathematical representations. The findings also indicated that representation—especially visual and contextual—was the weakest aspect for most students. Interviews confirmed that the teacher’s teaching methods, particularly the pace of explanation and lack of repetition, significantly influenced conceptual understanding. This study concludes that strengthening conceptual understanding should be carried out through more concrete, gradual, and representation-based learning to prevent misconceptions and improve students’ ability to solve integer multiplication problems.

 

Keywords: Conceptual Understanding; Integers; Multiplication; Misconception; Mathematical Representation; Mathematics Learning

References

Alqawas, M. A., & Alhadad, S. Y. (2024). A Proposed Model for Balancing between Conceptual and Procedural Knowledge when Teaching Mathematics. The Educational Journal, 152. https://doi.org/10.34120/joe.v38i152.253

Amalia, P., & Putri, J. H. (2025). Analisis Miskonsepsi dalam Penyelesaian Soal Cerita Matematika pada Materi Bilangan Bulat di SDN 060907. JagoMIPA: Jurnal Pendidikan Matematika Dan IPA, 5(3), 1094–1103. https://doi.org/10.53299/jagomipa.v5i3.2504

Barumbun, M., & Kharisma, D. (2022). Procedural Knowledge or Conceptual Knowledge? Developing the So-Called Proceptual Knowledge in Mathematics Learning. Beta: Jurnal Tadris Matematika, 15(2), 167–180. https://doi.org/10.20414/betajtm.v15i2.472

Buyung. (2021). Analisis Profil Kemampuan Pemahaman Konsep Matematis Siswa pada Materi Operasi Bilangan Bulat Siswa SMP Kelas VII. MES: Journal of Mathematics Education and Science, 7(1), 29–34. https://doi.org/10.30743/mes.v7i1.441

Cahyaningrum, I. Y., Fuady, A., & Faradiba, S. S. (2023). Karakterisasi Representasi Matematis Visual dan Simbolik Siswa Kelas IX pada Materi Transformasi. Jurnal Cendekia: Jurnal Pendidikan Matematika, 07(3), 2646–2659. https://doi.org/10.31004/cendekia.v7i1.1944

Cetin, H. (2019). Explaining the Concept and Operations of Integer in Primary School Mathematics Teaching : Opposite Model Sample. Universal Journal of Educational Research, 7(2), 365–370. https://doi.org/10.13189/ujer.2019.070208

Decaro, M. S. (2016). Inducing Mental Set Constrains Procedural Flexibility and Conceptual Understanding in Mathematics. Memory & Cognition, 44, 1138–1148. https://doi.org/10.3758/s13421-016-0614-y

Dwi, D. F., & Audina, R. (2021). Analisis Faktor Penyebab Kesulitan Belajar Matematika Kelas IV Sekolah Dasar Negeri. Cybernetics: Journal Educational Research and Social Studies, 2(3), 94–106.

Febriyanto, B., Haryanti, Y. D., & Komalasari, O. (2018). Peningkatan Pemahaman Konsep Matematis Melalui Penggunaan Media Kantong Bergambar pada Materi Perkalian Bilangan di Kelas II Sekolah Dasar. Jurnal Cakrawala Pendas, 4(2), 32–44. https://doi.org/10.31949/jcp.v4i2.1073

Galeos, A. W. J., Magno, S. M., Galeos, W. S., & Apdian, F. B. (2024). The Impact of the Diagnostic Teaching Approach on Students ’ Conceptual Understanding , Misconceptions , and Performance in Mathematics. International Journal of Science and Management Studies (IJSMS), 7(3), 258–264. https://doi.org/10.51386/25815946/ijsms-v7i3p115

Gelling, L. (2015). Qualitative Research. Nursing Standard, 29(30), 43–47. https://doi.org/10.7748/ns.29.30.43.e9749

Harun, N. A. J., Cuevas, K. G. A., Asakil, O. I., Alviar, J. V, & Solon, L. J. V. (2023). Assessing Students ’ Mastery and Misconceptions in the Fundamental Operations on Integers. International Journal of Science, Technology, Engineering and Mathematics, 3(3), 36–55. https://doi.org/10.53378/353000

Haydn, T. (2019). Triangulation in History Education Research, and Its Limitations : A View From The UK. History Education Research Journal, 16(1), 35–49. https://doi.org/10.18546/HERJ.16.1.04

Hurrell, D. (2021). Conceptual knowledge OR procedural knowledge or conceptual knowledge AND Procedural Knowledge: Why the conjunction is important to teachers. Australian Journal of Teacher Education, 46(2), 57–71. https://doi.org/10.14221/ajte.2021v46n2.4

Ijuddin, R., Fitriawan, D., & Sayu, S. (2022). Analisis Materi Sulit Dipahami dan Miskonsepsi Mahasiswa dalam Mata Kuliah Kalkulus Integral. Journal Numeracy, 9(1), 27–38. https://doi.org/10.46244/numeracy.v9i1.1682

Kallio, H., Pietil, A., Johnson, M., & Kangasniemi, M. (2016). Systematic Methodological Review : Developing A Framework for A Qualitative Semi-Structured Interview Guide. Journal of Advanced Nursing, 1–12. https://doi.org/10.1111/jan.13031

Kania, N., Saepudin, A., & Gürbüz, F. (2025). Assessing Cognitive Obstacles in Learning Number Concepts : Insights from Preservice Mathematics Teachers. Journal of Research and Advances in Mathematics Education, 10(3), 146 – 166. https://doi.org/10.23917/jramathedu.v10i3.8638

Kumalasari, T., Julia, N. T., Asriati, W. W., & Rambe, I. W. (2025). Pendekatan Problem Solving untuk Meningkatkan Representasi Matematis Siswa SMP Pangeran Antasari. Jurnal Fibonaci : Jurnal Pendidikan Matematika, 6(1), 58–67. https://doi.org/10.24114/jfi.v6i1.65847

Kurudirek, A., Karim, B., Sarhang, D., & Tulqin, S. (2025). Math Misconceptions : Mistakes, Misunderstanding, and Confusion. Educenter: Jurnal Ilmiah Pendidikan, 4(1), 16–25. https://doi.org/10.55904/educenter.v4i1.1322

Lim, W. M. (2025). What Is Qualitative Research ? An Overview and Guidelines. Australasian Marketing Journal, 33(2), 199–229. https://doi.org/10.1177/14413582241264619

Maemuna, S., Kadir, Busnawir, & Salim. (2023). Kesalahan Peserta Didik dalam Menyelesaikan Operasi Hitung Bilangan Bulat pada Garis Bilangan. Jurnal Amal Pendidikan, 4(1), 67–78. https://doi.org/10.36709/japend.v4i1.48

Mainali, B. (2021). Representation in Teaching and Learning Mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 1–21. https://doi.org/10.46328/ijemst.1111

Maizora, S., & Rosjanuardi, R. (2020). Konsepsi Siswa Kelas Tiga Sekolah Dasar Tentang Bilangan Bulat. PYTHAGORAS : Jurnal Matematika Dan Pendidikan Matematika, 15(2), 201–215. https://doi.org/10.21831/pg.v15i2.37645

Mardiani, Sugiatno, Fitriawan, D., Halini, & Yani T, A. (2024). Kemampuan Representasi Matematis Siswa dalam Materi Teorema Pythagoras. Jurnal Pembelajaran Matematika Inovatif, 7(5), 875–890. https://doi.org/10.22460/jpmi.v7i5.23524

Messaoudi, I., & Sakale, S. (2023). Triangulation in Research: Exploring Moroccan EFL University Graduate Students’ Knowledge and Familiarity. International Journal of Linguistics, Literature and Translation, 6(11), 98–105. https://doi.org/10.32996/ijllt.2023.6.11.13

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

Novita, R., Herman, T., Suryadi, D., Dasari, D., Putra, M., & Fitra, R. (2022). Analisis Pengetahuan Konseptual dan Prosedural Mahasiswa Calon Guru Sekolah Dasar pada Bilangan Rasional. JNPM (Jurnal Nasional Pendidikan Matematika), 6(2), 384–402. https://doi.org/10.33603/jnpm.v6i2.7056

Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic Analysis : Striving to Meet the Trustworthiness Criteria. International Journal of Qualitative Methods, 16, 1–13. https://doi.org/10.1177/1609406917733847

Nugraha, D. G. A. P., Astawa, I. W. P., & Ardana, I. M. (2019). Pengaruh Model Pembelajaran Blended Learning terhadap Pemahaman Konsep dan Kelancaran Prosedur Matematis. Jurnal Riset Pendidikan Matematika, 6(1), 75–86. https://doi.org/10.21831/jrpm.v6i1.20074

Qetrani, S., Ouailal, S., & Achtaich, N. (2021). Enhancing Students’ Conceptual and Procedural Knowledge Using A New Teaching Approach of Linear Equations Based on The Equivalence Concept. Eurasia Journal of Mathematics, Science and Technology Education, 17(7), 1–17. https://doi.org/10.29333/EJMSTE/10938

Rau, M. A. (2017). Conditions for the Effectiveness of Multiple Visual Representations in Enhancing STEM Learning. Educ Psychol Rev, 29, 717–761. https://doi.org/10.1007/s10648-016-9365-3

Resbiantoro, G., Setiani, R., & Dwikoranto. (2022). A Review of Misconception in Physics : The Diagnosis , Causes , and Remediation. Journal of Turkish Science Education, 19(2), 403–427. https://doi.org/10.36681/tused.2022.128

Rittle-Johnson, B., & Schneider, M. (2015). Developing Conceptual and Procedural Knowledge of Mathematics. In The Oxford Handbook of Numerical Cognition (pp. 1102–1118). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014

Rosyidah, A. N. K., Maulyda, M. A., Jiwandono, I. S., Oktaviyanti, I., & Gunawan, G. (2021). Misconceptions and Errors in Integer Operations : A Study in Preservice Elementary School Teachers ( PGSD ). Journal of Physics: Conference Series, 1779, 012078. https://doi.org/10.1088/1742-6596/1779/1/012078

Sari, R. N., & In’am, A. (2021). Students Misconception and Errors in Solving Relations and Functions Problems. Amca Journal of Education and Behavioral Change, 1(2), 24–32. https://doi.org/10.51773/ajeb.v1i2.96

Setiani, N., Roza, Y., & Maimunah. (2022). Analisis Kemampuan Siswa dalam Pemahaman Konsep Matematis Materi Peluang pada Siswa SMP. Jurnal Cendekia: Jurnal Pendidikan Matematika, 06(02), 2286–2297. https://doi.org/10.31004/cendekia.v6i2.1476

Sopia, N., Sugiatno, & Hartoyo, A. (2019). Pengembangan Pemahaman Konseptual dan Disposisi Matematis Siswa Melalui Penerapan Pendekatan Problem Solving di SMA. J-PiMat Jurnal Pendidikan Matematika, 1(1), 11–20. https://doi.org/10.31932/j-pimat.v1i1.405

Suryani, Ramdhani, L., & Nurwalidainismawati. (2024). Analysis Of Misconceptions In Mathematical Problem Solving Integer Counting Operations Class Iv Students Of SDN 3 Lape Sumbawa. Jurnal Ilmiah Mandala Education (JIME), 10(4), 1015–1023. https://doi.org/10.58258/jime.v10i4.7586

Wilujeng, H., Aristiawan, & Alvarez, J. I. (2025). Students ’ Misconceptions in Algebraic Concepts : A Four-Tier Diagnostic Test Approach. Jurnal Elemen, 11(1), 120–132. https://doi.org/10.29408/jel.v11i1.27604

Yurniwati. (2018). Improving Conceptual and Procedural of Knowledge of Prospective Teachers Through Multisensory Approach: Experience from Indonesia. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(2), 106–117. https://doi.org/10.23917/jramathedu.v3i2.6374

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Published

2025-12-31