ELEMENTARY SCHOOL TEACHERS’ AND MATHEMATICS TEACHER CANDIDATES’ UNDERSTANDING OF DIVISION WITH REMAINDERS

Kristoforus Djawa Djong; Meryani Lakapu; Irmina Veronika  Uskono; Yohanes Ovaritus Jagom; Wilfridus Beda Nuba  Dosinaeng; Samuel Igo  Leton

doi:10.37478/jpm.v6i4.6277

Authors

Kristoforus Djawa Djong Universitas Katolik Widya Mandira, Kupang, Indonesia
Meryani Lakapu Universitas Katolik Widya Mandira, Kupang, Indonesia
Irmina Veronika Uskono Universitas Katolik Widya Mandira, Kupang, Indonesia
Yohanes Ovaritus Jagom Universitas Katolik Widya Mandira, Kupang, Indonesia
Wilfridus Beda Nuba Dosinaeng Universitas Katolik Widya Mandira, Kupang, Indonesia
Samuel Igo Leton Universitas Katolik Widya Mandira, Kupang, Indonesia

DOI:

https://doi.org/10.37478/jpm.v6i4.6277

Abstract

Mathematics is studied from basic education to higher education. Understanding math concepts is important to learn because it is related to numeracy skills and also to form the basis of understanding at a higher level. One of the important materials to study is division, especially remainder division. This study aims to analyze and compare the understanding of elementary school teachers and prospective mathematics teachers in solving division problems with remainders. This research is a descriptive qualitative. Data were collected through descriptive tests and in-depth interviews with 13 elementary school teachers and 19 mathematics education study program students. The results showed that 92.3% of teachers used the porogapit method in solving the remaining division problems, and the rest used the Gasing method. Meanwhile, 63.16% of student teachers used the porogapit method and the rest showed more method variations. Although student teachers tended to be more thorough in completing the work, errors were still found due to inaccuracy and lack of conceptual understanding. Both groups have not shown a thorough mastery of the concept of remainder division. These findings provide a basis for improving the quality of mathematics learning.

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Keywords:

Elementary school teacher, Teacher candidates, Division with remainders, Conceptual understanding

References

Amaliyah, A., Mardiyanto, M. S., Odicus, D. A., Ardhiansyah, R. G., & Ramadhani, A. N. (2022). Analisis Kognitif Siswa Dalam Menyelesaikan Masalah Pembagian Bilangan Bulat Di MI ASY Syukriyyah Tangerang. PANDAWA: Jurnal Pendidikan dan Dakwah, 4(2), 255–268. https://doi.org/10.36088/pandawa.v4i2.1826

Arifendi, R. F., & Irianti, N. P. (2020). Efektivitas Penggunaan Porogapit Card dalam Pemahaman Penyelesaian Soal Pembagian dan Motivasi Belajar Siswa di Tingkat Sekolah Dasar. MUST: Journal of Mathematics Education, Science and Technology, 5(1), 29. https://doi.org/10.30651/must.v5i1.4848

Aspreliha, I., Damariswara, R., & Rohmah, D. S. (2022). Peningkatan Hasil Belajar Siswa pada Pembagian Desimal Melalui Media Sipintar Kelas IV SDN Burengan 2 Kota Kediri. Jurnal Cendekia?: Jurnal Pendidikan Matematika, 06(01), 1092–1104. https://doi.org/https://doi.org/10.31004/cendekia.v6i1.1334

Astuti, E. B., Yuliawati, F., & Khorini’mah, S. M. (2024). Identifikasi Faktor Penyebab Kesulitan Pembagian Porogapit Empat Digit pada Siswa Kelas VI Sekolah Dasar. Jurnal Basicedu, 8(4), 2534–2541. https://doi.org/10.31004/basicedu.v8i4.7776

Bela, S., Rohman, R., & Erviana, R. (2024). Kemampuan Pemahaman Konsep Matematis Siswa Melalui Model Pembelajaran Kooperatif Tipe Team Game Tournament. Prima Magistra: Jurnal Ilmiah Kependidikan, 5(4), 278–286. https://doi.org/10.37478/jpm.v5i4.4431

Cooper, J., & Karsenty, R. (2018). Can teachers and mathematicians communicate productively? The case of division with remainder. Journal of Mathematics Teacher Education, 21(3), 237–261. https://doi.org/10.1007/s10857-016-9358-7

Ermawati, D., Pratiwi, F. D. A., Ummayyah, M., & Khotimah, K. (2024). Analisis Kesulitan Belajar Berhitung Pembagian dalam Menyelesaikan Soal Cerita Matematika Siswa Kelas IV SD. Jurnal Pendidikan Tambusai, 8(1), 4698–4709. https://doi.org/https://doi.org/10.31004/jptam.v8i1.13111

Faizah, A. N., Manasikana, C. A., & Sutriyani, W. (2022). Peran Media Pembelajaran Corong Berhitung Terhadap Pemahaman Konsep Pembagian Di Kelas II SDN 1 Tahunan. Cartesius: Jurnal Pendidikan Matematika, 5(1), 15–24. https://doi.org/https://ejournal.ust.ac.id/index.php/CARTESIUS/article/view/2073

Giriansyah, F. E., Pujiastuti, H., & Ihsanudin, I. (2022). Kemampuan Pemahaman Matematis Siswa Berdasarkan Teori Skemp Ditinjau dari Gaya Belajar. Jurnal Cendekia: Jurnal Pendidikan Matematika, 07(01), 751–765. https://doi.org/10.31004/cendekia.v6i3.1515

Guntur, M., Salsabilla, A., Sahronih, S., & Sholeha, H. H. (2025). Efektifitas Model Problem Based Learning Berbasis Artificial Intelligence-Slidesgo Untuk Meningkatkan Kemampuan Pemecahan Masalah Matematis Siswa Sekolah Dasar. Prima Magistra: Jurnal Ilmiah Kependidikan, 6(1), 1–11. https://doi.org/10.37478/jpm.v6i1.4958

He, J. (2025). Decimal multiplication and division in mathematics textbooks for prospective elementary teachers. International Electronic Journal of Mathematics Education , 20(2). https://doi.org/10.29333/iejme/15898

Husna, A., & Sari, R. N. (2018). Pendampingan Belajar Matematika Dengan Metode “GASING” Kepada Murid Sekolah Dasar Negeri 008 Belakang Padang. MINDA BAHARU, 2(2), 188. https://doi.org/10.33373/jmb.v2i1.1505

?ncikab?, L., Ayano?lu, P., & Uysal, R. (2020). Sixth-grade students’ procedural and conceptual understandings of division operation in a real-life context. International Electronic Journal of Elementary Education, 13(1), 35–45. https://doi.org/10.26822/iejee.2020.171

Kadir, & Rosiyanti, H. (2011). Teknik Pola Bilangan dan Hasil Belajar Operasi Pembagian dalam Pembelajaran Matematika Siswa Madrasah Ibtidaiyah Kelas IV. Jurnal Pendidikan Dan Kebudayaan, 17, 525–538. https://doi.org/10.24832/jpnk.v17i5.46

Korkmaz, E. (2021a). Instructional Explanations of Class Teachers and Primary School Mathematics Teachers about Division. International Journal of Progressive Education, 17, 2021. https://doi.org/10.29329/ijpe.2020.332.3

Korkmaz, E. (2021b). Instructional Explanations of Class Teachers and Primary School Mathematics Teachers about Division. International Journal of Progressive Education, 17, 2021. https://doi.org/10.29329/ijpe.2020.332.3

Kusuma, M. W. K., Jampel, I. N., & Bayu, G. W. (2018). Pengaruh Metode Pembelajaran Matematika Gasing Terhadap Hasil Belajar Matematika. Jurnal Pedagogi dan Pembelajaran, 1(1), 37–46. https://doi.org/https://doi.org/10.23887/jp2.v1i1.19330

Lakapu, M., Dosinaeng, W. B. N., Uskono, I. V., Jagom, Y. O., Leton, S. I., & Djong, K. D. (2023). Belajar Matematika Sambil Bermain Bersama Siswa Sekolah Dasar dan Sekolah Menengah. Losari: Jurnal Pengabdian Kepada Masyarakat, 5(2), 2684–9887. https://doi.org/10.53860/losari

Lautert, S. L., Spinillo, A. G., & Correa, J. (2012). Children’s difficulties with division: an intervention study. Educational Research, 3(5), 447–456. https://doi.org/https://www.interesjournals.org/articles/childrens-difficulties-with-division-an-intervention-study.pdf

Maulida, L., Annisa, N. S., Rizki, L. Z., & Hidayati, D. (2025). Upaya Guru Dalam Meningkatkan Pemahaman Konsep Matematika Melalui Pendekatan Matematika Realistik Pada Materi Pembagian Kelas III. Jurnal Inovasi Pembelajaran Dan Pendidikan Islam. https://doi.org/10.30596/jippi.v3i1.81

Ndalichako, J. L. (2013). Analysis of Pupils’ Difficulties in Solving Questions Related to Fractions: The Case of Primary School Leaving Examination in Tanzania. Creative Education, 04(09), 69–73. https://doi.org/10.4236/ce.2013.49B014

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. https://doi.org/10.33603/jnpm.v6i2.7056

Nuari, L. F., Charitas, R., Prahmana, I., & Fatmawati, I. (2019). Learning of Division Operation for Mental Retardations’ Student Through Math Gasing. JME: Journal on Mathematics Education, 10(1), 127–142. https://doi.org/https://jme.ejournal.unsri.ac.id/index.php/jme/article/view/3782?

Ortiz-Laso, Z., & Diego-Mantecón, J. M. (2020). Strategies of Pre-Service Early Childhood Teachers for Solving Multi-Digit Division Problems. Sustainability (Switzerland), 12(23), 1–20. https://doi.org/10.3390/su122310217

Pacheco-Muñoz, E., Nava-Lobato, S., Antonio Juárez-López, J., & Ponce De León-Palacios, M. (2023). Division problems with remainder: A study on strategies and interpretations with fourth grade Mexican students. Mathematics Teaching Research Journal, 15(2), 120–141. https://doi.org/https://files.eric.ed.gov/fulltext/EJ1394401.pdf?

Pacheco-Muñoz, E., Nava-Lobato, S., Juárez-López, J. A., & León-Palacios, M. P. de. (2023). Division problems with remainder: A study on strategies and interpretations with fourth grade Mexican students. Mathematics Teaching Research Journal, 15(2), 120–142. https://files.eric.ed.gov/fulltext/EJ1394401.pdf?

Rochma, N. A., Suwanti, V., & Pranyata, Y. I. P. (2023). Analisis Kemampuan Pemahaman Konsep Siswa dalam Menyelesaikan Masalah Perbandingan Berdasarkan Teori Pirie-Kieren. JMPM: Jurnal Matematika Dan Pendidikan Matematika, 8(2), 100–113. https://doi.org/10.26594/jmpm.v8i2.3889

Safiati, O. A., Dafik, & Prastiti, T. D. (2021). On division operation of any numbers: Introducing a new technique. Journal of Physics: Conference Series, 1836(1). https://doi.org/10.1088/1742-6596/1836/1/012055

Safiati, O. A., Dafik, Prastiti, T. D., & Ridlo, Z. R. (2021). On student’s metacognition skill in solving division operation under the research-based learning implementation. IOP Conference Series: Earth and Environmental Science, 747(1). https://doi.org/10.1088/1755-1315/747/1/012118

Sari, E. P., & Fikrati, A. N. (2023). Analisis Kesalahan Siswa SD Dalam Menyelesaikan Soal Pembagian Bersusun Porogapit Berdasarkan Kemampuan Matematika. Edumath: Jurnal Program Studi Pendidikan Matematika, 15(1), 1–6. https://doi.org/https://doi.org/10.32682/edumath.v15i1.2901

Star, J. R., & Newton, K. J. (2009). The Nature and Development of Experts’ Strategy Flexibility for Solving Equations. ZDM Mathematics Education, 41(5), 557–567. https://doi.org/10.1007/s11858-009-0185-5

Susanti, E. P., Yantoro, Y., & Kurniawan, A. R. (2020). Strategi Guru dalam Pembelajaran Berhitung Pembagian di Sekolah Dasar. Al-Adzka: Jurnal Ilmiah Pendidikan Guru Madrasah Ibtidaiyah, 10(1), 53. https://doi.org/10.18592/aladzkapgmi.v10i1.3691

Taufan, M., Nandang, N., & Hakam, F. (2024). Analisis Kesulitan Siswa dalam Menyelesaikan Soal Pembagian Materi Bilangan Bulat dengan Menggunakan Metode Porogapit. Indo-MathEdu Intellectuals Journal, 5(5), 6077–6087. https://doi.org/https://doi.org/10.54373/imeij.v5i5.1913

Tosho, T. G. (2022). Buku Panduan Guru Matematika Untuk SD KELAS III (M. Isoda, Ed.; M. Ali & A. D. Saffanah, Trans.; 1st ed., Vol. 1). Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi. https://doi.org/https://static.buku.kemdikbud.go.id