Exploring a Slow Learner’s Use of The Standard Multiplication Algorithm
Abstract
The standard multiplication algorithm requires the coordinated use of place value, multiplication facts, regrouping, and accurate recording of results. This study examined how these components were applied within a single case involving a learner identified as a slow learner when solving two-digit-by-one-digit multiplication problems. A qualitative descriptive single-case design involved one purposively selected student identified as a slow learner at an inclusive public junior high school in Surabaya. Instruments comprised a 15-item multiplication worksheet and a semi-structured interview guide. Data were collected through individual worksheet completion and an interview immediately afterward. Analysis followed data condensation, data display, and conclusion drawing and verification across five aspects: place-value identification, place-value-based multiplication, regrouping, recording of results, and final-answer accuracy. Initial written work and interview explanations were compared item by item to identify cross-item patterns. The results showed consistent application of the algorithm on 11 problems. Four problems displayed discrepancies between the initial work and the procedures stated or reconstructed during the interview. The findings indicate that place-value alignment and most regrouping steps were relatively stable, whereas operation selection and the recording of results remained inconsistent. Instruction should therefore target the unstable components through explicit comparison of multiplication and addition, multiplication-fact practice, expanded notation, and partial products rather than reteaching the entire algorithm.
References
Barbieri, C. A., Booth, J. L., Begolli, K. N., & McCann, N. (2021). The effect of worked examples on student learning and error anticipation in algebra. Instructional Science, 49(4), 419–439. https://doi.org/10.1007/s11251-021-09545-6
Barbieri, C. A., Miller-Cotto, D., Clerjuste, S. N., & Chawla, K. (2023). A meta-analysis of the worked examples effect on mathematics performance. Educational Psychology Review, 35(1), Article 11. https://doi.org/10.1007/s10648-023-09745-1
Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Pearson Education, Inc.
Elvierayani, R. R., Lusiana, R., Suwandayani, B. I., & Silvia, I. A. (2025). Understanding mathematical concepts in students with borderline intellectual functioning: Insights from representational gestures. Jurnal Elemen, 11(4), 930–950. https://doi.org/10.29408/jel.v11i4.31388
Fauziah, A., & Pandra, V. (2024). Analyzing elementary school students’ misconceptions in number sense using a five-tier diagnostic test. Jurnal Riset Pendidikan Matematika, 11(2), 134–144. https://doi.org/10.21831/jrpm.v11i2.76086
Firmansyah, A., Wardono, W., & Isnarto, I. (2025). Analysis enhancing math problem solving skills in slow learners: The impact of differentiated learning and educational games. Mosharafa: Jurnal Pendidikan Matematika, 14(4), 949–964. https://doi.org/10.31980/mosharafa.v14i4.2518
Hafidah, H., & Rukli, R. (2022). Treating slow learners in learning repeated addition using Realistic Mathematics Education approach. Mimbar Sekolah Dasar, 9(3), 396–412. https://doi.org/10.53400/mimbar-sd.v9i3.48586
Hasibuan, H. Y., Santosa, C. A. H. F., & Syamsuri, S. (2022). Slow learners’ performance in solving mathematical problems in the inclusive classroom. Jurnal Elemen, 8(2), 449–465. https://doi.org/10.29408/jel.v8i2.5181
Jannah, U. R., Sholihah, W., Basri, H., Dewi, N. P., Rahmad, & Hafsi, A. R. (2025). Optimizing slow learners’ understanding through environment-based manipulative media on the number operation topic. Jurnal Pendidikan MIPA, 26(3), 1679–1704. https://doi.org/10.23960/jpmipa.v26i3.pp1679-1704
Jensen, S., Gasteiger, H., & Bruns, J. (2024). Place value and regrouping as helpful constructs to diagnose difficulties in understanding the place value system. Journal für Mathematik-Didaktik, 45(2), Article 11. https://doi.org/10.1007/s13138-024-00234-8
Lewis, K. E., & Fisher, M. B. (2018). Clinical interviews: Assessing and designing mathematics instruction for students with disabilities. Intervention in School and Clinic, 53(5), 283–291. https://doi.org/10.1177/1053451217736864
Lin, T.-H., Riccomini, P. J., & Liang, Z. (2025). Mathematical error patterns of students with mathematics difficulty: A systematic review. Learning Disability Quarterly, 48(4), 242–256. https://doi.org/10.1177/07319487241310873
Listiawati, N., Sabon, S. S., Siswantari, Subijanto, Wibowo, S., Zulkardi, & Riyanto, B. (2023). Analysis of implementing Realistic Mathematics Education principles to enhance mathematics competence of slow learner students. Journal on Mathematics Education, 14(4), 683–700. https://doi.org/10.22342/jme.v14i4.pp683-700
Malola, M., & Seah, W. T. (2024). Primary school teachers’ knowledge for teaching multiplicative thinking. Journal on Mathematics Education, 15(4), 1175–1196. https://doi.org/10.22342/jme.v15i4.pp1175-1196
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). SAGE Publications, Inc.
Mix, K. S., Bower, C. A., Hancock, G. R., Yuan, L., & Smith, L. B. (2022). The development of place value concepts: Approximation before principles. Child Development, 93(3), 778–793. https://doi.org/10.1111/cdev.13724
Mutaqin, E. J., Herman, T., Wahyudin, & Muslihah, N. N. (2023). Hypothetical learning trajectory in place value concepts in elementary school. Mosharafa: Jurnal Pendidikan Matematika, 12(1), 125–134. https://doi.org/10.31980/mosharafa.v12i1.761
Novikasari, I., & Dede, Y. (2024). Toward proficiency: Developing a multiplication mathematical content knowledge test for pre-service mathematics teachers in Indonesia and Türkiye. Journal on Mathematics Education, 15(1), 115–130. https://doi.org/10.22342/jme.v15i1.pp115-130
Nyoto, & Mutiara, A. (2025). Error analysis in fraction arithmetic operations among fourth grade students. JTP - Jurnal Teknologi Pendidikan, 27(1), 199–207. https://doi.org/10.21009/jtp.v27i1.52943
Putra, D. T., Firdaus, F., & Oktari, V. (2023). Pengembangan KOSIKA (komik sekitar kita) berbasis pendekatan Realistic Mathematics Education untuk memfasilitasi pemahaman perkalian. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 12(4), 3683–3695. https://doi.org/10.24127/ajpm.v12i4.8135
Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587–597. https://doi.org/10.1007/s10648-015-9302-x
Rohimah, S. M., Putri, S. A., & Helsa, Y. (2026). Conceptual and procedural errors of pre-service elementary teachers in solving educational research statistics problems. Jurnal Elemen, 12(1), 49–65. https://doi.org/10.29408/jel.v12i1.32327
Setiyani, Waluya, S. B., Sukestiyarno, Y. L., & Cahyono, A. N. (2024). Construction of reflective thinking: A field independent student in numerical problems. Journal on Mathematics Education, 15(1), 151–172. https://doi.org/10.22342/jme.v15i1.pp151-172
Susilo, C. Y., & Prihatnani, E. (2022). Scaffolding for slow learner children on integer operations. Kreano, Jurnal Matematika Kreatif-Inovatif, 13(1), 113–125. https://doi.org/10.15294/kreano.v13i1.34363
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2016). Elementary and middle school mathematics: Teaching developmentally (9th ed.). Pearson Education Limited.
Wafiroh, H., & Harun. (2022). The barriers in the implementation of mathematics learning for slow learner during the COVID-19. Jurnal Elemen, 8(1), 144–160. https://doi.org/10.29408/jel.v8i1.4525
Wanabuliandari, S., Wardono, Susilo, B. E., Bintoro, H. S., & Mariani, S. (2025). A systematic literature review on slow learners’ problem-solving in mathematics education. International Journal of Learning, Teaching and Educational Research, 24(3), 699–724. https://doi.org/10.26803/ijlter.24.3.33
Wibawa, K. A., Atmaja, I. M. D., & Widarnandana, I. G. D. (2026). Deep scaffolding based on RME to reduce slow learners’ errors in numeracy problem solving. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 15(2), 1049–1062. https://doi.org/10.24127/ajpm.v15i2.14862
Zakaria, & Dewantara, A. H. (2024). Understanding multiplication concept: Exploring PMRI-enhanced thematic learning using traditional games for primary teachers. Jurnal Elemen, 10(1), 55–69. https://doi.org/10.29408/jel.v10i1.19838
Zhang, Y., Tolmie, A., & Gordon, R. (2023). The relationship between working memory and arithmetic in primary school children: A meta-analysis. Brain Sciences, 13(1), Article 22. https://doi.org/10.3390/brainsci13010022
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