Exploring Fifth Graders’ Learning Obstacles in Multiplication and Division of Fractions

Puji Lestari; Unik Ambarwati; Yoppy Wahyu Purnomo; Kinanti Pangestu

doi:10.35445/alishlah.v17i3.6907

Exploring Fifth Graders’ Learning Obstacles in Multiplication and Division of Fractions

Puji Lestari, Unik Ambarwati, Yoppy Wahyu Purnomo, Kinanti Pangestu

Abstract

Fractions serve as a critical foundation in mathematics education, preparing students for more advanced topics such as algebra and probability. Despite their importance, fractions are often difficult for elementary school students to grasp due to their abstract nature, especially when not taught within meaningful contexts. This study investigates the learning obstacles faced by fifth-grade students in understanding the multiplication and division of fractions. Utilizing a qualitative case study approach, data were collected through tests, interviews, classroom observations, and documentation at Lempuyangwangi Elementary School in Yogyakarta. The analysis revealed three primary categories of learning obstacles: (1) Ontogenic obstacles, including students’ inability to simplify fractions correctly, frequent computational errors, and low motivation in learning mathematics; (2) Didactical obstacles, such as difficulties in interpreting word problems and applying appropriate procedures; and (3) Epistemological obstacles, particularly in understanding and applying the inverse concept required for dividing fractions. These findings highlight the need for more contextually relevant and cognitively aligned instructional strategies. Addressing these obstacles can support the development of more effective teaching approaches to enhance students’ conceptual understanding of fraction operations.

Keywords

fraction operation; learning obstacle; conceptual understanding

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References

Anugraheni, I., & Sartono, E. K. E. (2022). Analisis Kemampuan Berpikir Kritis Matematis Berbasis Realistik. Scholaria: Jurnal Pendidikan Dan Kebudayaan, 12(3), 244–249.

Braithwaite, D. W., & Siegler, R. S. (2021). Putting fractions together. Journal of Educational Psychology, 113(3), 556–571. https://doi.org/10.1037/edu0000477

Diputra, K. S., Suryadi, D., Herman, T., & Jupri, A. (2023). Analysis of the Elementary School Students’ Learning Obstacles: A Case Study on the Concept of Fractions. Al Ibtida: Jurnal Pendidikan Guru MI, 10(1), 13. https://doi.org/10.24235/al.ibtida.snj.v10i1.13078

Fauzi, I., & Suryadi, D. (2020). Learning Obstacle the Addition and Subtraction of Fraction in Grade 5 Elementary Schools. Jurnal Kajian Pendidikan Islam, 12(1).

Gravemeijer, K., Stephan, M., Julie, C., Lin, F. L., & Ohtani, M. (2017). What Mathematics Education May Prepare Students for the Society of the Future? International Journal of Science and Mathematics Education, 15, 105–123. https://doi.org/10.1007/s10763-017-9814-6

Hendriyanto, A., Suryadi, D., Juandi, D., Dahlan, J. A., Hidayat, R., Wardat, Y., … Muhaimin, L. H. (2024). The didactic phenomenon: Deciphering students’ learning obstacles in set theory. Journal on Mathematics Education, 15(2), 517–544. https://doi.org/10.22342/jme.v15i2.pp517-544

Hidayah, A., & Maemonah, M. (2022). Analisis Hambatan Belajar Siswa Kelas IV Pada Mata Pelajaran Matematika. Symmetry: Pasundan Journal of Research in Mathematics Learning and Education, 7(2), 232–240. https://doi.org/10.23969/symmetry.v7i2.6737

Mills, J. (2019). Making multiplication meaningful: Teaching for conceptual understanding. Teachers and Curriculum, 19(1), 17–25. https://doi.org/10.15663/tandc.v19i1.334

Milton, J. H., Flores, M. M., Moore, A. J., Taylor, J. J., & Burton, M. E. (2019). Using the Concrete Representational Abstract Sequence to Teach Conceptual Understanding of Basic Multiplication and Division. Learning Disability Quarterly, 42(1), 32–45. https://doi.org/10.1177/0731948718790089

Muharram, M. R. W., Prabawanto, S., & Jupri, A. (2019). Analysis of students’ critical thinking skill of fractions on primary school. Journal of Physics: Conference Series, 1157(3). Institute of Physics Publishing. https://doi.org/10.1088/1742-6596/1157/3/032119

Nurani, L. A., Nur’aeni, E., Apriani, I. F., Rijal, M., Muharram, W., Pendidikan Indonesia, U., … Edu, L. (2021). ANALISIS LEARNING OBSTACLE SISWA PADA MATERI PECAHAN SENILAI DI KELAS IV SEKOLAH DASAR. Journal of Elementary Education, 04, 5.

Permata, D., Wijayanti, P., & Masriyah. (2019). Students’ misconceptions on the algebraic prerequisites concept: Operation of integer numbers and fractions. Journal of Physics: Conference Series, 1188(1). Institute of Physics Publishing. https://doi.org/10.1088/1742-6596/1188/1/012059

Purnomo, Y. W. (2022). Riset Rekayasa Didakti upaya Menyusun Pengetahuan Matematis untuk Mengajar di Sekolah Dasar (1st ed.; A. Kristiyani, Ed.). Yogyakarta: UNY Press.

Purnomo, Y. W., Pasri, Aziz, T. A., Shahrill, M., & Prananto, I. W. (2022). Students’ failure to understand fraction multiplication as part of a quantity. Journal on Mathematics Education, 13(4), 681–702. https://doi.org/10.22342/jme.v13i4.pp681-702

Purnomo, Y. W., Widowati, C., & Ulfah, S. (2019). Incomprehension of The Indonesian Elementary School Students on Fraction Division Problem. Infinity Journal, 8(1), 57–74. https://doi.org/10.22460/infinity.v8i1.p57-74

Roesslein, R. I., & Codding, R. S. (2019, March 1). Fraction interventions for struggling elementary math learners: A review of the literature. Psychology in the Schools, Vol. 56, pp. 413–432. Wiley-Liss Inc. https://doi.org/10.1002/pits.22196

Rosid, A. A. A., Fitriyani, A. D., & Muflivia, R. (2022). Hambatan Belajar Siswa Pada Pembelajaran Matematika Materi Pecahan di Kelas V Sekolah Dasar. JURNAL PENDIDIKAN GURU SEKOLAH DASAR, 7(3), 61–70.

Ruli, R. M., Karawang, S., Ronggo Waluyo, J. H., Timur, T., Karawang, K., & Barat, J. (2021). IDENTIFIKASI HAMBATAN BELAJAR SISWA PADA KONSEP PERSAMAAN KUADRAT. Jurnal Pembelajaran Matematika Inovatif, 4(4). https://doi.org/10.22460/jpmi.v4i4.941-948

Salim Nahdi, D., & Gilar Jatisunda, M. (2020). Conceptual Understanding and Procedural Knowledge: A Case Study on Learning Mathematics of Fractional Material in Elementary School. Journal of Physics: Conference Series, 1477(4). Institute of Physics Publishing. https://doi.org/10.1088/1742-6596/1477/4/042037

Simon, M. A, Kara, M., & Placa, N. (2018). Promoting reinvention of a multiplication-of-fractions algorithm: A study of the Learning Through Activity research program. The Journal of Mathematical Behavior, 52, 174–187.

Simon, Martin A, Placa, N., Avitzur, A., & Kara, M. (2018). Running head: PROMOTING A CONCEPT OF FRACTION-AS-MEASURE 1 Promoting a Concept of Fraction-As-Measure: A Study of the Learning Through Activity Research Program.

Sukarma, I. K., Isnawan, M. G., & Alsulami, N. M. (2023). Understanding Learning Barriers in Fractional Multiplication: An Investigation Using Hermeneutics Phenomenology. International Journal of Social Science and Education Research Studies, 03(08), 1563–1569. https://doi.org/10.55677/ijssers/V03I8Y2023-07

Sulistyani, N., Prasojo, L. D., Purnomo, Y. W., Ardhana, S. S., Fitriya, Y., & Putri, Y. D. (2024). Epistemological Didactical Situation of Learning Factors and Multiples in Elementary School Students. Mathematics Teaching Research Journal, 66(5), 66–91.

Suryadi, D. (2019). Landasan filosofis : penelitian desain didaktis (DDR) (1st ed.; Tim Gapura Press, Ed.). Bandung: Gapura Press.

Ulfa, N, Jupri, A., & Turmudi, T. (2021). Analisis Hambatan Belajar Pada Materi Pecahan. Research and Development Journal of Education, 7(2), 226. https://doi.org/10.30998/rdje.v7i2.8509

Ulfa, Nadia, Jupri, A., & Turmudi, T. (2021). Analisis Hambatan Belajar Pada Materi Pecahan. Research and Development Journal of Education, 7(2), 226. https://doi.org/10.30998/rdje.v7i2.8509

Unaenah, E., Suryadi, D., & Turmudi. (2023). Students’ Learning Obstacles on Fractions in Elementary School. https://doi.org/10.2991/978-2-38476-020-6_16

Walle, J. A. V, Karp, K. S., & Williams, J. M. B. (2013). Elementary and Middle School Mathematics: Teaching Developmentally (8th ed.; A. Manalili, Ed.). Pearson.

Wulandari, D., & Amir, M. F. (2022). Analysis of Elementary School Students’ Difficulties in Fraction Addition. KREANO Creative-Innovative Mathematics (Education) Journal , 13(1), 43–54. Retrieved from http://journal.unnes.ac.id/nju/index.php/kreano

DOI: https://doi.org/10.35445/alishlah.v17i3.6907