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The purpose of the study is to investigate the Indonesian students’ performance in solving fraction division case including the difficulties, relations, and implications for classroom instruction. This study employed a descriptive case study to achieve it. The procedures of data collecting were initiated by giving a context-based problem to 40 elementary school students and it then according to the test result was selected three students for semi- structure interviewed. The findings of the study showed that the tendency of students’ procedural knowledge dominated to their conceptual knowledge in solving the fraction  division problem. Furthermore, it  was  found  several mistakes. First, the students were not accurate when solving the problem and unsuccessful to figure out the problem. Second, students’ conceptual knowledge was incomplete. The last was is to apply the laws and strategies of fraction division irrelevant. These findings emphasized other sub-construct of fractions instead of part-to-whole in the teaching and learning process. Teaching and learning of fraction in the mathematics classroom should take both conceptual and procedural knowledge into account as an attempt to prevent  faults  and  misconceptions.  In  conclusion,  it  was  substantial  to present context-based problems at the beginning of the lesson in order for students to be able to learn fraction division meaningfully.


Fraction division Fractional parts Conceptual knowledge Procedural knowledge Elementary school students Indonesia

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  1. Alenazi, A. (2016). Examining middle school pre-service teachers’ knowledge of fraction division interpretations. International Journal of Mathematical Education in Science and Technology, 47(5), 696–716.
  2. Clarke, D., Clarke, B., & Roche, A. (2011). Building teachers’ expertise in understanding, assessing and developing children’s mathematical thinking: The power of task-based, one-to-one assessment interviews. ZDM - International Journal on Mathematics Education, 43(6), 901–913.
  3. Forrester, T., & Chinnappan, M. (2010). The Predominance of Procedural Knowledge in Fractions. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia (pp. 185–192). Retrieved from
  4. Geller, E. H., Son, J. Y., & Stigler, J. W. (2017). Conceptual explanations and understanding fraction comparisons. Learning and Instruction, 52, 122–129.
  5. Hallett, D., Nunes, T., & Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. Journal of Educational Psychology, 102(2), 395–406.
  6. Kilpatrick, J., Swafford, J., & Findell, B. (2001). The strands of mathematical proficiency. In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Adding it up: Helping children learn mathematics (pp. 115–118). Washington, DC: National Academy Press.
  7. Kribs-Zaleta, C. (2006). Invented Strategies for Division of Fractions. In Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 371–376).
  8. Lauritzen, P. (2012). Conceptual and procedural knowledge of mathematical functions. Publications of the University of Eastern Finland.
  9. Lin, C.-Y., Becker, J., Ko, Y.-Y., & Byun, M.-R. (2013). Enhancing pre-service teachers’ fraction knowledge through open approach instruction. The Journal of Mathematical Behavior, 32(3), 309–330.
  10. Purnomo, Y. W. (2015a). Pembelajaran Matematika untuk PGSD: Bagaimana Guru Mengembangkan Penalaran Proporsional Siswa. Jakarta: Erlangga.
  11. Purnomo, Y. W. (2015b). Pengembangan desain pembelajaran berbasis penilaian dalam pembelajaran matematika. Cakrawala Pendidikan, XXXIV(2), 182–191.
  12. Purnomo, Y. W. (2016). Perbaikan Instruksional dalam Implementasi Assessment-Based Learning di Kelas Matematika. Cakrawala Pendidikan, XXXV(3), 403–411.
  13. Purnomo, Y. W., Kowiyah, Alyani, F., & Assiti, S. S. (2014). Assessing number sense performance of Indonesian elementary school students. International Education Studies, 7(8), 74–84.
  14. Purnomo, Y. W., Suryadi, D., & Darwis, S. (2016). Examining pre-service elementary school teacher beliefs and instructional practices in mathematics class. International Electronic Journal of Elementary Education, 8(4), 629–642.
  15. Purnomo, Y. W., Widowati, C., Aziz, T. A., & Pramudiani, P. (2017). Fractions division knowledge of elementary school student: The case of Lala. In AIP Conference Proceedings (Vol. 1868).
  16. Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–362.
  17. Sharp, J., & Adams, B. (2002). Children’s constructions of knowledge for fraction division after solving realistic problems. Journal of Educational Research, 95(6), 333–347.
  18. Sidney, P. G., Hattikudur, S., & Alibali, M. W. (2015). How do contrasting cases and self-explanation promote learning? Evidence from fraction division. Learning and Instruction, 40, 29–38.
  19. Siebert, D., & Gaskin, N. (2006). Creating, Naming, and Justifying Fractions. Teaching Children Mathematics, 12(8), 394–400.
  20. Sinicrope, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller (Ed.), Making sense of fractions, ratios, and proportions (pp. 153–161). Reston, Va.: National Council of Teachers of Mathematics Reston.
  21. Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77(1), 20–26.
  22. Skemp, R. R. (1987). The psychology of learning mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
  23. Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25.
  24. Trivena, V., Ningsih, A. R., & Jupri, A. (2017). Misconception on Addition and Subtraction of Fraction at Primary School Students in Fifth-Grade. Journal of Physics: Conference Series, 895(1), 12139. Retrieved from
  25. Van de Walle, J. A., Karp, K. S., & Bay-William, J. M. (2010). Elementary and Middle School Mathematics: Teaching Developmentally (Seventh Edition). Boston, MA: Pearson Education, Inc.
  26. Wang, H.-S., Chen, Y.-T., & Lin, C.-H. (2014). The learning benefits of using eye trackers to enhance the geospatial abilities of elementary school students. British Journal of Educational Technology, 45(2), 340–355.
  27. Wijaya, A. (2017). The Relationships between Indonesian Fourth Graders’ Difficulties in Fractions and the Opportunity to Learn Fractions: A Snapshot of TIMSS Results. International Journal of Instruction, 10(4), 221–236.
  28. Yim, J. (2010). Children’s strategies for division by fractions in the context of the area of a rectangle. Educational Studies in Mathematics, 73(2), 105–120.