INCOMPREHENSION OF THE INDONESIAN ELEMENTARY SCHOOL STUDENTS ON FRACTION DIVISION PROBLEM

Yoppy Wahyu Purnomo; Chairunnisa Widowati; Syafika Ulfah

doi:10.22460/infinity.v8i1.p57-74

INCOMPREHENSION OF THE INDONESIAN ELEMENTARY SCHOOL STUDENTS ON FRACTION DIVISION PROBLEM

Yoppy Wahyu Purnomo
Chairunnisa Widowati
Syafika Ulfah

Abstract

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.

Keywords

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

Full Text:

PDF

References

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. https://doi.org/10.1080/0020739X.2015.1083127

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. https://doi.org/10.1007/s11858-011-0345-2

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 http://files.eric.ed.gov/fulltext/ED520859.pdf

Geller, E. H., Son, J. Y., & Stigler, J. W. (2017). Conceptual explanations and understanding fraction comparisons. Learning and Instruction, 52, 122–129. https://doi.org/10.1016/j.learninstruc.2017.05.006

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. https://doi.org/10.1037/a0017486

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.

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).

Lauritzen, P. (2012). Conceptual and procedural knowledge of mathematical functions. Publications of the University of Eastern Finland.

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. https://doi.org/10.1016/j.jmathb.2013.03.004

Purnomo, Y. W. (2015a). Pembelajaran Matematika untuk PGSD: Bagaimana Guru Mengembangkan Penalaran Proporsional Siswa. Jakarta: Erlangga.

Purnomo, Y. W. (2015b). Pengembangan desain pembelajaran berbasis penilaian dalam pembelajaran matematika. Cakrawala Pendidikan, XXXIV(2), 182–191. https://doi.org/10.21831/cp.v2i2.4823

Purnomo, Y. W. (2016). Perbaikan Instruksional dalam Implementasi Assessment-Based Learning di Kelas Matematika. Cakrawala Pendidikan, XXXV(3), 403–411. https://doi.org/10.21831/cp.v35i3.8821

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. https://doi.org/10.5539/ies.v7n8p74

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.

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). https://doi.org/10.1063/1.4995148

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. https://doi.org/10.1037/0022-0663.93.2.346

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. https://doi.org/10.1080/00220670209596608

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. https://doi.org/10.1016/j.learninstruc.2015.07.006

Siebert, D., & Gaskin, N. (2006). Creating, Naming, and Justifying Fractions. Teaching Children Mathematics, 12(8), 394–400.

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.

Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77(1), 20–26.

Skemp, R. R. (1987). The psychology of learning mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.

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. https://doi.org/10.2307/749817

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 http://stacks.iop.org/1742-6596/895/i=1/a=012139

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.

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. https://doi.org/10.1111/bjet.12011

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.

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. https://doi.org/10.1007/s10649-009-9206-0

DOI: https://doi.org/10.22460/infinity.v8i1.p57-74