International Electronic Journal of Mathematics Education

Learning to Make Sense of Fractions: Some Insights from the Malaysian Primary 4 Pupils
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Kor L, Teoh S, Binti Mohamed SSE, Singh P. Learning to Make Sense of Fractions: Some Insights from the Malaysian Primary 4 Pupils. Int Elect J Math Ed. 2019;14(1), 169-182. https://doi.org/10.29333/iejme/3985
APA 6th edition
In-text citation: (Kor et al., 2019)
Reference: Kor, L., Teoh, S., Binti Mohamed, S. S. E., & Singh, P. (2019). Learning to Make Sense of Fractions: Some Insights from the Malaysian Primary 4 Pupils. International Electronic Journal of Mathematics Education, 14(1), 169-182. https://doi.org/10.29333/iejme/3985
Chicago
In-text citation: (Kor et al., 2019)
Reference: Kor, Liew-Kee, Sian-Hoon Teoh, Siti Syardia Erdina Binti Mohamed, and Parmjit Singh. "Learning to Make Sense of Fractions: Some Insights from the Malaysian Primary 4 Pupils". International Electronic Journal of Mathematics Education 2019 14 no. 1 (2019): 169-182. https://doi.org/10.29333/iejme/3985
Harvard
In-text citation: (Kor et al., 2019)
Reference: Kor, L., Teoh, S., Binti Mohamed, S. S. E., and Singh, P. (2019). Learning to Make Sense of Fractions: Some Insights from the Malaysian Primary 4 Pupils. International Electronic Journal of Mathematics Education, 14(1), pp. 169-182. https://doi.org/10.29333/iejme/3985
MLA
In-text citation: (Kor et al., 2019)
Reference: Kor, Liew-Kee et al. "Learning to Make Sense of Fractions: Some Insights from the Malaysian Primary 4 Pupils". International Electronic Journal of Mathematics Education, vol. 14, no. 1, 2019, pp. 169-182. https://doi.org/10.29333/iejme/3985
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Kor L, Teoh S, Binti Mohamed SSE, Singh P. Learning to Make Sense of Fractions: Some Insights from the Malaysian Primary 4 Pupils. Int Elect J Math Ed. 2019;14(1):169-82. https://doi.org/10.29333/iejme/3985

Abstract

The teaching and learning fractions is one of the most problematic areas in primary school mathematics. A large number of studies have engaged paper-and-pencil test to measure students’ instrumental understanding about fractions but few have sought to learn about children’s fraction sense. This paper reports a study that investigated fraction sense possessed by the Malaysian primary pupils. A 16-item Fraction Sense Test (FST) was developed and administered to a group of 198 Primary 4 pupils to test their fraction sense in solving problems about fractions. From the FST result, six respondents were selected from the low ability, intermediate ability, and high ability group. These respondents underwent a series of clinical interviews. Results show that the low and intermediate achievers lack fraction sense. The high achievers demonstrated flexibility in visualizing and recognizing the representations of unfamiliar fractions. They developed mental referents for fractions. They noticed the number of parts and were aware that these parts must be equal when comparing fractions. They could visualize and perform operations mentally with larger value numerators and denominators. They have good sense of estimation and applied equivalence of fractions. These findings are useful to teachers who prepare teaching activities to enhance fraction sense.

References

  • Abdul Ghani SN, & Maat SM (2018). Misconception of fraction among middle grade Year Four pupils at primary school. Research on Education and Psychology (REP), 2(1), 111-125. Retrieved from http://journalrep.com
  • Abdul Halim Abdullah, Nur Liyana Zainal Abidin, & Marlina Ali. (2015). Analysis of students’ errors in solving higher order thinking skills (HOTS): Problems for the topic of fraction. Asian Social Science, 11(21), 133-142. https://doi.org/10.5539/ass.v11n21p133
  • Anghileri, J. (2000) Teaching number sense. London: Continuum.
  • Behr, M., Harel, G., Post, T., & Lesh, R. (1993). Rational Numbers: Toward a Semantic Analysis - Emphasis on the Operator Construct. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational Numbers: An Integration of Research (pp. 13-47). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Bentley, B., & Bossé, M. J. (2018). College students’ understanding of fraction operations. International Electronic Journal of Mathematics Education, 13(3), 233-247. https://doi.org/10.12973/iejme/3881
  • Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625. https://doi.org/10.1037/rev0000072
  • Bruce, C., Chang, D., Flynn, T., & Yearley, S. (2013). Foundations to learning and teaching fractions: Addition and subtraction. Curriculum and Assessment Branch: Ontario Ministry of Education. Retrieved from http://www.edugains.ca/resourcesDP/Resources/PlanningSupports/FINALFoundationstoLearningandTeachingFractions.pdf
  • Carpenter, T. P., Fennema, E., Romberg, T. A. (1993) Toward a unified discipline of scientific inquiry. In T.P. Carpenter, E. Fennema and T.A. Romberg (Eds.), Rational Numbers: An Integration of Research (pp. 1–11). New Jersey: Lawrence Erlbaum Associates.
  • Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64, 293-316 https://doi.org/10.1007/s10649-006-9036-2
  • Chinnappan, M. (2005). Children’s mappings of part-whole construct of fractions. In P. Clarkson & A. Downtown (Eds.), Conference of the Mathematics Education Research Group of Australasia (pp. 241-248). Sydney: MERGA.
  • Clarke, D., Roche, A., & Mitchell, A. (2008). Practical tips for making fractions come alive and make sense. Mathematics Teaching in the Middle School, 13(7), 372-379.
  • Fazio, L., & Siegler, R. (2011). Teaching fractions. Retrieved from http://unesdoc.unesco.org/images/0021/002127/212781e.pdf
  • Gabriel, F., Coché, F., Szucs, D., Carette, V., Rey, B., & Content, A. (2013). A componential view of children’s difficulties in learning fractions. Frontiers in Psychology, 4, 715. https://doi.org/10.3389/fpsyg.2013.00715
  • Ginsburg, H. P. (1997). Entering the child’s mind: The clinical interview in psychological research and practice. New York: Cambridge University Press. https://doi.org/10.1017/CBO9780511527777
  • Ginsburg, H. P., Jacobs, S. F., & Lopez, L. S. (1998). The teacher’s guide to flexible interviewing in the classroom: Learning what children know about math. Boston: Allyn and Bacon.
  • Gould, P. (2011). Developing an understanding of the size of fractions. In J., Way, & J., Bobis (Eds.), Fractions: Teaching for understanding (pp.63–70). Adelaide: The Australian Association of Mathematics Teachers (AAMT). Retrieved from https://www.aamt.edu.au/content/download/19931/273047/file/tdt_F_gould1.pdf
  • Kass, C. E., & Maddux, C. D. (2005). A human development view of learning disabilities: From theory to practice (2nd ed.). Springfield, IL, US: Charles C Thomas Publisher.
  • Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 49-84). Hillsdale, NJ: Lawrence Erlbaum.
  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • Lamon, J. (1999). Teaching fractions and ratios for understanding: Essential content and instructional strategies for children. Nova Jersey: Lawrence Erlbaum.
  • Lazića, B., Abramovichb, S., Mrđaa, M., & Romano, D. A. (2017). On the teaching and learning of fractions through a conceptual generalization approach. International Electronic Journal of Mathematics Education, Vol.12, No. 8, 749-767.
  • Liu, C., Xin, Z., & Li, X. (2012). The development of Chinese students’ understanding of the concept of fractions from fifth to eighth grade. Journal of Mathematics Education, 5(1), 45-62.
  • McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12, 2-8.
  • McNamara, J., & Shaughnessy, M. M. (2015) (2nd ed.). Beyond pizzas & pies, Grades 3-5: 10 Essential Strategies for Supporting Fraction Sense. CA: Math Solutions
  • Mullis, I.V.S., Martin, M.O., Foy, P., & Arora, A. (2012). TIMSS 2011 International Results in Mathematics. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
  • Pantziara, M., & Philippou, G. (2012). Levels of students’ “conception” of fractions. Educational Studies in Mathematics, 79(1), 61-83. https://doi.org/10.1007/s10649-011-9338-x
  • Patton, M. Q. (2002). Qualitative interviewing. Qualitative Research and Evaluation Methods, 3, 344-347.
  • Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Science, 17, 13–19. https://doi.org/10.1016/j.tics.2012.11.004
  • Tan, K. J., Ismail Z, & Abidin M (2018). A comparative analysis on cognitive domain for the Malaysian primary four textbook series. EURASIA Journal of Mathematics, Science and Technology Education, 14(4), 1273-1286. https://doi.org/10.29333/ejmste/82625
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.
  • Way, J. (2011). Developing number sense using learning objects. In J., Way, & J., Bobis (Eds.), Fractions: Teaching for understanding (pp.153–166). Adelaide: The Australian Association of Mathematics Teachers (AAMT) Inc.
  • Way, J. (2013). AAMT - Top Drawer Teachers resource: Fractions. Retrieved from https://topdrawer.aamt.edu.au/Fractions/Good-teaching/Fraction-sense/Fractions-as-numbers
  • 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. https://doi.org/10.12973/iji.2017.10413a
  • Wittmann, G. (2013). The consistency of students’ error patterns in solving computationalproblems with fractions. In B. Ubuz, C. Haser & M. A. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in Mathematics Education (pp.393–402). Antalya.
  • Woodward, T. L. (1998). An exploration of grade 8 students’ fraction sense. Thesis submitted in partial fulfillment of the requirements for the degree of Master of Arts in the Faculty of Education, Simon Fraser University. Retrieved from https://www.collectionscanada.gc.ca/obj/s4/f2/dsk2/ftp01/MQ37668.pdf
  • Zazkis, R., & Hazzan, O. (1999). Interviewing in Mathematics Education Research: Choosing the Questions. Journal of Mathematical Behavior, 17(4), 429-439. https://doi.org/10.1016/S0732-3123(99)00006-1

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.