A Test for Understanding Simple Fractions Among 5th Grade Students at the Beginning of Lower Secondary Education

Tímea Karika; Csaba Csíkos

doi:10.29333/ejmste/11654

Full Text (PDF)

Tímea Karika ¹ , Csaba Csíkos ² ^*

More Detail

¹ Doctoral School in Mathematics, ELTE Eötvös Loránd University, HUNGARY² Department of Educational Evaluation and Planning, University of Szeged, HUNGARY^* Corresponding Author

Abstract

In this research, a new test for understanding simple fractions has been developed for students at the beginning of lower secondary education. In many countries, mathematics education in Grade 5 builds on elementary students’ developing concepts of fractions. Understanding fractions causes many difficulties for students, and research on mental representations of fractions suggests that different visualizations may be helpful in teaching and learning. The sample consisted of 124 5^th-grade students, and the reliability of the test proved to be high (alpha=.95). Out of the three types of visualization, the pie chart was the easiest to recognize, and 1/2 (half) proved to be the easiest, and 1/3 (one-third) the most difficult to be recognized. The type of visualization has a stronger effect on students’ performance than the type of fraction (unit versus non-unit fractions). Most surprisingly, students were better at recognizing 2/4 and 2/3 than their unit fraction counterparts, 1/2 and 1/3. The test was supplemented by questions on attitude towards learning fractions.

Keywords

fractions
visualization
lower secondary students

Supplementary Files

Appendix

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.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 18, Issue 2, February 2022, Article No: em2081

https://doi.org/10.29333/ejmste/11654

Publication date: 01 Feb 2022

Article Views: 1899

Article Downloads: 1728

Open Access Disclosures References How to cite this article

Disclosure

Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Braithwaite, D. W., & Siegler, R. S. (2021). Putting fractions together. Journal of Educational Psychology, 113(3), 556-571. https://doi.org/10.1037/edu0000477
Cady, J. A., Hodges, T. E., & Collins, R. L. (2015). A comparison of textbooks’ presentation of fractions. School Science and Mathematics, 115(3), 105-116. https://doi.org/10.1111/ssm.12108
Chahine, I. (2011). The role of translations between and within representations on the conceptual understanding of fraction knowledge: A trans-cultural study. Journal of Mathematics Education, 4(1), 47-59.
Deringol, Y. (2019). Misconceptions of primary school students about the subject of fractions. International Journal of Evaluation and Research in Education, 8(1), 29-38. https://doi.org/10.11591/ijere.v8i1.16290
Fazio, L., & Siegler, R. (2011). Teaching fractions. educational practices series-22. UNESCO International Bureau of Education.
Fonseca, J. R. S. (2012). Students’ attitudes toward math learning. In N. M. Seel (Ed.), Encyclopedia of the sciences of learning (pp. 3214-3219). Springer. https://doi.org/10.1007/978-1-4419-1428-6_1078
Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., Jordan, N. C., Siegler, R., Gersten, R., & Changas, P. (2013). Improving at-risk learners’ understanding of fractions. Journal of Educational Psychology, 105(3), 683-700. https://doi.org/10.1037/a0032446
Hunting, R. P., & Davis, G. E. (1991). Dimensions of young children’s knowledge of the fraction one half (pp 27-53). Springer. https://doi.org/10.1007/978-1-4612-3194-3_3
Hunting, R. P., & Korbosky, R. K. (1984) Processes used to learn fractions. Report to the Academic Staff Development Committee, Western Australian Institute of Technology.
Karika, T., & Csíkos, C. (2018). A törtfogalom fejlődésének segítése az alsó és a felső tagozat határán [Fostering the concept of fractions at the boundary of primary and lower secondary school grades]. Gyermeknevelés Tudományos Folyóirat [Parenting Scientific Journal], 6(1), 86-98. https://doi.org/10.31074/gyn201818698
Kerslake, D. (1986). Fractions: Children’s strategies and errors. A report of the strategies and errors in secondary mathematics project. NFER-NELSON.
Kieren, T. E. (1983). Partitioning, equivalence, and the construction of rational number ideas. In M. Zweng (Ed.), Proceedings of the 4th International Congress on Mathematical Education (pp. 506-508). Birkhauser.
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). Lawrence Erlbaum Associates.
Mata, M. D. L., Monteiro, V., & Peixoto, F. (2012). Attitudes towards mathematics: Effects of individual, motivational, and social support factors. Child Development Research, 2012, Art. 876028. https://doi.org/10.1155/2012/876028
McMullen, J., Laakkonen, E., Hannula-Sormunen, M., & Lehtinen, E. (2015). Modeling the developmental trajectories of rational number concept(s). Learning and Instruction, 37, 14-20. https://doi.org/10.1016/j.learninstruc.2013.12.004
Merenluoto, K., & Lehtinen, E. (2002). Conceptual change in mathematics: Understanding the real numbers. In M. Limon, & L. Mason (Eds.), Reconsidering conceptual change: Issues in theory and practice (pp. 233-258). Kluwer.
Norton, S. (2006). Pedagogies for the engagement of girls in the learning of proportional reasoning through technology practice. Mathematics Education Research Journal, 18(3), 69-99. https://doi.org/10.1007/BF03217443
Sari, E. A. P., Juniati, D., & Patahudin, S. M. (2012). Early fractions learning of 3rd grade students in SD Laboratorium Unesa. Indonesian Mathematical Society Journal on Mathematics Education, 3(1), 17-28. https://doi.org/10.22342/jme.3.1.617.17-28
Schmithorst, V. J., & Brown, R. D. (2004). Empirical validation of the triple-code model of numerical processing for complex math operations using functional MRI and group Independent Component Analysis of the mental addition and subtraction of fractions. Neuroimage, 22(3), 1414-1420. https://doi.org/10.1016/j.neuroimage.2004.03.021
Streefland, L. (1984). Unmasking N-distractors as a source of failures in learning fractions. In B. Southwell, R. Eyland, M. Cooper, J. Conroy, & K. Collis (Eds.), Proceedings of the Eighth Annual Conference of the International Conference for the Psychology of Mathematics Education (pp. 142-152). Mathematical Association of New South Wales.
Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5-13. https://doi.org/10.1016/j.learninstruc.2014.03.002
Tunc-Pekkan, Z. (2015). An analysis of elementary school children’s fractional knowledge depicted with circle, rectangle, and number line representations. Educational Studies in Mathematics, 89, 419-441. https://doi.org/10.1007/s10649-015-9606-2
Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31(3), 344–355. https://doi.org/10.1016/j.jmathb.2012.02.001
Vosniadou, S., & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching. Learning and Instruction, 14(5), 445-451. https://doi.org/10.1016/j.learninstruc.2004.06.014
Wong, M., Evans, D., & Anderson, J. (2006). Developing a diagnostic assessment instrument for identifying students’ understanding of fraction equivalence [Paper presentation]. The ACSPRI Social Science Methodology Conference, University of Sydney. http://old.acspri.org.au/conference2006/proceedings/streams/Paper%2019%20wong_monica_submitted.pdf
Zhang, X., Clements, M. K., & Ellerton, N. F. (2015). Conceptual mis(understandings) of fractions: From area models to multiple embodiments. Mathematics Education Research Journal, 27(2), 233-261. https://doi.org/10.1007/s13394-014-0133-8

How to cite this article

APA

Karika, T., & Csíkos, C. (2022). A Test for Understanding Simple Fractions Among 5th Grade Students at the Beginning of Lower Secondary Education. Eurasia Journal of Mathematics, Science and Technology Education, 18(2), em2081. https://doi.org/10.29333/ejmste/11654

Vancouver

Karika T, Csíkos C. A Test for Understanding Simple Fractions Among 5th Grade Students at the Beginning of Lower Secondary Education. EURASIA J Math Sci Tech Ed. 2022;18(2):em2081. https://doi.org/10.29333/ejmste/11654

AMA

Karika T, Csíkos C. A Test for Understanding Simple Fractions Among 5th Grade Students at the Beginning of Lower Secondary Education. EURASIA J Math Sci Tech Ed. 2022;18(2), em2081. https://doi.org/10.29333/ejmste/11654

Chicago

Karika, Tímea, and Csaba Csíkos. "A Test for Understanding Simple Fractions Among 5th Grade Students at the Beginning of Lower Secondary Education". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 2 (2022): em2081. https://doi.org/10.29333/ejmste/11654

Harvard

Karika, T., and Csíkos, C. (2022). A Test for Understanding Simple Fractions Among 5th Grade Students at the Beginning of Lower Secondary Education. Eurasia Journal of Mathematics, Science and Technology Education, 18(2), em2081. https://doi.org/10.29333/ejmste/11654

MLA

Karika, Tímea et al. "A Test for Understanding Simple Fractions Among 5th Grade Students at the Beginning of Lower Secondary Education". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 2, 2022, em2081. https://doi.org/10.29333/ejmste/11654