A cross-national comparison of fourth and eighth grade students’ understanding of fraction magnitude

Rachel Angela Ayieko; Giovanna Moreano; Lauren Harter

doi:10.29333/iejme/12287

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Rachel Angela Ayieko ¹ ^* , Giovanna Moreano ² , Lauren Harter ¹

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¹ Duquesne University, Pittsburgh, PA, USA² Peru Ministry of Education, Lima, PERU^* Corresponding Author

Abstract

Without a conceptual understanding of fraction magnitude, students have difficulties understanding more advanced mathematics in high school and beyond. The purpose of this study is to highlight 4^th and 8^th grade students’ misconceptions in fraction magnitude using the Trends in International Mathematics and Science Study-2015 data. The study is informed by the theory of numerical development that focuses on the understanding of the magnitude of numbers and the recognition of the location of numbers on a number line. The results indicate that fraction magnitude understanding is a challenge at the 8^th grade. Implications for higher education are elaborated.

Keywords

fractions
large scale studies
misconceptions

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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

INT ELECT J MATH ED, 2022, Volume 17, Issue 4, Article No: em0703

https://doi.org/10.29333/iejme/12287

Publication date: 28 Jul 2022

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Article Downloads: 420

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References

Aliustaoglu, F., Tuna, A., & Biber, A. C. (2018). The misconceptions of sixth grade secondary school students on fractions. International Electronic Journal of Elementary Education, 10(5), 591-599. https://doi.org/10.26822/iejee.2018541308
Ayieko, R. A. (2014). The influence of opportunity to learn to teach mathematics on pre-service teachers’ knowledge and belief: A comparative study [PhD dissertation, Michigan State University].
Bailey, D. H., Zhou, X., Zhang, Y., Cui, J., Fuchs, L. S., Jordan, N. C., Gersten, R., & Siegler, R. S. (2015). Development of fraction concepts and procedures in U.S. and Chinese children. Journal of Experimental Child Psychology, 129, 68-83. https://doi.org/10.1016/j.jecp.2014.08.006
Beckmann, S. (2017). Mathematics for elementary teachers with activities. Pearson.
Blömeke, S., & Kaiser, G. (2014). Homogeneity or heterogeneity? Profiles of opportunities to learn in primary teacher education and their relationship to cultural context and outcomes. In S. Blömeke, F.-J. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 299-325). Springer. https://doi.org/10.1007/978-94-007-6437-8_14
Durkin, K., & Rittle-Johnson, B. (2015). Diagnosing misconceptions: Revealing changing decimal fraction knowledge. Learning and Instruction, 37, 21-29. https://doi.org/10.1016/j.learninstruc.2014.08.003
Fazio, L., & Siegler, R. (2011). Teaching fractions. Educational practices series-22. UNESCO International Bureau of Education.
Green, M., Piel, J. A., & Flowers, C. (2008). Reversing education majors’ arithmetic misconceptions with short-term instruction using manipulatives. The Journal of Educational Research, 101(4), 234-242. https://doi.org/10.3200/JOER.101.4.234-242
Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843-859. https://doi.org/10.1037/a0019824
Holmes, V.-L., Miedema, C., Nieuwkoop, L., & Haugen, N. (2013). Data-driven intervention: Correcting mathematics students’ misconceptions, not mistakes. The Mathematics Educator, 23(1), 24-44.
Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143. https://doi.org/10.1080/07370000701798529
Kloosterman, P. (2010). Mathematics skills of 17-year-olds in the United States: 1978 to 2004. Journal for Research in Mathematics Education, 41(1), 20-51. https://doi.org/10.5951/jresematheduc.41.1.0020
Li, X., & Li, Y. (2008). Research on students’ misconceptions to improve teaching and learning in school mathematics and science. School Science and Mathematics, 108(1), 4-7. https://doi.org/10.1111/j.1949-8594.2008.tb17934.x
Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422-441. https://doi.org/10.2307/749431
Mohyuddin, R. G., & Khalil, U. (2016). Misconceptions of students in learning mathematics at primary level. Bulletin of Education and Research, 38(1), 133-162.
Ozkan, M., & Bal, A. P. (2016). Analysis of the misconceptions of 7th grade students on polygons and specific quadrilaterals. Eurasian Journal of Educational Research, 16(67), 161-182. https://doi.org/10.14689/ejer.2017.67.10
Perso, T. (1992). Making the most of errors. Australian Mathematics Teacher, 48(2), 12-14.
Rhine, S., Harrington, R., & Starr, C. (2018). How students think when doing algebra. IAP.
Saenz-Ludlow, A. (1994). Michael’s fraction schemes. Journal for Research in Mathematics Education, 25(1), 50-85. https://doi.org/10.2307/749292
Siegler, R. S., & Pyke, A. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49(10), 1994-2004. https://doi.org/10.1037/a0031200
Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296. https://doi.org/10.1016/j.cogpsych.2011.03.001
Zhang, X., Clements, M. A. (K.), & Ellerton, N. F. (2015a). Engaging students with multiple models of fractions. Teaching Children Mathematics, 22(3), 138-147. https://doi.org/10.5951/teacchilmath.22.3.0138
Zhang, X., Clements, M. A. (K.), & Ellerton, N. F. (2015b). Enriching student concept images: Teaching and learning fractions through a multiple-embodiment approach. Mathematics Education Research Journal, 27, 201-231. https://doi.org/10.1007/s13394-014-0137-4

How to cite this article

APA

Ayieko, R. A., Moreano, G., & Harter, L. (2022). A cross-national comparison of fourth and eighth grade students’ understanding of fraction magnitude. International Electronic Journal of Mathematics Education, 17(4), em0703. https://doi.org/10.29333/iejme/12287

Vancouver

Ayieko RA, Moreano G, Harter L. A cross-national comparison of fourth and eighth grade students’ understanding of fraction magnitude. INT ELECT J MATH ED. 2022;17(4):em0703. https://doi.org/10.29333/iejme/12287

AMA

Ayieko RA, Moreano G, Harter L. A cross-national comparison of fourth and eighth grade students’ understanding of fraction magnitude. INT ELECT J MATH ED. 2022;17(4), em0703. https://doi.org/10.29333/iejme/12287

Chicago

Ayieko, Rachel Angela, Giovanna Moreano, and Lauren Harter. "A cross-national comparison of fourth and eighth grade students’ understanding of fraction magnitude". International Electronic Journal of Mathematics Education 2022 17 no. 4 (2022): em0703. https://doi.org/10.29333/iejme/12287

Harvard

Ayieko, R. A., Moreano, G., and Harter, L. (2022). A cross-national comparison of fourth and eighth grade students’ understanding of fraction magnitude. International Electronic Journal of Mathematics Education, 17(4), em0703. https://doi.org/10.29333/iejme/12287

MLA

Ayieko, Rachel Angela et al. "A cross-national comparison of fourth and eighth grade students’ understanding of fraction magnitude". International Electronic Journal of Mathematics Education, vol. 17, no. 4, 2022, em0703. https://doi.org/10.29333/iejme/12287