Underprepared College Students’ Understanding of and Misconceptions with Fractions

Hea-Jin Lee; Irina Boyadzhiev

doi:10.29333/iejme/7835

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Hea-Jin Lee ¹ ^* , Irina Boyadzhiev ¹

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¹ Ohio State University, Lima, USA^* Corresponding Author

Abstract

This study investigated understanding of and misconceptions with fractions in college students enrolled in a remedial mathematics course. Data were collected from 22 college students for one semester. The analysis of 41 fraction problems revealed that participants’ common misconceptions were associated with a lack of understanding of basic definition of fractions, least common denominators/least common multiples, and order of operations. In addition, some students were able to recall the procedures but could not compute fractions accurately due to the misconceptions listed above.

Keywords

remedial class
underprepared students
fraction computational skills
misconceptions about fraction

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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, 2020, Volume 15, Issue 3, Article No: em0583

https://doi.org/10.29333/iejme/7835

Publication date: 17 Mar 2020

Article Views: 3465

Article Downloads: 3165

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References

Achieve, Inc. (2005). Rising to the challenge: Are high school graduates prepared for college and work? Washington, DC: Author.
Achieve, Inc. (2015). Closing the expectations gap: 2014 annual report on the alignment of state K-12 policies and practice with the demands of college and careers. Washington, DC: Author.
Ameis, J. A. (2011). The Truth about PEMDAS, Mathematics Teaching in the Middle School, 17(7), 414-420.
Georgia Department of Education (2012) Georgia Performance Standards. Retrieved from https://www.georgiastandards.org/Pages/default.aspx
Bonato, M., Fabbri, S., Umilta, C., & Zorzi, M. (2007). The mental representation of numerical fractions: real or integer? Journal of Experimental Psychology: Human Perception and Performance, 33(6), 1410-1419. https://doi.org/10.1037/0096-1523.33.6.1410
Chen, X. (2016). Remedial Course taking at U.S. Public 2- and 4-Year Institutions: Scope, Experiences, and Outcomes (NCES 2016-405). U.S. Department of Education. Washington, DC: National Center for Education Statistics.
Conley, D. (2008). Rethinking College Readiness. New Directions for Higher Education, 144, 3-12. https://doi.org/10.1002/he.321
Creswell, J. W. (1994). Research design: qualitative and quantitative approaches. Thousand Oaks: Sage Publications.
Creswell, J. W. (2015). A concise introduction to mixed methods research. Thousand Oaks, CA: Sage.
DeWolf, D., & Vosniadou, S. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39-29. https://doi.org/10.1016/j.learninstruc.2014.07.002
Ding, Y., & Moore-Russo, D. (2017). Evaluating College Students’ Confidence Judgement of Fraction. In E. Galindo, & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators. Retrieved from https://www.pmena.org/pmenaproceedings/PMENA%2039%202017%20Proceedings.pdf
Eryilmaz, A. (2002). Effects of conceptual assignments and conceptual change discussions on students’ misconceptions and achievement regarding force and motion. Journal of Research in Science Teaching, 39, 1001-1015. https://doi.org/10.1002/tea.10054
Fazio, L. K., & Siegler, R. S. (2011). Teaching fractions. In Educational practices series (Vol. 22); (pp. 1-28). Geneva: International Academy of Education-International Bureau of Education.
Garfield, J., & Ben-Zvi, D (2007). How Students Learn Statistics Revisited: A Current Review of Research on Teaching and Learning Statistics. International Statistical Review, 75, 372-396. https://doi.org/10.1111/j.1751-5823.2007.00029.x
Hiebert, J., & Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 199-223). Hillsdale, NJ: Lawrence Erlbaum Associates.
Hoosain, E., & Naraine, B. (2012). Teachers’ and students’ knowledge and understanding of order of operations. Review of Higher Education and Self-Learning, 5(15), 84-89.
Howard, L., & Whitaker, M. (2011). Unsuccessful and successful mathematics learning: Developmental students’ perception. Journal of Developmental Education, 35(2), 2-16.
Hoyt, J., & Sorensen, T. (2001). High school preparation, placement testing, and college remediation. Journal of Developmental Education, 25(2), 26-33.
Irwin, K. C. (2001). Using everyday knowledge of decimals to enhance under-standing. Journal for Research in Mathematics Education, 32, 399-420. https://doi.org/10.2307/749701
Kajander, A., & Lovric, M. (2005). Transition from secondary to tertiary mathematics: McMaster University experience. International Journal of Mathematics Education in Science and Technology, 36(2-3), 149-160. https://doi.org/10.1080/00207340412317040
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Retrieved from https://www.nap.edu/catalog/9822/adding-it-up-helping-children-learn-mathematics
Lee, H. J., & Boyadzhiev, I. (2015). Making sense of fractions with GeoGebra in the USA. Mathematics Teaching, 244, 29-32.
Mack, N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422e441. https://doi.org/10.2307/749431
Martin, W. G., Strutchens, M. E., & Elliot, P. C. (2007). The Learning of Mathematics, 69th Yearbook. Reston, VA: National Council of Teachers of Mathematics.
McNeil, N. M., & Alibali, M. W. (2005). Why won’t you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development, 76(4), 883-899. https://doi.org/10.1111/j.1467-8624.2005.00884.x
Meert, G., Gregoire, J., & No€el, M. P. (2010). Comparing 5/7 and 2/9: adults can do it by accessing the magnitude of the whole fractions. Acta Psychologica, 135(3), 284-292. https://doi.org/10.1016/j.actpsy.2010.07.014
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors. Retrieved from http://www.corestandards.org/Math/
Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: the origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52. https://doi.org/10.1207/s15326985ep4001_3
Panaoura, A., Gagatsis, A., Deliyianni, E., & Elia, I. (2009). The structure of students’ beliefs about the use of representations and their performance on the learning of fractions, Educational Psychology: An International Journal of Experimental Educational Psychology, 29, 713-728. https://doi.org/10.1080/01443410903229437
Rambhia, S. (2002). A New Approach to an Old Order, Mathematics Teaching in the Middle School, 8(4), 193-195.
Richland, L., Stigler, J., & Holyoak, K. (2012). Teaching the conceptual structure of mathematics. Educational Psychologist, 47(3), 189-203. https://doi.org/10.1080/00461520.2012.667065
Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107, 909-918. https://doi.org/10.1037/edu0000025
Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of numerical value of fractions. Learning and Instruction, 14(5), 503-518. https://doi.org/10.1016/j.learninstruc.2004.06.015
Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation. Cognition and Instruction, 28(2), 181-209. https://doi.org/10.1080/07370001003676603
Vosniadou, S., & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching. Learning and Instruction, 14(5), 445-451.

How to cite this article

APA

Lee, H.-J., & Boyadzhiev, I. (2020). Underprepared College Students’ Understanding of and Misconceptions with Fractions. International Electronic Journal of Mathematics Education, 15(3), em0583. https://doi.org/10.29333/iejme/7835

Vancouver

Lee HJ, Boyadzhiev I. Underprepared College Students’ Understanding of and Misconceptions with Fractions. INT ELECT J MATH ED. 2020;15(3):em0583. https://doi.org/10.29333/iejme/7835

AMA

Lee HJ, Boyadzhiev I. Underprepared College Students’ Understanding of and Misconceptions with Fractions. INT ELECT J MATH ED. 2020;15(3), em0583. https://doi.org/10.29333/iejme/7835

Chicago

Lee, Hea-Jin, and Irina Boyadzhiev. "Underprepared College Students’ Understanding of and Misconceptions with Fractions". International Electronic Journal of Mathematics Education 2020 15 no. 3 (2020): em0583. https://doi.org/10.29333/iejme/7835

Harvard

Lee, H.-J., and Boyadzhiev, I. (2020). Underprepared College Students’ Understanding of and Misconceptions with Fractions. International Electronic Journal of Mathematics Education, 15(3), em0583. https://doi.org/10.29333/iejme/7835

MLA

Lee, Hea-Jin et al. "Underprepared College Students’ Understanding of and Misconceptions with Fractions". International Electronic Journal of Mathematics Education, vol. 15, no. 3, 2020, em0583. https://doi.org/10.29333/iejme/7835