Fraction Division Representation-Experience in a Teacher Education Course Focused on the Reference Unit
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Abstract
This study focuses on the knowledge revealed and developed by Elementary Mathematics
teachers, in a teacher education course related to the representation of fraction division and
the flexibility of the reference unit. The teachers solved a task aimed at mobilizing (and
accessing) their knowledge related to their approaches to the sense of division, representation,
and reference unit regarding fraction division. The results suggest that teachers face
challenges when representing and justifying fraction divisions using pictorial models,
especially when the divisor is a non-unit fraction. This is based in a gap regarding the
flexibility of the reference unit to which the numbers refer in their representations, as well as
a challenge concerning the sense of fraction division and the different forms of
representation. With this research we intend to contribute to reducing the scarcity of
empirical studies in the area and the importance of this specialized teachers’ knowledge to
deal with this topic.
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Adu-Gyamfi, K., Schwartz, C. S., Sinicrope, R., & Bossé, M. J. (2019). Making sense of fraction division: domain and representation knowledge of preservice elementary teachers on a fraction division task. Mathematics Education Research Journal, 31, 507-528. https://doi.org/10.1007/S13394-019-00265-2
Google Scholar CrossrefBalll, D. (1988) The subject matter preparation of prospective mathematics teachers: Challenging the myths. The National Center for Research on Teacher Education. https://eric.ed.gov/?id=ED301468
Google Scholar CrossrefBall, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144. https://doi.org/10.2307/749140
Google Scholar CrossrefBorko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23, 194–222. https://doi.org/10.2307/749384
Google Scholar CrossrefBütüner, S.O. (2021). Content and problem analysis in Turkish and Singaporean mathematics textbooks: The case of multiplying fractions. REDIMAT – Journal of Research in Mathematics Education, 10(2), 117-151. https://doi.org/10.17583/redimat.2021.4379
Google Scholar CrossrefCarrillo, J. et al. (2018) The mathematics teacher’s specialized knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236–253. https://doi.org/10.1080/14794802.2018.1479981
Google Scholar CrossrefEmpson, S. B., Junk, D., Dominguez, H., & Turner, E. (2005). Fractions as the coordination of multiplicatively related quantities: A cross-sectional study of children’s thinking. Educational Studies in Mathematics, 63(1), 1-28. https://www.jstor.org/stable/25472109
Google Scholar CrossrefFazio, L. & Siegler, R. (2011). Educational practices series: teaching fractions. International Bureau of Education. http://alearningplace.com.au/wp-content/uploads/2021/01/Teaching-Fractions-Fazio-Steigler.pdf
Google Scholar CrossrefFischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17. https://doi.org/10.2307/748969
Google Scholar CrossrefFuentes, M., & Olmos, P. (2019). La comprensión de la relación inversa en la división en edades tempranas. REDIMAT – Journal of Research in Mathematics Education, 8(3), 267-292. http://dx.doi.org/10.17583/redimat.2019.4546
Google Scholar CrossrefGreen, M.; Piel, J. A.; Flowers, C. (2008) Reversing Education Majors' Arithmetic Misconceptions with Short-Term Instruction Using Manipulatives. Journal of Educational Research, 101(4), 234-242. https://doi.org/10.3200/JOER.101.4.234-242
Google Scholar CrossrefIzsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26, 95-143. https://doi.org/10.1080/07370000701798529
Google Scholar CrossrefJansen, A., & Hohensee, C. (2016). Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions. Journal of Mathematics Teacher Education, 19(6), 503-522. https://doi.org/10.1007/s10857-015-9312-0
Google Scholar CrossrefLamon, S. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Lawrence Erlbaum Associates Publishers. https://doi.org/10.4324/9780203803165
Google Scholar CrossrefLee, M. Y. (2017). Pre-service teachers’ flexibility with referent units in solving a fraction division problem. Educational Studies in Mathematics, 96, 327-348. https://link.springer.com/journal/10649
Google Scholar CrossrefLee, S. J., Brown, R. E., & Orrill, C. H. (2011). Mathematics teachers’ reasoning about fractions and decimals using drawn representations. Mathematical Thinking and Learning, 13(3), 198-220. https://doi.org/10.1080/10986065.2011.564993
Google Scholar CrossrefLi, Y., Chen, X., & An, S. (2009). Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: the case of fraction division. ZDM Mathematics Education, 41, 809-826. https://link.springer.com/journal/11858
Google Scholar CrossrefLi, Y., & Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: the case of fraction division. ZDM Mathematics Education, 40, 833-843. http://dx.doi.org/10.1007/s11858-008-0148-2
Google Scholar CrossrefLo, J. J., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15(6), 481-500 https://link.springer.com/journal/10857
Google Scholar CrossrefLubinski, C. A., Fox, T., & Thomason, R. (1998). Learning to make sense of division of fractions: One K-8 preservice teacher’s perspective. School Science and Mathematics, 98(5), 247–251. https://doi.org/10.1111/J.1949-8594.1998.TB17298.X
Google Scholar CrossrefMa, L. (1999). Knowing and teaching elementary mathematics. Lawrence Erlbaum.
Google Scholar CrossrefMellone, M., Tortona, R., Jakobsen, A., & Ribeiro, M. (2017) Prospective teachers interpret student responses: Between assessment, educational design and research. In: CERME, 10, Dublin, Ireland. https://hal.science/hal-01949034
Google Scholar CrossrefNorton, A., & Hackenberg, A. (2010). Continuing research on students’ fraction schemes. In L. Steffe & J. Olive (Eds.), Children’s Tractional Knowledge (pp. 341–352). Springer Media. https://link.springer.com/chapter/10.1007/978-1-4419-0591-8_11
Google Scholar CrossrefStohlmann, M.S., Yang, Y., Huang, X., & Olson, T.A. (2019). Fourth to Sixth Grade Teachers’ Invented Real World Problems and Pictorial Representations for Fraction Division. International Electronic Journal of Mathematics Education, v15(1), em 0557. https://doi.org/10.29333/iejme/5939
Google Scholar CrossrefRizvi, N. F., & Lawson, M. J. (2007). Prospective teachers’ knowledge: Concept of division. International Education Journal, 8(2), 377-392. http://www.iejcomparative.org
Google Scholar CrossrefRibeiro, M., Almeida, A. & Mellone, M. (2021). Conceitualizando Tarefas Formativas para Desenvolver as Especificidades do Conhecimento Interpretativo e Especializado do Professor. Perspectivas da Educação Matemática,14(35), 1-32. https://doi.org/10.46312/pem.v14i35.13263
Google Scholar CrossrefSimon, M. A. (1993) Prospective Elementary Teachers’ Knowledge of Division. Journal for Research in Mathematics Education, v. 24, n. 3, p. 233–254. https://doi.org/10.2307/749346
Google Scholar CrossrefSinicrope, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp. 153–161). National Council of Teachers of Mathematics.
Google Scholar CrossrefShin, L., & Lee, S. J. (2018). The alignment of student fraction learning with textbooks in Korea and United States. Journal of Mathematical Behavior, 51, 129-149. https://doi.org/10.1016/j.jmathb.2017.11.005
Google Scholar CrossrefTirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research of Mathematics Education, 31(1), 5-25. http://dx.doi.org/10.2307/749817
Google Scholar CrossrefTurner, F. (2008). Beginning elementary teachers’ use of representations in mathematics teaching. Research in Mathematics Education, 10(2), 209-210. http://dx.doi.org/10.1080/14794800802233795
Google Scholar CrossrefTzur, R., & Hunt, J. H. (2015). Iteration: Unit fraction knowledge and the French fry tasks. Teaching Children Mathematics, 22(3), 149-157. https://doi.org/10.5951/teacchilmath.22.3.0148
Google Scholar CrossrefWahyu, K., Kuzu, T.E., Subarinah, S., Ratnasari, D., & Mahfudy, S. (2020). Partitive Fraction Division: Revealing and Promoting Primary Students’ Understanding. Journal on Mathematics Education, 11(2), 237-258. http://dx.doi.org/10.22342/jme.11.2.11062.237-258
Google Scholar CrossrefWijaya, A., Van den Heuvel-Panhuizen, M., & Doorman, M. (2015) Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics. http://dx.doi.org/10.1007/s10649-015-9595-1
Google Scholar CrossrefWu, H. (1999). Some remarks on the teaching of fractions in elementary school. Available at: http://math.berkeley.edu/~wu/fractions2.pdf
Google Scholar CrossrefZembat, I. O. (2004). Conceptual development of prospective elementary teachers: The case of division of fractions. [Ph.D. dissertation, The Pennsylvania State University]. https://etda.libraries.psu.edu/files/final_submissions/2428
Google Scholar CrossrefPublished
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