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Fraction Division Representation-Experience in a Teacher Education Course Focused on the Reference Unit

  • Faria Barcelos Gibim, Gabriela [1] ; Rifo, Laura [1] ; Climent, Nuria [2] ; Ribeiro , Miguel [1]
    1. [1] Universidade Estadual de Campinas

      Universidade Estadual de Campinas

      Brasil

    2. [2] Universidad de Huelva

      Universidad de Huelva

      Huelva, España

  • Localización: REDIMAT, ISSN-e 2014-3621, Vol. 12, Nº. 3, 2023 (Ejemplar dedicado a: October), págs. 193-209
  • Idioma: inglés
  • DOI: 10.17583/redimat.13020
  • Títulos paralelos:
    • Representación de División de Fracciones: Experiencia en un Curso de Formación Docente Centrado en la Unidad de Referencia
  • Enlaces
  • Resumen
    • español

      Este estudio se centra en los conocimientos revelados y desarrollados por profesores de Matemáticas de Primaria, en un curso de formación de profesores relacionados con la representación de la división de fracciones y la flexibilidad de la unidad de referencia. Los docentes resolvieron una tarea destinada a movilizar (y acceder) a sus conocimientos relacionados con sus enfoques del sentido de la división, representación y unidad de referencia respecto a la división de fracciones. Los resultados sugieren que los maestros enfrentan desafíos al representar y justificar divisiones de fracciones usando modelos pictóricos, especialmente cuando el divisor es una fracción no unitaria. Esto se fundamenta en un vacío en cuanto a la flexibilidad de la unidad de referencia a la que se refieren los números en sus representaciones, así como un desafío en cuanto al sentido de la división de fracciones y las diferentes formas de representación. Con esta investigación, pretendemos contribuir a reducir la escasez de estudios empíricos en el área y la importancia del conocimiento de los docentes especializados para tratar este tema.

    • English

      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.

  • Referencias bibliográficas
    • Adu-Gyamfi, K., Schwartz, C. S., Sinicrope, R., & Bossé, M. J. (2019). Making sense of fraction division: domain and representation knowledge...
    • Balll, D. (1988) The subject matter preparation of prospective mathematics teachers: Challenging the myths. The National Center for Research...
    • Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education,...
    • Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice...
    • Bütüner, S.O. (2021). Content and problem analysis in Turkish and Singaporean mathematics textbooks: The case of multiplying fractions. REDIMAT...
    • Carrillo, J. et al. (2018) The mathematics teacher’s specialized knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236–253....
    • Empson, S. B., Junk, D., Dominguez, H., & Turner, E. (2005). Fractions as the coordination of multiplicatively related quantities: A cross-sectional...
    • Fazio, 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
    • Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication...
    • Fuentes, M., & Olmos, P. (2019). La comprensión de la relación inversa en la división en edades tempranas. REDIMAT – Journal of Research...
    • Green, M.; Piel, J. A.; Flowers, C. (2008) Reversing Education Majors' Arithmetic Misconceptions with Short-Term Instruction Using Manipulatives....
    • Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26, 95-143. https://doi.org/10.1080/07370000701798529
    • Jansen, A., & Hohensee, C. (2016). Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive...
    • Lamon, S. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers....
    • Lee, M. Y. (2017). Pre-service teachers’ flexibility with referent units in solving a fraction division problem. Educational Studies in Mathematics,...
    • Lee, S. J., Brown, R. E., & Orrill, C. H. (2011). Mathematics teachers’ reasoning about fractions and decimals using drawn representations....
    • Li, Y., Chen, X., & An, S. (2009). Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and...
    • Li, Y., & Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: the case of fraction division. ZDM Mathematics...
    • Lo, J. J., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education,...
    • Lubinski, C. A., Fox, T., & Thomason, R. (1998). Learning to make sense of division of fractions: One K-8 preservice teacher’s perspective....
    • Ma, L. (1999). Knowing and teaching elementary mathematics. Lawrence Erlbaum.
    • Mellone, M., Tortona, R., Jakobsen, A., & Ribeiro, M. (2017) Prospective teachers interpret student responses: Between assessment, educational...
    • Norton, A., & Hackenberg, A. (2010). Continuing research on students’ fraction schemes. In L. Steffe & J. Olive (Eds.), Children’s...
    • Stohlmann, M.S., Yang, Y., Huang, X., & Olson, T.A. (2019). Fourth to Sixth Grade Teachers’ Invented Real World Problems and Pictorial...
    • Rizvi, N. F., & Lawson, M. J. (2007). Prospective teachers’ knowledge: Concept of division. International Education Journal, 8(2), 377-392....
    • Ribeiro, M., Almeida, A. & Mellone, M. (2021). Conceitualizando Tarefas Formativas para Desenvolver as Especificidades do Conhecimento...
    • Simon, M. A. (1993) Prospective Elementary Teachers’ Knowledge of Division. Journal for Research in Mathematics Education, v. 24, n. 3, p....
    • Sinicrope, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller & G. Bright (Eds.), Making...
    • Shin, L., & Lee, S. J. (2018). The alignment of student fraction learning with textbooks in Korea and United States. Journal of Mathematical...
    • Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research...
    • Turner, F. (2008). Beginning elementary teachers’ use of representations in mathematics teaching. Research in Mathematics Education, 10(2),...
    • Tzur, R., & Hunt, J. H. (2015). Iteration: Unit fraction knowledge and the French fry tasks. Teaching Children Mathematics, 22(3), 149-157....
    • Wahyu, K., Kuzu, T.E., Subarinah, S., Ratnasari, D., & Mahfudy, S. (2020). Partitive Fraction Division: Revealing and Promoting Primary...
    • Wijaya, A., Van den Heuvel-Panhuizen, M., & Doorman, M. (2015) Opportunity-to-learn context-based tasks provided by mathematics textbooks....
    • Wu, H. (1999). Some remarks on the teaching of fractions in elementary school. Available at: http://math.berkeley.edu/~wu/fractions2.pdf
    • Zembat, I. O. (2004). Conceptual development of prospective elementary teachers: The case of division of fractions. [Ph.D. dissertation, The...
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