Pre-Service Teachers Making Sense of Fraction Division with Remainders

• Autores: Nesrin Sahin, Rebecca Gault, Laura Tapp, Juli K. Dixon
• Localización: International Electronic Journal of Mathematics Education, ISSN-e 1306-3030, Vol. 15, Nº. 1, 2020
• Idioma: inglés
• Enlaces
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• Resumen

  • This study reports an analysis of how pre-service teachers (n=34) made sense of fraction division with remainders using pictorial modeling strategies, and how small-group and whole-class discussion helped them develop conceptual understanding. One and a half class sessions were video recorded, and 12 interviews were conducted. Results indicate that pre-service teachers can develop a conceptual understanding of fraction division with remainders using modeling strategies, and their understanding emerges in three levels: a) level one: ignoring the remainder or labeling it incorrectly; b) level two: interpreting the remainder in the original unit but not relating it to the new unit; and c) level three: interpreting the remainder both in the original unit and the new unit flexibly.

• Referencias bibliográficas
  • Ball, D. L. (1990). The mathematical understandings that preservice teachers bring to teacher education. The Elementary School Journal, 90(4),...
  • Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in Teaching and Learning to Teach: Knowing and Using Mathematics. In...
  • Blanton, M. L. (2002). Using an undergraduate geometry course to challenge pre-service teachers’ notions of discourse. Journal of Mathematics...
  • Cramer, K., Monson, D., Whitney, S., Leavitt, S., & Wyberg, T. (2010). Dividing fractions and problem solving. Mathematics Teaching in...
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five traditions (2nd ed.) Thousand Oaks, CA: Sage.
  • Dixon, J. K., & Tobias, J. M. (2013). The Whole Story: Understanding Fraction Computation. Mathematics Teaching in the Middle School,...
  • Dixon, J. K., Egendoerfer, L. S., & Clements, T. (2009). Do they really need to raise their hands? Challenging a traditional social norm...
  • Elashhab, G. A. (1978). Division of Fractions—Discovery and Verification. School Science and Mathematics, 78(2), 159-162. https://doi.org/10.1111/j.1949-8594.1978.tb09334.x
  • Hanselman, C. (1997). Stop Using Foul Language in the Mathematics Classroom. Mathematics Teaching in the Middle School, 3(2), 154-160.
  • Lamon, S. (2007). Rational numbers and proportional reasoning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and...
  • Li, Y., & Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: the case of fraction division. ZDM-The International...
  • 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. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States....
  • National Governors Association (NGA) Center for Best Practices & Council of Chief State School Officers (CCSSO). (2010). Common core state...
  • National Mathematics Advisory Panel (NMAP). (2008). Foundations for success: The final report of the National Mathematics Advisory Panel....
  • National Research Council (NRC). (2001). Adding It Up: Helping Children Learn Mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.)....
  • Nillas, L. (2003). Division of Fractions: Preservice Teachers’ Understanding and Use of Problem Solving Strategies. The Mathematics Educator,...
  • Nolan, K. (2012). Dispositions in the field: Viewing mathematics teacher education through the lens of Bourdieu’s social field theory. Educational...
  • Olanoff, D. A. (2011). Mathematical Knowledge for Teaching Teachers: The Case of Multiplication and Division of Fractions (Unpublished doctoral...
  • Rayner, V., Pitsolantis, N., & Osana, H. (2009). Mathematics anxiety in preservice teachers; Its relationship to their conceptual and...
  • Riddle, M., & Rodzwell, B. (2000). Fractions: What happens between kindergarten and the army?. Teaching children mathematics, 7(4), 202.
  • Sharp, J., & Adams, B. (2002). Children’s constructions of knowledge for fraction division after solving realistic problems. The Journal...
  • Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909....
  • Wachira, P., Pourdavood, R. G., & Skitzki, R. (2013). Mathematics teacher’s role in promoting classroom discourse. International Journal...
  • Warrington, M. A. (1997). How Children Think about Division with Fractions. Mathematics Teaching in the Middle School, 2(6), 390-94.
  • Wearne, D., & Kouba, V. L. (2000). Rational Numbers. In E. A. Silver and P. A. Kenny (Eds.), Results from the Seventh Mathematics Assessment...
  • Wheeldon, D. A. (2008). Developing mathematical practices in a social context. [electronic resource] : an instructional sequence to support...
  • Woleck, K. R. (2001). Listen to their pictures: An investigation of children’s mathematical drawings. In A. A. Cuoco & F. R. Curcio (Eds.),...