Dividing Fractions Using an Area Model: A look at In-service Teachers’ Understanding


  • Teruni Lamberg
  • Lynda Wiest University of Nevada


This study investigated the thinking of elementary and middle school teachers in relation to solving a fraction-division problem using an area model. The teachers experienced some difficulty making meaning of the area model and expressing the quotient in terms of an appropriate referent unit. Discussion was integral to understanding the area model and the quotient during the problem-solving process.


Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.

Chamberlin, M. (2009). Teachers’ reflections on their mathematical learning experiences in a professional development course. Mathematics Teacher Education and Development, 11, 22-35.

Corbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Thousand Oaks, CA: Sage.

Cramer, K., Monson, D., Whitney, S., Leavitt, S., & Wyberg, T. (2010). Dividing fractions and problem solving. Mathematics Teaching in the Middle School, 15(6), 338-346.

Fazio, L., & Siegler, R. (2011). Teaching fractions. Belley, France: Gonnet Imprimeur.

Fosnot, C. T., & Dolk, M. (2002). Young mathematicians at work: Constructing fractions, decimals, and percents. Portsmouth, NH: Heinemann.

Lamon, S. J. (2012). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (3rd ed.). New York: Routledge.

Lee, S.-J., & Orrill, C. H. (2009). Middle grade teachers’ reorganization of measurement: Fraction division concepts. Swars, S. L., Stinson, D. W., & Lemons-Smith, S. (Eds.). (2009). Proceedings of the 31st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (vol. 5; pp. 1370-1377). Atlanta, GA: Georgia State University.

Li, Y. (2008). What do students need to learn about division of fractions? Mathematics Teaching in the Middle School, 13 (9), 546-552.

Orrill, C. H., de Araujo, Z., & Jacobson, E. D. (2010, April). Teachers’ emerging understanding of fractions division as proportional reasoning in professional development. Paper presented at the Annual Meeting of the American Educational Research Association, San Diego.

Perlwitz, M. D. (2005). Dividing fractions: Reconciling self-generated solutions with algorithmic answers. Mathematics Teaching in the Middle School, 10(6), 278-283.

Petit, M. M., Laird, R. E., & Marsden, E. L. (2010). A focus on fractions: Bringing research to the classroom. New York: Routledge.

Philipp, R. A. (2008). Motivating prospective elementary school teachers to learn mathematics by focusing upon children’s mathematical thinking. Issues in Teacher Education, 17(2), 7-26.

Rizvi, N. F., & Lawson, M. J. (2007). Prospective teachers’ knowledge: Concept of division. International Educational Journal, 8(2), 377-392.

Sharp, J., & Adams, B. (2002). Children's constructions of knowledge for fraction division after solving realistic problems. Journal of Educational Research, 95(6), 333-347.

Son, J.-W. (2011). A global look at math instruction. Teaching Children Mathematics, 17(6), 360-370.

Van de Walle, J. A., Karp, K. M., Bay-Williams, J. M. (2008). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Boston: Pearson.

Wu, H. (2011). The mis-education of mathematics teachers. Notices of the AMS, 58(3), 372-384.

Yimer, A. (2009). Engaging in-service teachers in mathematical problem-solving activities during professional development programs. Journal of Mathematics Education, 2(1), 99-114.