Preservice Elementary Teachers’ Understanding of Fraction Multiplication and Division in Multiple Contexts
Keywords:
Preservice elementary teachers, teacher knowledge, fraction multiplication, fraction division, teaching practiceAbstract
The present study examined preservice elementary teachers’ performance on the problems of multiplication and division of fractions and compared their performances and analyzed the misconceptions. An instrument including 11 fraction multiplication and division tasks was given and the task involved three contexts: making own story problem, computations, representing operation using visual model. The findings reported that among the three contexts, making a diagram was the most challenging task for both operations, and their division performance varied depending on the division problem types. The author suggests that specific emphasis with rich story problem with different whole(s) in fraction, carefully designed context with different types of division concept, and building fractional number sense can help both PSTs and students reduce misconceptions and enhance deeper understanding of fraction operations
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References
Adu-Gyamfi, K., Schwartz, C. S., Cinicrope, 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.
Ball, D. L. (1990a) The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466
Cengiz, N. C. & Rathouz, M. (2011). Take a bite out of fraction division. Mathematics teaching in the middle school, 17 (3), 146–153.
Common Core State Standards Initiative [CCSSI]. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. Retrieved February 21, 2017, http://corestandards.org/assets/CCSSI_Math%20 Standards.pdf
Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102.
Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143
Kent, L. B, Empson, S.B., & Nielsen L. (2015). Richness of children’s fraction strategies, Teaching Children Mathematics, 22 (2), 84-90.
Lee, M. Y. (2017). Preservice teachers’ flexibility with referent units in solving a fraction division problem. Educational Studies in Mathematics, 96, 327-348.
Lee, M. Y., & Lee, J. E. (2021). Spotlight on area models: Pre-service teachers’ ability to link fractions and geometric measurement. International Journal of Science and Mathematics Education, 19(5), 1079-1102.
Lee, 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.
Lo, J. J., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15(6), 481–500.
Luo, F., Lo, J., & Leu, Y. (2011) Fundamental fraction knowledge of preservice elementary teachers: A cross-national study in the United States and Taiwan. School science and mathematics, 111(4), 164-177
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the Unites States. Mahwah, NJ: Lawrence Erlbaum.
Mack, N. K. (1998). Building a foundation for understanding the multiplication of fractions. Teaching Children Mathematics, 5(1), 34-38
Mack, N. K. (2001). Building informal knowledge through instruction in a complex content domain: partitioning, units, and understanding multiplication of fractions. Journal for research in mathematics education, 32 (3), 267-295.
Morano, S., & Riccomini, P. J. (2020). Demonstrating conceptual understanding of fraction arithmetic: An analysis of pre-service special and general educators’ visual representations. Teacher Education and Special Education, 43(4), 314-331.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VAL Author.
Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions, American Educational Research Journal, 45 (5), 1080-1110
Park, J., Gucler, B., & McCrory, R. (2013). Teaching prospective teachers about fractions: historical and pedagogical perspectives, Educational Studies in Mathematics, 82 (3), 455-479.
Seaman, C. E., & Szydlik, J. E. (2007). Mathematical sophistication among preservice elementary teachers. Journal of Mathematics Teacher Education, 10(3), 167–182.
Son, J. W., & Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235–261.
Son, J. W., & Lee, J. E. (2016). Preservice teachers understanding of fraction multiplication, representational knowledge, and computational skills. Mathematics Teacher Education and Development, 18(2), 5-28.
Tirosh, D., & Graeber, A. O. (1990). Evoking cognitive conflict to explore preservice teachers' thinking about division. Journal for Research in Mathematics Education, 21(2), 98-108.
Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.) Boston, MA: Pearson Allyn & Bacon
Yao, Y., Hwang, S., & Cai, J. (2021). Preservice teachers’ mathematical understanding exhibited in problem posing and problem solving. ZDM–Mathematics Education, 1-13.
Ball, D. L. (1990a) The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466
Cengiz, N. C. & Rathouz, M. (2011). Take a bite out of fraction division. Mathematics teaching in the middle school, 17 (3), 146–153.
Common Core State Standards Initiative [CCSSI]. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. Retrieved February 21, 2017, http://corestandards.org/assets/CCSSI_Math%20 Standards.pdf
Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102.
Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143
Kent, L. B, Empson, S.B., & Nielsen L. (2015). Richness of children’s fraction strategies, Teaching Children Mathematics, 22 (2), 84-90.
Lee, M. Y. (2017). Preservice teachers’ flexibility with referent units in solving a fraction division problem. Educational Studies in Mathematics, 96, 327-348.
Lee, M. Y., & Lee, J. E. (2021). Spotlight on area models: Pre-service teachers’ ability to link fractions and geometric measurement. International Journal of Science and Mathematics Education, 19(5), 1079-1102.
Lee, 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.
Lo, J. J., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15(6), 481–500.
Luo, F., Lo, J., & Leu, Y. (2011) Fundamental fraction knowledge of preservice elementary teachers: A cross-national study in the United States and Taiwan. School science and mathematics, 111(4), 164-177
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the Unites States. Mahwah, NJ: Lawrence Erlbaum.
Mack, N. K. (1998). Building a foundation for understanding the multiplication of fractions. Teaching Children Mathematics, 5(1), 34-38
Mack, N. K. (2001). Building informal knowledge through instruction in a complex content domain: partitioning, units, and understanding multiplication of fractions. Journal for research in mathematics education, 32 (3), 267-295.
Morano, S., & Riccomini, P. J. (2020). Demonstrating conceptual understanding of fraction arithmetic: An analysis of pre-service special and general educators’ visual representations. Teacher Education and Special Education, 43(4), 314-331.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VAL Author.
Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions, American Educational Research Journal, 45 (5), 1080-1110
Park, J., Gucler, B., & McCrory, R. (2013). Teaching prospective teachers about fractions: historical and pedagogical perspectives, Educational Studies in Mathematics, 82 (3), 455-479.
Seaman, C. E., & Szydlik, J. E. (2007). Mathematical sophistication among preservice elementary teachers. Journal of Mathematics Teacher Education, 10(3), 167–182.
Son, J. W., & Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235–261.
Son, J. W., & Lee, J. E. (2016). Preservice teachers understanding of fraction multiplication, representational knowledge, and computational skills. Mathematics Teacher Education and Development, 18(2), 5-28.
Tirosh, D., & Graeber, A. O. (1990). Evoking cognitive conflict to explore preservice teachers' thinking about division. Journal for Research in Mathematics Education, 21(2), 98-108.
Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.) Boston, MA: Pearson Allyn & Bacon
Yao, Y., Hwang, S., & Cai, J. (2021). Preservice teachers’ mathematical understanding exhibited in problem posing and problem solving. ZDM–Mathematics Education, 1-13.
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Published
2023-01-19
How to Cite
Kang, H. J. (2023). Preservice Elementary Teachers’ Understanding of Fraction Multiplication and Division in Multiple Contexts. International Electronic Journal of Elementary Education, 15(2), 109–121. Retrieved from https://iejee.com/index.php/IEJEE/article/view/1918
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