Sumeyra Dogan Coskun


The current study aims to examine meanings and error types associated with pre-service elementary teachers’ semi-structured problems for the multiplication and division of fractions. A total of 83 junior pre-service elementary teachers were recruited in the spring semester of the 2016-2017 academic year. A researcher-developed Problem Posing Test consisting of eight items was used to collect the data of this study. The findings indicated that the pre-service elementary teachers were not proficient in posing appropriate problems for the multiplication and division of fractions. Furthermore, while the most frequent error type found was a failure in expressing the multiplication operation in the question root for the multiplication of fractions, it was assigning natural number meaning to fractions for the division of fractions.


Article visualizations:

Hit counter



error types, multiplication of fractions, division of fractions, problem posing

Full Text:



Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers' problem solving performance. Journal of Science and Mathematics Education, 25(1), 56-69.

Barlow, A. T., & Cates, J. M. (2006). The impact of problem posing on elementary teachers' beliefs about mathematics and mathematics teaching. School Science and Mathematics, 106(2), 64-73.

Brown, S. I., & Walter, M. I. (1993). Problem posing: Reflection and application. Hillsdale, NJ: Erlbaum Associates.

Bulgar, S. (2003). Children’s sense-making of division of fractions. The Journal of Mathematical Behavior, 22(3), 319-334.

Cathcart, W. G., Pothier, V. M., Vance, T. H., & Bezuk, N. S. (2003). Learning mathematics in elementary and middle schools. (3rd Ed.) River, N.J: Merrill/Prentice Hall.

Chapman, O. (2012). Prospective elementary school teachers ways of making sense of mathematical problem posing. Pna, 6(4), 135-146.

Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing process. ZDM-The International Journal on Mathematics Education, 37(3), 149-158.

Cunningham, R. F. (2004). Problem posing: An opportunity for increasing student responsibility. Mathematics and Computer Education, 38(1), 83-89.

Darley, J. W. (2005). Ninth graders' interpretations and use contextualized models of fractions and algebraic properties: A classroom-based approach. Available from ProQuest Dissertations & Theses Global. (305415727).

De Lange, J. (2003). Mathematics for literacy. In B. L. Madison & L. A. Steen (Eds.), Quantitative literacy: Why numeracy matters for schools and colleges (pp. 75–89). Princeton, NJ: National Council on Education and the Disciplines.

English, L. D. (2003). Engaging students in problem posing in an inquiry-oriented mathematics classroom. In F. Lester & R. Charles (Eds.), Teaching mathematics through problem solving: Prekindergarten-grade 6 (pp. 187-198). Reston, Virginia: National Council of Teachers of Mathematics.

Graeber, A., Tirosh, D., & Glover, R. (1986). Pre-service teachers’ beliefs and performance on partitive and measurement division problems. Paper presented at the Eighth Annual Meeting of the North American Chapter of the Study Group for the Psychology of Mathematics Education, East Lansing, MI.

Greer, B. (1994). Extending the meaning of multiplication and division. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 61-85). Albany, NY: State University of New York Press.

Isik, C. & Kar, T. (2012). 7. Sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi. Elementary Education Online, 11(4), 1021-1035.

Kamii, C. & Dominick, A. (1998). The harmful effects of algorithms in grades 1-4. In L. J. Morrow & M. J. Kenney (Eds.), The teaching and learning of algorithms in school mathematics (pp. 130-140). Reston, VA: National Council of Teachers of Mathematics.

Kilic, C. (2013). Pre-service primary teachers’ free problem-posing performances in the context of fractions: An example from Turkey. The Asia-Pacific Education Researcher, 22(4), 677-686.

Lamon, S. J. (2006). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. (2nd Ed.). Erlbaum, Mahwah, NJ.

Lavy, I., & Bershadsky, I. (2003). Problem posing via “what if not?” strategy in solid geometry-a case study. The Journal of Mathematical Behavior, 22(4), 369-387.

Leung, K. C. I., & Carbone, R. E. (2013). Pre-service teachers’ knowledge about fraction divisions reflected through problem posing. The Mathematics Educator, 14(1), 80-92.

Li, Y., & Huang, R. (2008). Chinese elementary mathematics teachers’ knowledge in mathematics and pedagogy for teaching: The case of fraction division. ZDM: International Journal on Mathematics Education, 40(5), 845-859.

Lo, J. J., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15(6), 481–500.

Luo, F. (2009). Evaluating the effectiveness and insights of pre-service elementary teachers’ abilities to construct word problems for fraction. Journal of Mathematics Education, 2(1), 83–98.

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.

McAllister, C. J., & Beaver, C. (2012). Identification of error types in pre-service teachers' attempts to create fraction story problems for specified operations. School Science and Mathematics, 112(2), 88-98.

Mewborn, D. (2001). Teachers content knowledge, teacher education, and their effects on the preparation of elementary teachers in the United States. Mathematics Education Research Journal, 3(1), 28-36.

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

National Mathematics Advisory Panel. (2008). The Final Report of the National Mathematics Advisory Panel. Retrieved from

Ni, Y., & Zhou, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27–52

Redmond, A., & Utley, J. (2007). Prospective elementary teachers understanding of and attitudes towards the division of fractions. Paper presented at the Research Council on Mathematics Learning Annual Convention, Oklahoma City, OK.

Rizvi, N. F. (2004). Prospective teachers’ ability to pose word problems. International Journal for Mathematics Teaching and Learning, 12, 1-22.

Rudnitsky, A., Etheredge, S., Freeman, S. J. M., & Gilbert, T. (1995). Learning to solve addition and subtraction word problems through a structure-plus-writing approach. Journal for Research in Mathematics Education, 26(5), 467-486.

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.

Silver, E. A., & Cai, J. (2005). Assessing students' mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.

Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. C. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Mathematics Education Research Group of Australasia. The University of Melbourne.

Toluk-Ucar, Z. (2009). Developing pre-service teachers understanding of fractions through problem-posing. Teaching and Teacher Education: An International Journal of Research and Studies, 25(1), 166–175.

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.

Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation. Cognition and instruction, 28(2), 181–209.



  • There are currently no refbacks.

Copyright (c) 2019 Sumeyra Dogan Coskun

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © 2015-2023. European Journal of Education Studies (ISSN 2501 - 1111) is a registered trademark of Open Access Publishing Group. All rights reserved.

This journal is a serial publication uniquely identified by an International Standard Serial Number (ISSN) serial number certificate issued by Romanian National Library (Biblioteca Nationala a Romaniei). All the research works are uniquely identified by a CrossRef DOI digital object identifier supplied by indexing and repository platforms. All authors who send their manuscripts to this journal and whose articles are published on this journal retain full copyright of their articles. All the research works published on this journal are meeting the Open Access Publishing requirements and can be freely accessed, shared, modified, distributed and used in educational, commercial and non-commercial purposes under a Creative Commons Attribution 4.0 International License (CC BY 4.0).