# Fraction Multiplication and Division Word Problems Posed by Different Years of Pre-Service Elementary Mathematics Teachers

Tuba Aydogdu Iskenderoglu

**APA 6th edition**

Iskenderoglu, T.A. (2018). Fraction Multiplication and Division Word Problems Posed by Different Years of Pre-Service Elementary Mathematics Teachers.

*European Journal of Educational Research, 7*(2), 373-385. doi:10.12973/eu-jer.7.2.373

**Harvard**

Iskenderoglu T.A. 2018 'Fraction Multiplication and Division Word Problems Posed by Different Years of Pre-Service Elementary Mathematics Teachers',

*European Journal of Educational Research*, vol. 7, no. 2, pp. 373-385. Available from: http://dx.doi.org/10.12973/eu-jer.7.2.373

**Chicago 16th edition**

Iskenderoglu, Tuba Aydogdu . "Fraction Multiplication and Division Word Problems Posed by Different Years of Pre-Service Elementary Mathematics Teachers". (2018)

*European Journal of Educational Research*7, no. 2(2018): 373-385. doi:10.12973/eu-jer.7.2.373

### Abstract

**:** It is important for pre-service teachers to know the conceptual difficulties they have experienced regarding the concepts of multiplication and division in fractions and problem posing is a way to learn these conceptual difficulties. Problem posing is a synthetic activity that fundamentally has multiple answers. The purpose of this study is to analyze the multiplication and division of fractions problems posed by pre-service elementary mathematics teachers and to investigate how the problems posed change according to the year of study the pre-service teachers are in. The study employed developmental research methods. A total of 213 pre-service teachers enrolled in different years of the Elementary Mathematics Teaching program at a state university in Turkey took part in the study. The “Problem Posing Test” was used as the data collecting tool. In this test, there are 3 multiplication and 3 division operations. The data were analyzed using qualitative descriptive analysis. The findings suggest that, regardless of the year, pre-service teachers had more conceptual difficulties in problem posing about the division of fractions than in problem posing about the multiplication of fractions.

**Keywords:*** Pre-service mathematics teachers, fractions, problem posing, multiplication, division.*

### References

Abramovich, S. (2014). Revisiting mathematical problem solving and posing in the digital era: toward pedagogically sound uses of modern technology. *International Journal of Mathematical Education in Science and Technology, 45*(7), 1034-1052.

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

Akay, H., Soybas, D. & Argun, Z. (2006). Problem posing experiences and using open-ended questions in mathematics teaching. *Kastamonu University Kastamonu Education Journal, 14*(1), 129-146.

Armstrong, B.E. & Bezuk, N. (1995). *Multiplication and division of fractions: The search for meaning.* In J. Sowder & B.P. Schappelle (Eds), Providing a foundation for teaching mathematics in the middle grades (pp.85-119). Albany, NY:State University of New York Press.

Ball, D. L. (1990). Pre-service elementary and secondary teachers’ understanding of division. *Journal for Research in Mathematics Education, 21*(2), 132-144.

Ball, D.L. & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics*.* In J. Boaler (Ed.), *Multiple Perspectives on Teaching and Learning* (pp. 83-104). Westport CT: Ablex Publishing.

Ball, D.L., Lubienski, S. & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge*.* In V. Richardson (Ed.), *Handbook of Research on Teaching* (pp. 433-456). Washington, DC: American Educational Research Association.

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.

Behr, M. J., Harel, G., Post, T. R. & Lesh, R. (1992). *Rational number, ratio, and proportion.* In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 296–333). New York: Macmillan.

Behr, M. J., Lesh, R., Post, T. & Silver, E. A. (1983). *Rational number concepts.* In R. Lesh, & M. Landau (Eds.), Acquisitions of mathematics concepts and processes (pp. 92–126). New York: Academic Press.

Cankoy, O. & Darbaz, S. (2010). Effect of a problem posing based problem solving instruction on understanding problem. *Hacettepe University Journal of Education, 38,* 11-24.

Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. *PNA, 6*(4), 135–146.

Chen, L., Dooren, W.V., Chen, Q. & Verschaffel, L. (2011). An investigation on Chinese teachers’ realistic problem posing and problem solving ability and beliefs. *International Journal of Science and Mathematics Education,* *9*, 919-948.

Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. *Educational Studies in Mathematics,* *52*, 243–270.

Cakan, M. (2004). Assessment-evaluation applications of teachers and their qualification levels: Primary and secondary education. *Ankara University Journal of Educational Sciences,* *3*7, 99–114.

Ervin, H.K. (2017). Fraction multiplication and division models: A practitioner reference paper. *International Journal of Research in Education and Science (IJRES), 3*(1), 258-279.

Hudson, P. (2013). Desirable attributes and practices for mentees: Mentor teachers’ expectations. *European Journal of Educational Research, 2*(3), 107-119.

Isik, C. (2011). Conceptual analysis of multiplication and division problems in fractions posed by preservice elementary mathematics teachers. *Hacettepe University Journal of Education,* 41, 231-243.

Isik, C., Isik, A. & Kar, T. (2011). Analysis of the problems related to verbal and visual representations posed by pre-service mathematics teachers. *Pamukkale University Journal of Education, 30*(2), 39-49.

Julie, H. (2017). The elementary school teachers’ ability in adding and subtracting fraction, and interpreting and computing multiplication and division fraction. *International Journal of Science and Applied Science: Conference Series, 1*(1), 55-63.

Kilic, C. (2013a). Determining the performances of pre-service primary school teachers in problem posing situations. *Educational Sciences: Theory & Practice, 13*(2), 1195-1211.

Kilic, C. (2013b). 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.

Kilic, C. (2015). Analyzing pre-service primary teachers’ fraction knowledge structures through problem posing. *Eurasia Journal of Mathematics, Science & Technology Education, 11*(6), 1603-1619.

Kieren, T. E. (1976). *On the mathematical, cognitive and instructional foundations of rational numbers.* In R. A. Lesh (Ed.), Number and measurement: Papers from a research workshop (pp. 101–144). Columbus: ERIC/SMEAC.

Kojima, K., Miwa, K. & Matsui, T. (2009). Study on support of learning from examples in problem posing as a production task. In. S.C. Kong, H. Ogata, H.C. Arnseth, C.K.K. Chan, T. Hirashima, F. Klett, J.H.M. Lee, C.C. Liu, C.K. Looi, M. Milrad, A. Mitrovic, K. Nakabayashi, S.L. Wong & S.J.H. Yang (eds.). *Proceedings of the 17th International Conference on Computers in Education [CDROM].* Hong Kong: Asia-Pacific Society for Computers in Education.

Korkmaz, E. & Gur, H. (2006). Determining of prospective teachers’ problem posing skills. Journal of *Balikesir University Institute of Science and Technology, 8*(1), 64-74.

Ma, L. (1999). *Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and The United States*. Erlbaum: Mahwah, NJ.

Mack, N. K. (1998). Building a foundation for understanding the multiplication of fractions. *Teaching Children Mathematics, 5*(1), 34-38.

Menard, S. (2008). *Handbook of longitudinal research: Design, measurement and analysis. *Academic Press, First Edition, London, UK.

Miller, S. A. (1998). *Developmental research methods* (2nd Edition). New Jersey, USA.

MEB - Milli Egitim Bakanligi [MOE - Ministry of Education], (2005). Ilkogretim Matematik (6, 7 ve 8. Siniflar) Dersi Ogretim Programi [Elementary School Mathematics Curriculum (6, 7 and 8. Grades)], Ankara.

MEB - Milli Egitim Bakanligi [MOE - Ministry of Education], (2013). Ortaokul Matematik (5, 6, 7 ve 8. Siniflar) Dersi Ogretim Programi [Middle School Mathematics Curriculum (5, 6, 7 and 8. Grades)], Ankara.

MEB - Milli Egitim Bakanligi [MOE - Ministry of Education], (2017). Matematik Dersi Ogretim Programi (1, 2, 3, 4, 5, 6, 7 ve 8. Siniflar) [Mathematics Curriculum (1, 2, 3, 4, 5, 6, 7 and 8. Grades)], Ankara.

Pagni, D. (1998). Giving meaning to multiplication and division of fractions. *Ohio Journal of School Mathematics, 54*(4), 11-13.

Romberg, T. A. & Carpenter, T. P. (1986). Research on teaching and learning mathematics: Two disciplines of scientific inquiry. In M. C. Witrock (Ed.), *Handbook of Research on Teaching* (pp. 850–873). New York: Macmillan.

Shulman, L.S. (1987). Knowledge and teaching: Foundations of the new reform. *Harvard Educational Review*, 57, 1-22.

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

Stoyanova, E. (2003). Extending students' understanding of mathematics via problem-posing. *Australian Mathematics Teacher, 59*(2), 32–40.

Tirosh, D. (2000). Enhancing pre-service teachers’ knowledge of children’s conceptions: The case of division of fractions. *Journal for Research in Mathematics Education, 31*(1), 5-25.

Tirosh, D. & Graeber, A. (1991). The effect of problem type and common misconceptions of preservice elementary teachers’ thinking about division. *School Science and Mathematics*, 91, 157-163.

Toluk, Z. (2002). Conceptual schemes used by elementary school students for relating division and rational numbers. *Bogazici University Journal of Education, 19*(2), 81-103.

Toluk-Ucar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. *Teaching and Teacher Education,* 25, 166–175.

Turhan, B. & Guven, M. (2014). The effect of mathematics instruction with problem posing approach on problem solving success, problem posing ability and views towards mathematics. *Cukurova University Faculty of Education Journal, 43*(2), 217-234.

Utley, J. & Redmond, A. (2008). Prospective elementary teachers attitudes towards and knowledge of the division of fractions. *Paper presented at the annual meeting of the Research Council on Mathematics Learning*, Oklahoma City, OK.

Whitin, D. J. (2004). *Building a mathematical community through problem posing.* In R. N. Rubenstein (Ed.), Perspectives on the teaching of mathematics: Sixty-sixth yearbook (pp. 129–140). Reston, VA: National Council of Teachers of Mathematics.

Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. *Educational Studies in Mathematics*, DOI 10.1007/s10649-017-9760-9.

Yim, J. (2010). Children’s strategies for division by fractions in the context of the area of a rectangle. *Educational Studies in Mathematics*, *73*, 105–120.