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

Yıl 2018, , 373 - 385, 15.04.2018

Tuba Aydogdu Iskenderoglu

https://doi.org/10.12973/eu-jer.7.2.373

Öz

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.

Anahtar Kelimeler

Pre-service mathematics teachers, fractions, problem posing, multiplication, division

Kaynakça

• 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, 37, 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.