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INVESTIGATING THE REPRESENTATIONAL FLUENCY OF PRE-SERVICE MATHEMATICS TEACHERS IN A MODELLING PROCESS

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Abstract

This article reports the results of a study that investigated pre-service mathematics teachers’ modelling processes in terms of representational fluency in a modelling activity related to a cassette player. A qualitative approach was used in the data collection process. Students’ individual and group written responses to the mathematical modelling activity, video-taped and transcribed group discussions, and classroom observations, were the main sources of data. This study was conducted during the spring semester in 2010. Fifty-five pre-service teachers were the participants in the study. Systematic coding and descriptive statistics were used in analysing the data. The data showed that a difficulty with modelling was closely related to the difficulty in the transformation of semiotic representations. During the modelling process, the two types of transformations, which were the treatments within a register and conversions between registers, occurred concurrently. In addition, the challenging and motivating nature of the modelling process in terms of directing participants to form consistent transformations between and within different representation registers was observed.

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References

  • Blum, W. & Niss, M. (1991). Applied mathematical problem solving, modelling, application, and links to other subjects-state, trends, and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.

    Article  Google Scholar 

  • Blum, W. (2002). ICMI study 14: Applications and modelling in mathematics education-discussion document. Educational Studies in Mathematics, 51, 149–171.

    Article  Google Scholar 

  • Carrejo, D. J. & Marshall, J. (2007). What is mathematical modelling? Prospective teachers’ use of experiments to connect mathematics to the study of motion. Mathematics Education Research Journal, 19(1), 45–56.

    Article  Google Scholar 

  • Cohen, L., Manion, L. & Morrison, K. (2000). Research methods in education (5th ed.). London: Routledge.

    Book  Google Scholar 

  • Creswel, J. W. (2003). Research design; qualitative, quantitative, and mixed methods approaches (2nd ed.). India: Sage Publications.

    Google Scholar 

  • Cramer, K. (2003). Using a translation model for curriculum development and classroom instruction. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching (pp. 449–463). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Doerr, H. M. (1997). Experiment, simulation and analysis: An integrated instructional approach to the concept of force. International Journal of Science Education, 19(3), 265–282.

    Article  Google Scholar 

  • Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. Galbraith, H. W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI Study (pp. 69–79). New York: Springer.

    Chapter  Google Scholar 

  • Department for Education (DFE). (1997). Mathematics in the national curriculum. London: DFE Welch Office.

    Google Scholar 

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131.

    Article  Google Scholar 

  • Elia, I., Gagatsis, A. & Demetriou, A. (2007a). The effects of different modes of representation on the solution of one-step additive problems. Learning and Instruction, 17, 658–672.

    Article  Google Scholar 

  • Elia, I., Panaoura, A., Eracleous, A. & Gagatsis, A. (2007b). Relations between secondary pupils’ conceptions about functions and problem solving in different representations. International Journal of Science and Mathematics Education, 5(3), 533–556.

    Article  Google Scholar 

  • English, L. (2003). Reconciling theory, research, and practice: A models and modelling perspective. Educational Studies in Mathematics, 54, 225–248.

    Article  Google Scholar 

  • Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. Journal of Mathematical Behavior, 17(2), 137–165.

    Article  Google Scholar 

  • Gravemeijer, K. & Stephan, M. (2002). Emergent models as an instructional design heuristic. In K. Gravemeijer, R. Lehrer, B. Oers & L. Verschaffel (Eds.), Symbolizing, modelling and tool use in mathematics education (pp. 145–169). Dordrecht, The Netherlands: Kluwer Academic.

    Chapter  Google Scholar 

  • Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293–307.

    Article  Google Scholar 

  • Johnson, T. & Lesh, R. (2003). A models and modelling perspective on technology-based representational media. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching (pp. 265–278). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Kaiser, G. & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik (ZDM), 38(3), 302–310.

    Article  Google Scholar 

  • Kertil, M., Delice, A. & Aydin, E. (2009). Investigating representational fluency in modelling process: The experience of pre-service teachers with a cassette problem. In M. Tzekaki, M. Kaldrimidou & C. Sakonidis (Eds.), Proceedings of the 33rd International Conference on the Psychology of Mathematics Education (Vol. 3, pp. 305–312). Thessaloniki, Greece: PME.

    Google Scholar 

  • Lesh, R. (1999). The development of representational abilities in middle school mathematics. In I. E. Sigel (Ed.), Development of mental representation: Theories and application (pp. 323–350). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Lesh, R. & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Lesh, R. & Harel, G. (2003). Problem solving, modelling, and local conceptual development. Mathematical Thinking and Learning, 5, 157–189.

    Article  Google Scholar 

  • Lesh, R. & Lehrer, R. (2003). Models and modelling perspectives on the development of students and teachers. Mathematical Thinking & Learning, 5(2&3), 109–129.

    Article  Google Scholar 

  • Lesh, R., Hoover, M., Hole, B., Kelly, A. & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. Lesh & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591–645). Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Lingefjärd, T. (2000). Mathematical modelling by prospective teachers. Electronically published doctoral dissertation, University of Georgia. Can be downloaded from http://ma-serv.did.gu.se/matematik/thomas.htm

  • Lingefjärd, T. (2002). Mathematical modelling for pre-service teachers: A problem from anaesthesiology. International Journal of Computers for Mathematical Learning, 7, 117–143.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Nunes, T., Schliemann, A. D. & Carraher, D. W. (1993). Mathematics in the streets and in schools. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Oliveira, A. M. P. & Barbosa, J. C. (2009). Mathematical modelling and the teachers’ tensions. In R. Lesh, P. Galbraith, C. Haines & A. Hurford (Eds.), Modelling students’ modelling competencies (pp. 511–517). New York: Springer.

    Google Scholar 

  • Reusser, K. & Stebler, R. (1997). Every word problem has a solution—the social rationality of mathematical modelling in schools. Learning and Instruction, 7(4), 309–327.

    Article  Google Scholar 

  • Santos, A. G. D., & Thomas, M. O. J. (2001). Representational fluency and symbolisation of derivative. Proceedings of the Sixth Asian Technology Conference in Mathematics, Melbourne, 282–291.

  • Schorr, R. Y., & Lesh, R. (2003). A modeling approach for providing teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspective (pp. 141–157). Mahwah, NJ: Lawrence Erlbaum Associates.

  • Sfard, A. (1995). The development of algebra: Confronting historical and psychological perspectives. Journal of Mathematical Behaviour, 14, 15–39.

    Article  Google Scholar 

  • Sriraman, B. & Lesh, R. (2006). Modelling conceptions revisited. ZDM–The International Journal on Mathematics Education, 38, 247–253.

    Article  Google Scholar 

  • Suh, P. & Moyer, P. S. (2007). Developing students’ representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching, 26(2), 155–173.

    Google Scholar 

  • Talim ve Terbiye Kurulu Başkanlığı (TTKB). (2005). Ortaöğretim matematik (9, 10, 11 ve 12. sınıflar) dersi öğretim programı. Ankara, Türkiye: Devlet Kitapları Müdürlüğü.

    Google Scholar 

  • Zbiek, R. M. & Conner, A. (2006). Beyond motivation: Exploring mathematical modelling as a context for deepening students’ understandings of curricular mathematics. Educational Studies in Mathematics, 69, 89–112.

    Article  Google Scholar 

  • Zbiek, R. M., Heid, M. K., Blume, G. W. & Dick, T. P. (2007). Research on technology in mathematics education: The perspective of constructs. In F. Lester (Ed.), Handbook of research on mathematics teaching and learning (Vol. 2, pp. 1169–1207). Charlotte, NC: Information Age.

    Google Scholar 

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Authors and Affiliations

  1. Atatürk Faculty of Education, Secondary School Science and Mathematics Education Department, Marmara University, Kadikoy, Istanbul, Turkey

    Ali Delice

  2. Secondary School Science and Mathematics Education Department, Marmara University, Kadikoy, Istanbul, Turkey

    Mahmut Kertil

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  1. Ali Delice
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  2. Mahmut Kertil
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Correspondence to Ali Delice.

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Delice, A., Kertil, M. INVESTIGATING THE REPRESENTATIONAL FLUENCY OF PRE-SERVICE MATHEMATICS TEACHERS IN A MODELLING PROCESS. Int J of Sci and Math Educ 13, 631–656 (2015). https://doi.org/10.1007/s10763-013-9466-0

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  • DOI: https://doi.org/10.1007/s10763-013-9466-0

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