Factors Revealed while Posing Mathematical Modelling Problems by Mathematics Student Teachers

Abstract

The purpose of this study is to reveal factors considered by mathematics student teachers while posing modelling problems. The participants were twenty-seven mathematics student teachers and posed their modelling problems within their groups. The data were obtained from the modelling problems posed by the participants, their solutions on these problems and the groups’ reflective diaries regarding their problem posing and solution processes. The data were analyzed by using content analysis and the codes were constructed according to the problems’ contents. The participants' diaries were examined in terms of generated codes and the expressions supporting/relating the codes were determined. While designing the problems, the participants considered the factors such as being interesting, understandable, appropriateness to real life and modelling process, model construction, and usability of different mathematical concepts. Their solutions were generally handled in terms of usage of the mathematical statements, appropriateness to the modelling process and being meaningful for real life. Modelling training should be provided to enable the student teachers to develop modelling problems and their designs should be examined and the feedbacks should be given.

Keywords

• Mathematical modelling; mathematics student teacher; modelling problem posing

Kaynakça

1. Ärlebäck, J. B. (2009). On the Use of Realistic Fermi Problems for Introducing Mathematical Modelling in School. The Montana Mathematics Enthusiast, 6(3), 331- 364.
2. Baki, A. (2002). Computer-aided mathematics for learners and teachers. Istanbul: BITAV-Ceren Publishing.
3. Berry, J., & Houston, K. (1995). Mathematical modelling. Bristol: J. W. Arrowsmith Ltd.
4. Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education-discussion document. Zentralblattfur Didaktik der Mathematik, 34(5), 229-239.
5. Blum, W., & Niss, M. (1989). Mathematical problem solving, modelling, applications, and links to other subjects – state, trends and issues in mathematics instruction. In M. Niss, W. Blum and I. Huntley (Eds), Modelling applications and applied problem solving (pp.1-19). England: Halsted Press.
6. 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.
7. Bonotto, C. (2010). Realistic mathematical modelling and problem posing. In R. Lesh, P. Galbraith, C. R. Haines, and A. Hurford (Eds), Modelling Students’ Mathematical Competencies (pp. 399–408). New York: Springer.
8. Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblattfur Didaktik der Mathematik, 38(2), 86-95.

9. Brown, S., & Walter, M. (2005). The art of problem posing (3rd Edition). Mahwah, NJ: Lawrence Erlbaum.
10. Bukova-Guzel, E. (2011). An Examination of pre-service mathematics teachers’ approaches to construct and solve mathematical modelling problems. Teaching Mathematics and Its Applications, 30(1), 19-36.
11. Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. Journal of Secondary Gifted Education, 17(1), 37-47.
12. Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralblatt fur Didaktik der Mathematik, 37(3), 149–158.
13. Creswell, J. W. (2013). Research design: Qualitative, quantitative and mixed method approaches (4nd ed.). Thousand Oaks, California: Sage Publications.
14. Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers' practices. Educational Studies in Mathematics, 52(3), 243-270.
15. Delice, A., & Kertil, M. (2015). Investigating the representational fluency of pre-service mathematics teachers in a modeling process. International Journal of Science and Mathematics Education, 13(3), 631-656.
16. Deniz, D., & Akgun, L. (2016). The sufficiency of high school mathematics teachers’ to design activities appropriate to model eliciting activities design principles. Karaelmas Journal of Educational Sciences, 4, 1-14.
17. Downton, A. (2013). Problem posing: A possible path way to mathematical modelling. In G. A. Stillman, G. Kaiser, W. Blum and J. P. Brown (Eds), Teaching Mathematical Modelling: Connecting to Research and Practice (pp. 527-536). New York: Springer.
18. English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106.
19. English, L. D. (2003) Mathematical modelling with young learners. S. J. Lamon, W. A. Parker and S. K. Houston (Eds), Mathematical Modelling: A Way of Life (pp. 3-18), Chichester: Horwood Publishing.
20. English, L. D., Fox, J. L., & Watters, J. J. (2005). Problem posing and solving with mathematical modelling. Teaching Children Mathematics, 12(3), 156–163.
21. Eraslan, A., & Kant, S. (2015). Modelling processes of 4th-year middle-school students and the difficulties encountered. Educational Sciences: Theory & Practice, 15(3), 809-824.
22. Fox, J. (2006). A justification for Mathematical Modelling Experiences in the Preparatory Classroom. In P. Grootenboer, R. Zevenbergen, and M. Chinnappan (Eds), Identities, Cultures, and Learning Spaces, Proceedings 29th annual conference of the Mathematics Education Research Group of Australasia (pp. 221-228), Canberra: MERGA.
23. Hansen, R., & Hana, G. M. (2015). Problem posing from a modelling perspective. In F. M. Singer, N. F. Ellerton, J. Cai (Eds), Mathematical Problem Posing (pp. 35-46). Springer New York.
24. Hohenwarter, M., Hohenwarter, J., Kreis, Y., & Lavicza, Z. (2008). Teaching and learning calculus with free dynamic mathematics software GeoGebra. In 11th International Congress on Mathematical Education. Monterrey, Nuevo Leon, Mexico.
25. Isik, C., & Kar, T. (2012). Pre-service elementary teachers’ problem posing skills. Mehmet Akif Ersoy University Journal of Education Faculty, 12(23), 190-214.
26. Lamberts, K. (2005). Mathematical modelling of cognition. In K. Lamberts and R. L., Goldstone (Eds), Handbook of Cognition (pp. 407-421). London: SAGE.
27. Lesh, R., & Doerr, H. M. (2003). (Eds). Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning and teaching. Mahwah, NJ: Lawrence Erlbaum.
28. Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. E. Kelly and R. A. Lesh (Eds), Handbook of Research Design In Mathematics and Science Education (pp. 591-645). New York: Routhlege.
29. Maaß, K. (2006). What are modelling competencies? Zentralblattfur Didaktik der Mathematik. 38(2), 113-142.
30. Merriam, S. B. (2013). Qualitative research: a guide to design and implementation. New York: John Wiley & Sons Inc.
31. Miles, M. B., & Huberman, A. M. (1994). An expanded source book: Qualitative data analysis. London: Sage Publications.
32. Mousoulides, N. G. (2009). Mathematical modelling for elementary and secondary school teachers. In A. Kontakos (Ed.), Research & Theories in Teacher Education. Greece: University of the Aegean.
33. Ozaltun Celik, A. (2018). Designing hypothetical learning trajectories and instructional sequences related to quadratic functions (Unpublished Master Dissertation). Dokuz Eylul University, Institute of Educational Sciences, Izmir, Turkey.
34. Paolucci, C., & Wessels, H. (2017). An Examination of preservice teachers’ capacity to create mathematical modeling problems for children. Journal of Teacher Education, 68(3), 330-344.
35. Peter-Koop, A. (2004). Fermi problems in primary mathematics classrooms: Pupils’ interactive modelling processes. In I. Putt, R. Farragher, and M. McLean (Eds), Mathematics Education for the Third Millenium: Towards 2010, Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 454-461). Townsville, Queensland: MERGA.
36. Pollak, H. O. (1979). The interaction between mathematics and other school subjects. In H. G. Steiner and B. Christiansen (Eds), New Trends in Mathematics Teaching IV (pp. 232-248). Paris: UNESCO.
37. Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. In A. Schoenfeld and H. Hillsdale (Eds), Mathematical Thinking and Problem Solving (pp. 53-69). NJ, Lawrence Erlbaum Associates.
38. Siller, H. S., & Greefrath, G. (2010). Mathematical modelling in class regarding to technology. In V. Durand-Guerrier, S. Soury-Lavergne and F. Arzarello, CERME 6, Proceedings of the sixth Congress of the European Society for Research in Mathematics Education (pp. 108-117). Lyon: Service des publications, INRP.
39. Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.
40. Stillman, G. (2015). Problem finding and problem posing for mathematical modelling. In N. H. Lee and D. K. E. Ng (Eds), Mathematical Modelling: From Theory to Practice (pp. 41-56). Singapore: World Scientific Publishing.
41. Sahin, N., & Eraslan, A. (2016). Modelling processes of primary school students: The Crime Problem. Education and Science, 41(183), 47-67.
42. Dede, A. T., Hidiroglu, C. N., & Guzel, E. B. (2017). Examining of model eliciting activities developed by mathematics student teachers. Journal on Mathematics Education, 8(2), 223-242.
43. Whitin, D. (2004). Building a mathematical community through problem posing. In R. Rubinstein and G. W. Bright (Eds), Perspectives on the Teaching of Mathematics (pp. 129–140). Reston, VA: NCTM.
44. Yoon, C., Dreyfus, T., & Thomas, M. O. (2010). How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity. Mathematics Education Research Journal, 22(2), 141-157.