International Association of Educators   |  ISSN: 1554-5210

Original article | International Journal of Progressive Education 2015, Vol. 11(2) 57-75

Prospective Mathematics Teachers’ Opinions about Mathematical Modeling Method and Applicability of This Method

Levent Akgün

pp. 57 - 75   |  Manu. Number: ijpe.2015.018

Published online: June 15, 2015  |   Number of Views: 1  |  Number of Download: 22


Abstract

The aim of this study is to identify prospective secondary mathematics teachers’ opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics teachers who were taking a “teaching practice” course. In the “Teaching Practice” course, mathematical modeling method was introduced to these selected prospective teachers and activity examples appropriate to this method were presented to them. Then, the prospective teachers prepared examples similar to the activity examples that were presented to them, and they implemented these examples in the schools where they served their internship. The semi-structured interview and observation forms were used as data collection tools in the study. An attempt was made to identify prospective secondary mathematics teachers’ opinions about mathematical modeling method and the applicability of this method via interviews, whereas an attempt was made to identify their efficacy in application the mathematical modeling method via observations. Descriptive analysis and content analysis methods were used in analyzing the data. In view of the study, it was found that many of the prospective teachers correctly understood what mathematical modeling meant, but they were not able to fully implement this method in classrooms. When the prospective teachers’ opinions about classroom applications of the mathematical modeling method were examined, it was observed that the reasons for the experienced difficults are the fact that there was not enough time and classroom management was difficult. As for the positive aspects of mathematical modeling, the prospective teachers stated that the mathematical modeling set forth the applicability of mathematics in daily life. Furthermore, all prospective teachers stated that they consider featuring problems that involve this method in their own courses in the future, but some of them stated that they would not be able to use it since its application is difficult and time consuming.

Keywords: Mathematical Model, Mathematical Modeling, Prospective Mathematics Teacher


How to Cite this Article?

APA 6th edition
Akgun, L. (2015). Prospective Mathematics Teachers’ Opinions about Mathematical Modeling Method and Applicability of This Method . International Journal of Progressive Education, 11(2), 57-75.

Harvard
Akgun, L. (2015). Prospective Mathematics Teachers’ Opinions about Mathematical Modeling Method and Applicability of This Method . International Journal of Progressive Education, 11(2), pp. 57-75.

Chicago 16th edition
Akgun, Levent (2015). "Prospective Mathematics Teachers’ Opinions about Mathematical Modeling Method and Applicability of This Method ". International Journal of Progressive Education 11 (2):57-75.

References
  1. Aydın, H. (2008). İngiltere’de öğrenim gören öğrencilerin ve öğretmenlerin matematiksel modelleme kullanımına yönelik fenomenografik bir çalışma. Unpublished master’s thesis, Gazi  University, Ankara. [Google Scholar]
  2. Bender, A. E. (1978). An introduction to mathematical modeling. New York: Wiley. [Google Scholar]
  3. Blum, W. (1991). Applications and modelling in mathematics teaching – a review of arguments and instruction aspects. M. Niss, W. Blum, & I. Huntley (Edt.), Teaching of mathematical modelling and applications (s.10-29). New York: Ellis Horwood. [Google Scholar]
  4. Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education- Discussion document.  Educational Studies in Mathematics, 51(1/2), 149-171. [Google Scholar]
  5. Blum, W., & Ferri, R. B. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Applications, 1(1), 45-58. [Google Scholar]
  6. Bonotto,  C.  (2010).  Engaging  students  in  mathematical  modelling  and  problem  posingactivities. Journal of Mathematical Modeling and Applications, 1(3), 18-22. [Google Scholar]
  7. Chan, E. C. M. (2009). Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms. Journal of Science and Mathematics Education in Southeast Asia, 32 (1), 36-61. [Google Scholar]
  8. Çiltaş, A. (2011). Dizi ve seriler konusunun matematiksel modelleme yoluyla öğretiminin ilköğretim matematik öğretmeni adaylarının öğrenme ve modelleme becerileri üzerine etkisi.  Unpublished doctoral dissertation, Atatürk University, Erzurum. [Google Scholar]
  9. Çiltaş, A., Deniz, D., Akgün, L., Işık, A., & Bayrakdar, Z. (2011). İlköğretim ikinci kademede görev yapmakta olan matematik öğretmenlerinin matematiksel modelleme ile ilgili görüşlerinin incelenmesi. Paper presented at the meeting of 10th Matematik Symposium, İstanbul. [Google Scholar]
  10. Doerr, H., & English, L. D. (2003). A Modeling perspective on students’ mathematical reasoning about data. Journal of Research in Mathematics Education, 34(2), 110-136. [Google Scholar]
  11. Doruk, B.   K. (2010). Matematiği günlük yaşama transfer etmede matematiksel modellemenin   etkisi. Unpublished doctoral dissertation. Hacettepe University, Ankara. [Google Scholar]
  12. English, L. D., Fox, L. J., & Watters, J. J. (2005).Problem posing and solving with mathematical modeling, Teaching Children Mathematics, 156-163. [Google Scholar]
  13. English, L. D. (2006a, Temmuz). Introducing young children to complex systems through modeling. Paper presented at the meeting of 29th Annual Conference of the Mathematics Education Research Group of Australasia, Canberra. [Google Scholar]
  14. English, L. D. (2006b). Mathematical modeling in the primary school: children's construction of a consumer guide. Educational Studies in Mathematics,  63(3), 303-323. [Google Scholar]
  15. Eraslan, A. (2011). İlköğretim matematik öğretmen adaylarının model oluşturma etkinlikleri ve bunların matematik öğrenimine etkisi hakkındaki görüşleri. Elementary Education Online, 10(1), 364-377. [Google Scholar]
  16. Eric, C. C. M. (2010). Tracing primary 6 students' model development within the mathematical modelling process. Journal of Mathematical Modelling and Application, 1(3), 40-57. [Google Scholar]
  17. Ferri, R. B., & Blum, W. (2009). Mathematical modelling in teacher education – experiences from a modelling seminar http://fractus.uson.mx/Papers/CERME6/wg11.pdf#page=7 [12 Mart 2013] [Google Scholar]
  18. Ferrucci, B. J., & Carter, J. A. (1999). Mathematical modeling, technology and the environment. http://math.unipa.it/~grim/Jferruccicarter.PDF [6 Mart 2013] [Google Scholar]
  19. Fox, J.  (2006). A justification for mathematical modelling experiences in the preparatory   classroom. [Google Scholar]
  20. P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Edt). 29th Annual Conference of Mathematics Education Group of Ausralasia içinde ( s.s 221-228).  Australia: Canberra. [Google Scholar]
  21. Frejd, P. (2012). Teachers’ conceptions of mathematical modelling at Swedish Upper Secondary school. Journal of Mathematical Modelling and Application, 1(5), 17-40. [Google Scholar]
  22. Gravemeijer, K. (1999). How emergent models may foster the construction of formal mathematics, Mathematical Thinking and Learning 1, 155–177. [Google Scholar]
  23. Greer, B. (1997). Modeling reality in mathematics classrooms: The case of word problems, Learning & Instruction 7, 293–307. [Google Scholar]
  24. Güzel, E. B., & Uğurel, I. (2010). Matematik öğretmen adaylarının analiz dersi akademik başarıları ile matematiksel modelleme yaklaşımları arasındaki ilişki. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 29(1), 69-90. [Google Scholar]
  25. Ikeda, T., & Kaiser, G. (2005). The role and the relevance of applications and modelling in Japan and Germany – a comparative study. http://www.erzwiss.uni-hamburg.de/Personal/GKaiser/pdf- publist/ikeda-kaiser_earcome.pdf [6 Mart 2013] [Google Scholar]
  26. Kaiser, G. (2005). Mathematical modelling in school- examples and experiences. http://www.erzwiss.uni-hamburg.de/personal/gkaiser/pdf-publist/16_Kaiser.pdf [6 Mart 2013] [Google Scholar]
  27. Kaiser, G., & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. Zentralblatt Für Didactik Der Mathematic, 38 (2), 196 – 208. [Google Scholar]
  28. Kawasaki, T., Moriya, S., Okabe, Y., & Maesako T. (2012).The problems of mathematical modelling introduction on mathematics education in Japanese school. Journal of Mathematical Modelling and Application, 1(5), 50-58. [Google Scholar]
  29. Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi. Unpublished  master’s  thesis, Marmara University, İstanbul. [Google Scholar]
  30. Kim, S. H., & Kim, S. (2010). The effects of mathematical modeling on creative production ability and self-directed learning attitude. Asia Pasific Education Review. 11, 109-120. doi: 10.1007/s12564-009-9052-x [Google Scholar] [Crossref] 
  31. Lesh, R.A. & Doerr, H. (2003). Foundations of a Models & Modeling Perspective on Mathematics Teaching and Learning’, in R.A. Lesh and H. Doerr (eds.), Beyond constructivism: A models and modeling perspective on mathematics teaching, learning, and problem solving, Erlbaum, Mahwah, NJ, pp. 3–34. [Google Scholar]
  32. Lingefjärd, T. (2002). Mathematical modeling for preservice teachers: a problem from anesthesiology. International Journal of Computers for Mathematical Learning, 7(2), 117-143. [Google Scholar]
  33. Lingefjärd, T. (2007). Mathematical modelling in teacher education- necessity or unnecessarily, W. Blum, P. L. Galbraith, H. W. Henn & M. Niss (Ed.), Modelling and applications in mathematics education: 14 th ICMI Study  (pp. 333-340), New York: Springer. [Google Scholar]
  34. Maaß, K. (2006). What are modeling competencies? ZDM, 38(2), 113-142. [Google Scholar]
  35. McMillan, H. J. (2000). Educational research: fundamentals for the consumer (3rd ed.). New York: Longman. [Google Scholar]
  36. Meyer, W. J. (1984).  Concepts of mathematical modeling. New York: McGraw-Hill. [Google Scholar]
  37. Milli  Eğitim  Bakanlığı  (2011).  Ortaöğretim  Matematik  Dersi  (9-12.  Sınıflar)  Öğretim Programı. http://ttkb.meb.gov.tr/program.aspx?islem=1&kno=86 [14 Ocak 2012] [Google Scholar]
  38. Özer Keskin, Ö. (2008). Ortaöğretim matematik öğretmen adaylarının matematiksel modelleme yapabilme becerilerinin geliştirilmesi üzerine bir araştırma. Unpublished doctoral  dissertation.  Gazi University, Ankara. [Google Scholar]
  39. Özturan Sağırlı, M. (2010). Türev konusunda matematiksel modelleme yönteminin ortaöğretim öğrencilerinin akademik başarıları ve öz-düzenleme becerilerine etkisi. Unpublished doctoral dissertation, Atatürk University, Erzurum. [Google Scholar]
  40. Özturan Sağırlı, M., Kırmacı, U., & Bulut, S. (2010). Türev konusunda uygulanan matematiksel modelleme yönteminin ortaöğretim öğrencilerinin akademik başarılarına ve özdüzenleme becerilerine etkisi. EÜFBED - Fen Bilimleri Enstitüsü Dergisi, 3(2), 221-247. [Google Scholar]
  41. Perrenet, J., & Zwaneveld, B. (2012). The many faces of the mathematical modeling cycle. Journal of Mathematical Modelling and Application, 1(6), 3-21. [Google Scholar]
  42. Schwarz, B., & Kaiser, G. (2007). Mathematical modelling in school—experiences from a Project integrating      school   and        university.          http://www.mathematik.uni- dortmund.de/~erme/CERME5b/WG13.pdf  [12 Mart 2012] [Google Scholar]
  43. Siller, H. S., & Kuntze, S. (2011). Modelling as a big idea in mathematics – Knowledge and views of pre-service and in-service teachers. Journal of Mathematical Modelling and Application, 1(6), 33-39. [Google Scholar]
  44. Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. Mathematics: Essential Research, Essential Practice, 2, 688-697. [Google Scholar]
  45. Türker, B., Sağlam, Y., & Umay, A. (2010). Preservice teachers’ performances at mathematical modeling process and views on mathematical modeling. Procedia Social and Behavioral Sciences, 2, 3099–3103. [Google Scholar]
  46. Van den Heuvel-Panhuizen (2003), The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage, Educational Studies in Mathematics 54, 9–35. [Google Scholar]
  47. Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri (7. Baskı) Ankara: Seçkin Yayıncılık. [Google Scholar]
  48. Yin, R. K. (2002). Case study research design and methods (3. baskı). London: Sage Publication. [Google Scholar]
  49. Zbiek, R. M., & Conner, A. (2006). Beyond motivation: exploring mathematical modeling as a  context for deepening students’ understandings of curiicular mathematics. Educational Studies in Mathematics, 63, 89–112. doi: 10.1007/s10649-005-9002-4 [Google Scholar] [Crossref]