MATEMATİK ÖĞRETMEN ADAYLARININ MATEMATİKSEL MODELLEME BECERİLERİNİN İNCELENMESİ

Öz

Bu çalışmanın amacı, matematik öğretmen adaylarının matematiksel modelleme becerilerini ve karşılaştıkları zorlukları incelemektir. Araştırmaya, ilköğretim matematik eğitimi ana bilim dalında bulunan 38 öğretmen adayı katılmıştır. Öğrencilere teorik ve deneysel modellemeye yönelik iki problem durumu verilmiştir. Verilerin analizinde betimsel analiz yapılmıştır. Öğrencilerin modelleme becerileri, matematiksel modelleme çemberinde yer alan aşamalar açısından incelenmiştir. Göze çarpan bulgular açısından bakıldığında; öğrencilerin büyük bir çoğunluğunun verilen gerçek yaşam problemi anlamada, matematiksel olarak ifade etmede, matematiksel bir model üretmede, modeli yorumlamada, aritmetik yerine cebiri kullanmada, matematiksel olarak bildikleri 1. dereceden 2 bilinmeyenli bir eşitsizliğin çözümünün analitik düzlemde gösteriminin gerçek yaşam probleminin çözümü sürecine transfer etmede başarılı olamadıkları belirlenmiştir.

Anahtar Kelimeler

• öğretmen adayları,matematiksel modelleme,modelleme becerisi

Examining Prospective Mathematics Teachers’ Abilities Of Mathematical Modeling

Abstract

The purpose of this study is to examine the prospective mathematics teachers’ mathematical modeling abilities and the difficulties encountered. 38 prospective primary mathematics teachers have attended to the research. Two problems concerning theoretical and empirical modelling have been given to the students. Descriptive analysis has been conducted in analyzing the data. The students’ modelling abilities have been analyzed with regard to the stages in mathematical modelling circle. It has been determined that most of the students have not been successful in understanding the real life problem given, expressing mathematically, producing a mathematical model, interpretating the model, using algebra instead of arithmetic, transferring drawing the solution of a first degree inequality in two variables into the process of the solution of the real life problem.

Keywords

• prospective mathematics teachers,mathematical modeling,modeling ability

References

1. Ang, K. C. (2001). Teaching mathematical modelling in Singapore schools. The Mathematics Educator, 6(1),63-75.
2. Angell, C., Kind, P. M., Henriksen, E. K. & Guttersrud, Ø. (2008). An empirical-mathematical modelling approach to upper secondary physics. Physics Education, 43(3), 256-264
3. Berry, J., & Houston, K. (1995). Mathematical Modelling. Bristol: J. W. Arrowsmith Ltd.
4. Berry, J. & Nyman, M. A.(1998). Introducing mathematical modelling skills to students and the use of posters in assestment. Primus, 8(2), 103-115.
5. Blomhoj, M. & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. ZDM, 38 (2), 163-177.
6. Blum, W., Galbraith, P., Henn, H-W., & Niss, M. (Eds.) (2007). Modelling and applications in mathematics education: New ICMI studies series No. 10. New York: Springer.
7. Blum, W., & Ferri, B. R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematica Modelling and Application, 1 (1), 45-58.
8. Burghes, D. N. & Huntley, L. (1982). Teaching mathematical modeling- reflections and advice. International Journal of Mathematical Education in Science and Technology, 13 (6), 735-754.

9. Christiansen, I. (2001) The effect of task organisation on classroom modelling activities. In J. Matos, W.Blum, K. Houston, & S. Carreira (Eds.), Modelling and Mathematics Education, ICTMA 9: Applications in Science and Technology (pp. 311-320). Chichester: Horwood Publishing.
10. Crouch, R., & Haines, C. (2004). Mathematical modelling: transitions between the real world and the mathematical model. Int. j. math. educ. sci. technol., 35 (2), 197–206.
11. Doruk, B. K. (2010). Matematiği Günlük yaşama Transfer Etmede Matematiksel Modellemenin Etkisi. Yayınlanmamış Doktora Tezi. Hacettepe Üniversitesi, Ankara.
12. English, L. & Watters, J. (2004). Mathematical Modeling in the Early School Years. Mathematics Education Research Journal , 16(3), 59-80.
13. Erdoğan, A. (2010). Primary teacher education students’ability to use functions as modeling tools. Procedia Social and Behavioral Sciences, 2, 4518–4522.
14. Galbraith, P. & Stillman, G. (2001). In J. F. Matos, W. Blum, S. K. Houston, & S. P. Carreira (eds), Modelling and Mathematics, (pp. 300). Chichester: Horwood Publishing.
15. Güzel, E. B. ve 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.
16. Haines, C., Crouch, R. & Davies, J (2001). Understanding students’ modelling skills. In J. Matos, W. Blum, K. Houston, & S. Carreira (Eds.), Modelling and Mathematics Education, ICTMA 9: Applications in Science and Technology (pp. 366-380). Chichester: Horwood Publishing.
17. Hodgson, T. (1997). On the use of open-ended, real-world problems. In: K. Houston, W. Blum, I. Huntley, N.T. Neill, (Eds.), Teaching and learning mathematical modelling. (pp.211-218). Chichester: Albion publishing limited.
18. Ikeda, T. & Stephens, M. (2001). The effects of students’discussion in mathematical modelling. In J.F. Matos, W. Blum, S.K. Houston & S.P. Carreira (eds.), Modelling and Mathematics Education, 381- 400. Chichester: Horwood Publishing.
19. Kaiser, G. (1986). Anwendungen im Mathematik-unterricht, Vol.2, Bad Salzdetfurth: Franzbecker.
20. Kaiser, G. (2005). Mathematical Modelling in School—Examples and Experiences. In Kaiser, G. & Henn, H.-W. (Eds.),Mathematikunterricht im Spannungsfeld von Evaluation und Evolution (pp. 99–108) Hildesheim: Franzbecker.
21. Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling, ICTMA 12: Education, engineering and economics: proceedings from the twelfth International Conference on the Teaching of Mathematical Modelling and Applications (pp. 110-119). Chichester: Horwood.
22. Kaiser, G. & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM, 38 (2), 196-208.
23. Keskin, Ö. Ö. (2008). Ortaöğretim Matematik Öğretmen Adaylarının Matematiksel Modelleme Yapabilme Becerilerinin Geliştirilmesi Üzerine Bir Araştırma. Yayınlanmamış Doktora Tezi. Gazi üniversitesi, Ankara.
24. Klymchuk, S., & Zverkova, T. (2001). In J. F. Matos, W. Blum, S. K. Houston, & S. P. Carriera (eds), Modelling and Mathematics Education, (pp. 227). Chichester: Horwood Publishing.
25. Leiss, D., Schukajlow, S., Blum, W., Messner, R., & Pekrun, R. (2010). The Role of the Situation Model in Mathematical Modelling— Task Analyses, Student Competencies, and Teacher Interventions. J Math Didakt, 31, 119–141.
26. Lesh, R. A., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second Handbook of research on mathematics teaching and learning (pp.763-804). Greenwich, CT: Information Age Publishing.
27. Lingefjärd, T (2006). Faces of mathematical modeling. Zentralblatt für Didaktik der Mathematik, 38 (2), 96-112.
28. Lingefjärd, T. & Holmquist, M. (2001). Mathematical modeling and technology in teacher education—Visions and reality. In J. Matos, W. Blum, K. Houston, S. Carreira (Eds.)Modelling and Mathematics Education ICTMA 9: Applications in Science and Technology (pp. 205–215). Horwood: Chichester.
29. Maaß, K. (2006). What are modelling competencies? ZDM, 38 (2), 113- 142
30. Mousoulides, N. & English, L. D. (2008). Modeling with data in Cypriot and Australian classrooms. The 32nd International Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, (pp 423-430). Morelia, Mexico.
31. Niss, M. (2001). University mathematics based on problem-oriented student projects: 25 years of experiences with the Roskilde model. In D. Holton (ed.): The teaching and learning of mathematics at university level: an ICMI study, (pp. 405-422). Dordrecht: Kluwer Academic Publishers.
32. Niss, M. (2003). Mathematical Competencies and the Learning of Mathematics: The Danish KOM Project. In: Gagatsis, A./Papastavridis, S. (Eds), 3rd Mediterranean Conference on Mathematical Education. Athens: The Hellenic Mathematical Society, 115–124.
33. OECD (2007). PISA 2006 - Science Competencies for Tomorrow's World, Vol. 1&2. Paris: OECD
34. Olkun, S.,Şahin, Ö., Akkurt, Z., Dikkartın, F.T. ve Gülbağcı, H. (2009). Modelleme Yoluyla Problem Çözme ve Genelleme: İlköğretim Öğrencileriyle Bir Çalışma. Eğitim ve Bilim, 34, 65-73.
35. Ostler, E. (2000). Mathematical Modeling: Some Ideas and Suggestions for Pre-service Teacher Preparation. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 2, 1-10.
36. Rita Borromeo Ferri, R. (2010). On the Influence of Mathematical Thinking Styles on Learners’ Modeling Behavior. J Math Didakt, 31, 99–118.
37. Tanner, H., Jones, S. (1995): Developing Metacognitive Skills in mathematical modelling – a socio-contructivist interpretation. In C. Sloyer, W. Blum, I. Huntley, (Eds.), Advances and perspectives in the teaching of mathematical modelling and applications (pp.61-70). Yorklyn: Water Street Mathematics.
38. Türker, Sağlam ve Umay (2010). Preservice teachers’performances at mathematical modeling process and views on mathematical modeling. Procedia Social and Behavioral Sciences, 2, 4622– 4628.
39. Ural, A. (2006). Fonksiyon öğreniminde kavramsal zorluklar. Ege Eğitim Dergisi, 7 (2), 75–94.
40. Ural, A. (2012). Fonksiyon kavramı: tanımsal bilginin kavramın çoklu temsillerine transfer edilebilmesi ve bazı kavram yanılgıları, Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 31, 91-103.
41. Verschaffel, L., De Corte, E. & Borghart, I. (1997). Pre-service teachers’conceptions and beliefs about the role of real-world knowledge in mathematical modeling of school word problems. Learning and Instruction, 7 (4), 339-359.