An Analysis of Pre-Service Mathematics Teachers' Behavior on Mathematical Modeling Cycle

Year 2021, , 571 - 585, 05.10.2021

Zeynep Çakmak Gürel , Ahmet Işık

https://doi.org/10.14686/buefad.871566

Cited By: 1

Abstract

The aim of the study is to determine the behavior on individual modeling cycle of pre-service teachers who participate in mathematical modeling learning environment and who do not. An action research method was employed in the study. The research participants consisted of 32 pre-service mathematics teachers, 17 of whom attended the learning environment while the rest did not. Two mathematical modeling tasks were used in the pre and post interview. In pre interviews, pre-service teachers were interviewed individually, and the modelling routes of the pre-service teachers were closely monitored. At the end of the 11-week action plan, the post interview was made individually with the pre-service teachers. The recorded dialogues were analyzed during modeling cycles. It was determined that all pre-service teachers had a nonlinear cycle in the pre and post interviews. Pre-service teachers experienced in modeling repeated many steps back and forth. It was determined that they tried to revise the model when they reached a conclusion, so they had more complex modeling cycles. In addition, they mostly act in the world of mathematics. Pre-service teachers who are not experienced in modeling made a direct transition to real results without creating a mathematical model. It has been found that their areas of action are generally in the real world and they move less in the modeling cycle.

Keywords

matematical modeling, modeling cycle, modeling route

Matematik Öğretmeni Adaylarının Matematiksel Modelleme Döngüsü Üzerindeki Davranışlarının İncelenmesi

Abstract

Bu çalışmanın amacı, matematiksel modellemeyi öğrenme ortamına katılan ve katılmayan öğretmen adaylarının bireysel modelleme döngüleri üzerindeki davranışlarını belirlemektir. Çalışmada eylem araştırması yöntemi kullanılmıştır. Çalışma grubu, 17’si öğrenme ortamına katılan ve geri kalanı öğrenme ortamına katılmayan olmak üzere 32 matematik öğretmen adayından oluşmaktadır. Ön ve son görüşmede iki adet modelleme durumu kullanılmıştır. Ön görüşmede öğretmen adayları ile bireysel olarak görüşme yapılmış ve öğretmen adaylarının modelleme rotaları yakından izlenmiştir. 11 haftalık eylem planı sonunda, son görüşmede yine öğretmen adaylarına bireysel olarak uygulanmıştır. Kaydedilen diyaloglar, modelleme döngüsü boyunca analiz edilmiştir. Tüm öğretmen adaylarının ön ve son görüşmede lineer olmayan modelleme döngüsüne sahip oldukları belirlenmiştir. Modellemeyi deneyimlemiş olan öğretmen adayları ileri geri birçok adımı tekrar etmişlerdir. Bir sonuca ulaştıklarında modeli revize etmeye çalıştıkları, bu yüzden de daha karmaşık modelleme döngülerine sahip oldukları belirlenmiştir. Ayrıca bu öğretmen adayları matematik dünyasında daha fazla hareket etmişlerdir. Modellemeyi deneyimlemeyen öğretmen adayları ise matematiksel model oluşturmadan gerçek sonuçlara doğrudan geçiş yapmışlardır. Hareket alanlarının genellikle gerçek dünyada olduğu ve modelleme döngüsünde daha az hareket ettikleri bulunmuştur.

Keywords

matematiksel modelleme, modelleme döngüsü, modelleme rotası

References

• 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. Berry, J. S., & Houstan, S. K. (1995). Mathematical modelling. London: Edward Arnold.
• Biccard, P., & Wessels D. C. J. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. In G. Kaiser, W. Blum, R. B. Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 375-383). New York: Springer. doi: 10.1007/978-94-007-0910-2_37
• Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1) 45-58.
• Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering, and economics (pp. 222–231). Chichester: Horwood.
• Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM International Journal on Mathematics Education, 38(2), 86–95.
• Borromeo Ferri, R. (2007). Modelling problems from a cognitive perspective. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering, and economics (pp. 260–270). Cambridge, UK: Woodhead Publishing Limited.
• Borromeo Ferri, R., (2010). On the influence of mathematical thinking styles on learners’modeling behavior. Journal für Mathematik-Didaktik, 31, 99-118. doi: 10.1007/s13138-010-0009-8
• Borromeo Ferri, R. (2011). Effective mathematical modelling without blockages-a commentary. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 181-185). New York: Springer.
• Borromeo Ferri, R. (2012, July). Mathematical thinking styles and their influence on teaching and learning mathematics. Paper presented at the meeting of the 12. International Congress on Mathematical Education. Korea: Seoul.
• Carr, W., & Kemmis, S. (2003). Becoming critical: education, knowledge and action research. New York: RoutledgeFarmer, Taylor & Francis.
• Czocher, J. A. (2016) Introducing modeling transition diagrams as a tool to connect mathematical modeling to mathematical thinking. Mathematical Thinking and Learning, 18(2), 77-106, doi: 10.1080/10986065.2016.1148530.
• Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modeling? In W. Blum, P.L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modeling and Applications in Mathematics Education (ICMI 14) (pp. 69–78). New York: Springer.
• Elliott, J. (1991). Action research for educational change. Philadelphia: Open University Press.
• Frejd, P., & Ärlebäck, J. B. (2011). First results from a study investigating Swedish upper secondary students’mathematical modelling competencies. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 407–416). Springer: New York.
• Galbraith, P. L., & Stillman, G. (2001). Assumptions and context: Pursuing their role in modeling activity. In J. F. Matos, W. Blum, K. Houston & S. P. Carreira (Eds.), Modeling and mathematics education: ICTMA9 applications in science and technology (pp. 300–310). Chichester: Horwood.
• Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM. 38(2), 143-162. doi: 10.1007/BF02655886.
• Gatabi, A. R., & Abdolahpour, K. (2013). Investigating students’modeling competency through grade, gender, and location. In B. Ubuz, C. Haser & M. A. Mariotti (Eds.), Proceedings of the 8th congress of the european society for research in mathematics education CERME 8 (pp. 1070-1077). Turkey: Middle East Technical University.
• Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modelling: approaches and developments from German speaking countries. ICME-13 Topical Surveys, 1-42, Switzerland: Springer International Publishing. doi: 10.1007/978-3-319-45004-9_1.
• Haines, C. R., & Crouch, R. (2010). Remarks on a modeling cycle and interpreting behaviours. In R. Lesh, P. Galbraith, C., R. Haines & A. Hurford (Eds.), Modelig students’mathematical modeling competencies (ICTMA 13) (pp. 145-154). New York: Springer.
• Ji, X. (2012, July). A quasi-experimental study of high school students’mathematics modelling competence. Paper presented at the meeting of the 12. International Congress on Mathematical Education. Korea: Seoul.
• Kehle, P.E., & Lester F. K. (2003). A semiotic look at modelling behavior. In R. Lesh & H. M. Doerr (Ed.), Beyond constructivism: models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 97-125). Mahwah N. J.:Lawrance Erlbaum Associates Publishers.
• Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modelling 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 N. J.:Lawrance Erlbaum Associates Publishers.
• Maaß, K. (2006). What are modelling competencies? Zentralblatt Für Didactik Der Mathematic, 38(2), 113-142. doi: 10.1007/BF02655885
• Matsuzaki, A. (2011). Using response analysis mapping to display modellers’mathematical modelling progress. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (ICTMA 14) (pp. 499-508). New York: Springer.
• Peter Koop, A. (2004). Fermi problems in primary mathematics classrooms: pupils’ınteractive modelling processes. In I. Putt, R. Farragher & 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.
• Schaap, S., Vos, P., & Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: Exploring a framework. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (ICTMA 14) (pp. 137-146). New York: Springer.
• Stillman, G. (2000). Impact of prior knowledge of task context on approaches to applications tasks. The Journal of Mathematical Behavior, 19(3), 333–361. doi:10.1016/S0732-3123(00)00049-3
• Swetz, F. and Hartzler, J. S. (1991). Mathematical modeling in the secondary school curriculum: A resource guide of classroom exercises. Reston, VA: NCTM.
• Thompson, M., & Yoon, C. (2007). Why build a mathematical model? A taxonomy of situations that create the need for a model to be developed. In D. K. Lyn, & D. English (Ed.), Handbook of international research in mathematics education (pp. 193–200). Mahwah, NJ: Routledge.
• Tomal, D. R. (2010). Action research for education (2. Ed.). Lanham, MD: Rowman and Littlefield Education.
• Voskoglou, M. G. (2006). The use of mathematical modelling as a tool for learning Mathematical. Quaderni di Ricerca in Didattica, 16, 53-60.