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Matematiksel Modelleme Sürecinde Öğretmen Adaylarının Modelleme Döngüleri: Güneş Enerji Sistemleri Görevi

Yıl 2023, Cilt: 20 Sayı: 1, 389 - 407, 17.04.2023
https://doi.org/10.33711/yyuefd.1215370

Öz

Bu çalışmanın amacı öğretmen adaylarının matematiksel modelleme etkinlikleri sırasında ortaya çıkan modelleme döngülerinin incelenmesidir. Araştırmada durum çalışması yöntemi kullanılmıştır. Çalışmaya 119 dördüncü sınıf öğretmen adayı katılmıştır. Öğretmen adayları gruplar halinde çalıştılar. Böylece toplamda 28 farklı grup bulunmaktadır. Modelleme görevi, modelleme kriterleri dikkate alınarak tasarlanmıştır. Veri toplama araçlarını öğretmen adaylarının çalışma kağıtları oluşturmaktadır. Verilerin analizinde ise içerik analizi yöntemi kullanılmıştır. Elde edilen bulgulara göre, öğretmen adaylarının dört farklı modelleme döngüsü oluşturduğu belirlenmiştir. Birincisi, grupların %7’ sini kapsamaktadır ve gerçek modele kadar ilerleyebilen öğretmen adaylarının oluşturduğu döngüdür. İkincisi, grupların %68’ ini oluşturmakta olup matematiksel model oluşturmadan gerçek modelden matematiksel sonuçlara kadar ilerleyen öğretmen adaylarının oluşturduğu döngüdür. Üçüncüsü, grupların %7’sini kapsayan ve matematiksel modele kadar ilerleyerek süreci sonlandıran öğretmen adaylarının oluşturduğu döngüdür. Dördüncüsü, grupların %18’ini içeren ve modelleme döngüsünü tamamlayan öğretmen adaylarının oluşturduğu döngüdür. Modelleme döngülerinden en fazla ikinci gruptaki döngünün gerçekleştiği tespit edilmiştir. Böylece öğretmen adayları, üçüncü ve dördüncü modelleme döngülerine geçiş yapmaları için desteklenebilir.

Kaynakça

  • Abay, S. & Gökbulut, Y. (2017). Sınıf öğretmeni adaylarının matematiksel modelleme becerileri: Fermi problemleri uygulamaları. Uluslararası Türk Eğitim Bilimleri, 9, 65-83.
  • Anhalt, C. O. Cortez, R. & Bennett, A. (2018). The emergence of mathematical modeling competencies: An investigation of prospective secondary mathematics teachers. Mathematical Thinking and Learning, 20(3), 202-221.
  • Ärlebäck, J. B. (2009). On the use of realistic Fermi problems for introducing mathematical modeling in school. The Montana Mathematics Enthusiast, 6(3), 331–364. https://doi.org/10.54870/1551-3440.1157. Author, (2018).
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modeling through project work. ZDM Mathematics Education, 38(2), 163-177. https://doi.org/10.1007/BF02655887
  • Blum, W. (2015). Quality teaching of mathematical modeling: What do we know, what can we do? In S. J. Cho (Ed.), The proceedings of the 12th international congress on mathematical education (pp. 73–96). Springer. https://doi.org/10.1007/978-3-319-12688-3_9.
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Application, 1(1), 45-58.
  • Blum, W., & Leibb, D. (2007). How do teachers deal with modeling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 222-231). Horwood Publishing. https://doi.org/10.1533/9780857099419.5.221
  • Bogdan, R. C., & Biklen, S. K. (2007). Qualitative research for education: an introduction to theory and methods (5. ed.). Pearson Education, Inc.
  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM—The International Journal on Mathematics Education, 38(2), 86–95.
  • Borromeo Ferri, R. (2007). Modeling problems from a cognitive perspective. In C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 260–270). Chichester: Horwood. https://doi.org/10.1533/9780857099419.5.260
  • 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 modeling without blockages-a commentary. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (pp. 181-185). New York: Springer. doi: 10.1007/978-94-007-0910-2_19
  • Borromeo Ferri, R. (2012, July). Mathematical thinking styles and their influence on teaching and learning mathematics [Paper presentation]. 12. International Congress on Mathematical Education, Korea, Seoul.
  • Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. New York: Springer.
  • 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. https://doi.org/10.1093/teamat/hrq015
  • Common Core State Standards Initiative [CCSI]. (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  • 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.
  • Çoksöyler A. & Bozkurt, G. (2021). Bilişsel perspektif bağlamında matematiksel modelleme süreci: Altıncı sınıf öğrencilerinin deneyimleri. Buca Eğitim Fakültesi, 52, 480-502. https://doi.org/10.53444/deubefd.930216
  • Deniz, D. & Akgün, L. (2018). İlköğretim matematik öğretmeni adaylarının matematiksel modelleme becerilerinin incelenmesi. Akdeniz Eğitim Araştırmaları Dergisi, 12(24), 294- 312. https://doi.org/10.29329/mjer.2018.147.16
  • Deniz, D. & Yıldırım, B. (2018). Fen bilgisi öğretmeni adaylarının matematiksel modelleme becerilerinin incelenmesi. Anemon Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi, 6, 87-93. https://doi.org/10.18506/anemon.463533.
  • 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 (pp. 69–78). New York: Springer. doi: 10.1007/978-0-387-29822-1_5
  • Frejd, P., & Ärlebäck, J. B. (2011). First results from a study investigating Swedish upper secondary students’ mathematical modeling competencies. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (pp. 407–416). Springer: New York. doi: 10.1007/978-94-007-0910-2_40
  • 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. doi: 10.1533/9780857099655.5.300
  • Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modeling process. Zentralblatt für Didaktik der Mathematik-ZDM. 38(2), 143-162. doi: 10.1007/BF02655886.
  • Genç, M. & Karataş, İ. (2017). Problem çözme süreçlerinde öğrencilerin modelleme seviyelerinin belirlenmesi. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(3), 608-632.
  • Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modeling: approaches and developments from German speaking countries. ICME-13 Topical Surveys, 1-42. 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.), Modeling students’ mathematical modeling competencies (pp. 145-154). New York: Springer. doi: 10.1007/978-94-007-6271-8_12
  • Ji, X. (2012, July). A quasi-experimental study of high school students’ mathematics modeling competence [Paper presentation]. 12. International Congress on Mathematical Education, Korea, Seoul.
  • Kaiser, G., & Stender, P. (2013). Complex modeling problem in cooperative learning environments self-directed. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modeling: Connecting to research and practice (pp. 277–294). Dordrecht: Springer. doi: 10.1007/978-94-007-6540-5_23
  • Kaya, D. & Keşan, C. (2022). İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Modelleme Süreçleri: Su İsrafı Örneği. Van Yüzüncü Yıl Üniversitesi Eğitim Fakültesi Dergisi , 19 (3) , 1068-1097 . DOI: 10.33711/yyuefd.1177845
  • Maaß, K. (2006). What are modelling competencies? ZDM–The International Journal on Mathematics Education, 38(2), 113-142. https://doi.org/10.1007/BF02655885
  • Matsuzaki, A. (2011). Using response analysis mapping to display modellers’mathematical modeling progress. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (ICTMA 14) (pp. 499-508). Springer. doi: 10.1007/978-94-007-0910-2_49
  • Mayring, P. (2015). Qualitative content analysis: Theoretical background and procedures. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 365–380). Dordrecht: Springer.
  • Ministry of National Education. (2013). Secondary school mathematics teaching program. Milli Eğitim Basımevi [National Education Printing House].
  • Niss, M. (2015). Prescriptive modeling—Challenges and opportunities. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modeling in education research and practice: Cultural, social and cognitive influences (pp. 67–79). Cham: Springer. doi: 10.1007/978-3-319-18272-8_5
  • Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modeling (1. ed.). Routledge. https://doi.org/10.4324/9781315189314
  • Özer, A. Ö. & Bukova Guzel, E. (2020). Bisim matematiksel modelleme etkinliğinin sınıf içi ve sınıf dışı uygulaması. International Journal of Educational Studies in Mathematics, 7(4), 289-308. DOI: 10.17278/ijesim.837316.
  • Perrenet, J., & Zwaneveld, B. (2012). The many faces of the mathematical modeling cycle. Journal of Mathematical Modeling and Application, 1(6), 3–21.
  • 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 (pp. 137-146). Springer. https://doi.org/10.1007/978-94-007-0910-2_15
  • Stender, S., & Kaiser, G. (2015). Scaffolding in complex modeling situations. ZDM Mathematics Education, 47(7). doi:10.1007/s11858-015-0741-0
  • 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.
  • Tekin Dede, A. (2016). Modelling difficulties and their overcoming strategies in the solution of a modelling problem. Acta Didactica Napocensia, 9(3), 21-34.
  • Wess, R., & Greefrath, G. (2019). Professional competencies for teaching mathematical modeling—Supporting the modeling-specific task competency of prospective teachers in the teaching laboratory. In U. T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), European research in mathematics: proceedings of the eleventh congress of the European society for research in mathematics education (pp. 1274–1283). Utrecht, Netherlands.
  • Vorhölter, K., Greefrath, G., Borromeo Ferri, R., Leiß, D. & Schukajlow, S. (2019). Mathematical Modelling. In: Jahnke, H., Hefendehl-Hebeker, L. (eds) Traditions in German-Speaking Mathematics Education Research. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-11069-7_4.
  • Vos, P. & Frejd, P. (2022, February). The modeling cycle as analytic research tool and how it can be enriched beyond the cognitive dimension [Paper presentation]. 12th Congress of the European Society for Research in Mathematics Education, Bolzano, Italy.
  • Zawojewski, J. S., Lesh, R. & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 3-33). Lawrance Erlbaum Associates Publishers
  • Zöttl, L., Ufer, S., & Reiss, K. (2010). Modeling with heuristic worked examples in the KOMMA learning environment. Journal für Mathematik-Didaktik, 31(1), 143-165. doi. 10.1007/s13138-010-0008-9.

The Pre-service Teachers' Modelling Cycles in the Mathematical Modelling Process: The Task of Solar Energy System

Yıl 2023, Cilt: 20 Sayı: 1, 389 - 407, 17.04.2023
https://doi.org/10.33711/yyuefd.1215370

Öz

This study aims to explore the modelling cycles that emerge during the pre-service teachers’ mathematical modelling activities. A case study method was employed in the research. 119 pre-service teachers who were in their fourth class participated in the research. The pre-service teachers worked in groups. So, there were a total of 28 different groups. The modelling task was posed by considering the modelling criteria. The data collection tools consisted of the pre-service teachers’ working papers. The content analysis method was applied in the data analysis. The preservice teachers created four different modelling cycles. The first consisted of 7% of the groups and was the cycles that included the pre-service teachers who could reach the real model. The second was the cycle that consisted of 68% of the groups and included the pre-service teachers who could reach the mathematical results from the real model without posing any mathematical model. The third was the cycle that consisted of 7% of the groups and included the pre-service teachers who completed the process by reaching the mathematical model. The fourth was the cycle that consisted of 18% of the groups and included the pre-service teachers who completed the modelling cycle. It was determined that the cycle in the second group occurred the most among the modelling cycles. The pre-service teachers can be supported to pass the third and fourth modelling cycles.

Kaynakça

  • Abay, S. & Gökbulut, Y. (2017). Sınıf öğretmeni adaylarının matematiksel modelleme becerileri: Fermi problemleri uygulamaları. Uluslararası Türk Eğitim Bilimleri, 9, 65-83.
  • Anhalt, C. O. Cortez, R. & Bennett, A. (2018). The emergence of mathematical modeling competencies: An investigation of prospective secondary mathematics teachers. Mathematical Thinking and Learning, 20(3), 202-221.
  • Ärlebäck, J. B. (2009). On the use of realistic Fermi problems for introducing mathematical modeling in school. The Montana Mathematics Enthusiast, 6(3), 331–364. https://doi.org/10.54870/1551-3440.1157. Author, (2018).
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modeling through project work. ZDM Mathematics Education, 38(2), 163-177. https://doi.org/10.1007/BF02655887
  • Blum, W. (2015). Quality teaching of mathematical modeling: What do we know, what can we do? In S. J. Cho (Ed.), The proceedings of the 12th international congress on mathematical education (pp. 73–96). Springer. https://doi.org/10.1007/978-3-319-12688-3_9.
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Application, 1(1), 45-58.
  • Blum, W., & Leibb, D. (2007). How do teachers deal with modeling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 222-231). Horwood Publishing. https://doi.org/10.1533/9780857099419.5.221
  • Bogdan, R. C., & Biklen, S. K. (2007). Qualitative research for education: an introduction to theory and methods (5. ed.). Pearson Education, Inc.
  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM—The International Journal on Mathematics Education, 38(2), 86–95.
  • Borromeo Ferri, R. (2007). Modeling problems from a cognitive perspective. In C. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 260–270). Chichester: Horwood. https://doi.org/10.1533/9780857099419.5.260
  • 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 modeling without blockages-a commentary. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (pp. 181-185). New York: Springer. doi: 10.1007/978-94-007-0910-2_19
  • Borromeo Ferri, R. (2012, July). Mathematical thinking styles and their influence on teaching and learning mathematics [Paper presentation]. 12. International Congress on Mathematical Education, Korea, Seoul.
  • Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. New York: Springer.
  • 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. https://doi.org/10.1093/teamat/hrq015
  • Common Core State Standards Initiative [CCSI]. (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  • 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.
  • Çoksöyler A. & Bozkurt, G. (2021). Bilişsel perspektif bağlamında matematiksel modelleme süreci: Altıncı sınıf öğrencilerinin deneyimleri. Buca Eğitim Fakültesi, 52, 480-502. https://doi.org/10.53444/deubefd.930216
  • Deniz, D. & Akgün, L. (2018). İlköğretim matematik öğretmeni adaylarının matematiksel modelleme becerilerinin incelenmesi. Akdeniz Eğitim Araştırmaları Dergisi, 12(24), 294- 312. https://doi.org/10.29329/mjer.2018.147.16
  • Deniz, D. & Yıldırım, B. (2018). Fen bilgisi öğretmeni adaylarının matematiksel modelleme becerilerinin incelenmesi. Anemon Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi, 6, 87-93. https://doi.org/10.18506/anemon.463533.
  • 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 (pp. 69–78). New York: Springer. doi: 10.1007/978-0-387-29822-1_5
  • Frejd, P., & Ärlebäck, J. B. (2011). First results from a study investigating Swedish upper secondary students’ mathematical modeling competencies. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (pp. 407–416). Springer: New York. doi: 10.1007/978-94-007-0910-2_40
  • 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. doi: 10.1533/9780857099655.5.300
  • Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modeling process. Zentralblatt für Didaktik der Mathematik-ZDM. 38(2), 143-162. doi: 10.1007/BF02655886.
  • Genç, M. & Karataş, İ. (2017). Problem çözme süreçlerinde öğrencilerin modelleme seviyelerinin belirlenmesi. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 18(3), 608-632.
  • Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modeling: approaches and developments from German speaking countries. ICME-13 Topical Surveys, 1-42. 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.), Modeling students’ mathematical modeling competencies (pp. 145-154). New York: Springer. doi: 10.1007/978-94-007-6271-8_12
  • Ji, X. (2012, July). A quasi-experimental study of high school students’ mathematics modeling competence [Paper presentation]. 12. International Congress on Mathematical Education, Korea, Seoul.
  • Kaiser, G., & Stender, P. (2013). Complex modeling problem in cooperative learning environments self-directed. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modeling: Connecting to research and practice (pp. 277–294). Dordrecht: Springer. doi: 10.1007/978-94-007-6540-5_23
  • Kaya, D. & Keşan, C. (2022). İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Modelleme Süreçleri: Su İsrafı Örneği. Van Yüzüncü Yıl Üniversitesi Eğitim Fakültesi Dergisi , 19 (3) , 1068-1097 . DOI: 10.33711/yyuefd.1177845
  • Maaß, K. (2006). What are modelling competencies? ZDM–The International Journal on Mathematics Education, 38(2), 113-142. https://doi.org/10.1007/BF02655885
  • Matsuzaki, A. (2011). Using response analysis mapping to display modellers’mathematical modeling progress. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modeling (ICTMA 14) (pp. 499-508). Springer. doi: 10.1007/978-94-007-0910-2_49
  • Mayring, P. (2015). Qualitative content analysis: Theoretical background and procedures. In A. Bikner-Ahsbahs, C. Knipping & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 365–380). Dordrecht: Springer.
  • Ministry of National Education. (2013). Secondary school mathematics teaching program. Milli Eğitim Basımevi [National Education Printing House].
  • Niss, M. (2015). Prescriptive modeling—Challenges and opportunities. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modeling in education research and practice: Cultural, social and cognitive influences (pp. 67–79). Cham: Springer. doi: 10.1007/978-3-319-18272-8_5
  • Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modeling (1. ed.). Routledge. https://doi.org/10.4324/9781315189314
  • Özer, A. Ö. & Bukova Guzel, E. (2020). Bisim matematiksel modelleme etkinliğinin sınıf içi ve sınıf dışı uygulaması. International Journal of Educational Studies in Mathematics, 7(4), 289-308. DOI: 10.17278/ijesim.837316.
  • Perrenet, J., & Zwaneveld, B. (2012). The many faces of the mathematical modeling cycle. Journal of Mathematical Modeling and Application, 1(6), 3–21.
  • 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 (pp. 137-146). Springer. https://doi.org/10.1007/978-94-007-0910-2_15
  • Stender, S., & Kaiser, G. (2015). Scaffolding in complex modeling situations. ZDM Mathematics Education, 47(7). doi:10.1007/s11858-015-0741-0
  • 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.
  • Tekin Dede, A. (2016). Modelling difficulties and their overcoming strategies in the solution of a modelling problem. Acta Didactica Napocensia, 9(3), 21-34.
  • Wess, R., & Greefrath, G. (2019). Professional competencies for teaching mathematical modeling—Supporting the modeling-specific task competency of prospective teachers in the teaching laboratory. In U. T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), European research in mathematics: proceedings of the eleventh congress of the European society for research in mathematics education (pp. 1274–1283). Utrecht, Netherlands.
  • Vorhölter, K., Greefrath, G., Borromeo Ferri, R., Leiß, D. & Schukajlow, S. (2019). Mathematical Modelling. In: Jahnke, H., Hefendehl-Hebeker, L. (eds) Traditions in German-Speaking Mathematics Education Research. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-11069-7_4.
  • Vos, P. & Frejd, P. (2022, February). The modeling cycle as analytic research tool and how it can be enriched beyond the cognitive dimension [Paper presentation]. 12th Congress of the European Society for Research in Mathematics Education, Bolzano, Italy.
  • Zawojewski, J. S., Lesh, R. & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 3-33). Lawrance Erlbaum Associates Publishers
  • Zöttl, L., Ufer, S., & Reiss, K. (2010). Modeling with heuristic worked examples in the KOMMA learning environment. Journal für Mathematik-Didaktik, 31(1), 143-165. doi. 10.1007/s13138-010-0008-9.
Toplam 47 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Zeynep Çakmak Gürel 0000-0003-0913-3291

Erken Görünüm Tarihi 20 Nisan 2023
Yayımlanma Tarihi 17 Nisan 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 20 Sayı: 1

Kaynak Göster

APA Çakmak Gürel, Z. (2023). The Pre-service Teachers’ Modelling Cycles in the Mathematical Modelling Process: The Task of Solar Energy System. Van Yüzüncü Yıl Üniversitesi Eğitim Fakültesi Dergisi, 20(1), 389-407. https://doi.org/10.33711/yyuefd.1215370