The Investigation of Creation and Solving Processes of Mathematical Modeling Activities of Mathematics Teachers
Öz
The aim of this study is to evaluate the suitability of the mathematical modeling activities created and solved by mathematics teachers. The activities created are examined according to modeling principles and their solutions are investigated according to solution steps, and the data obtained is analyzed and reported. About 9 hours of theoretical mathematical modeling activities was given to 17 mathematics teachers who participated in the study. Then at the end of five weeks asked them to create a mathematical modeling activity. Using a method of case study, the study highlighted the short-comings of the teachers with regards to "structure documentation" and "model generalization" which are essential features of the activity. To understand the nature of the mathematical modeling activity a long-term project, workshop and in-service training activities are recommended to the teachers in order to earn more experience in the process of creating a mathematical modeling activity. So, it can be ensured that teachers gain more experience in the process of preparing and applying activities.
Anahtar Kelimeler
Mathematical modelling mathematical modelling principles mathematics teacher
Kaynakça
- Aydın-Güç, F. (2014). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi. Doktora tezi, Karadeniz Teknik Üniversitesi, Trabzon. Bilgili, S. & Çiltaş, A. (2018). A Multi-variable study of primary school pre-service teachers' abilities to generate and solve mathematical modelling activities. International Journal of Educational Studies in Mathematics. 5(2), 66-77. Blum, W. (1991). Applications and modelling in mathematics teaching - A review of arguments and instructional aspects. In M. Niss, W. Blum, and I. Huntley (Eds.), Teaching of Mathematical Modelling and Applications (S. 10-29). England: Ellis Horwood. Blum, W. & Kaiser, G. (1997). Vergleichende empirische Untersuchungen zu mathematischen Anwendungsfahigkeiten von englischen und deutschen Lernenden. Unpublished application for a DFG-sponsoship. Borromeo Ferri, R. (2014). Matematiksel modelleme öğrenimi ve öğretimi. 3. Matematik Eğitimi Uygulamaları Matematiksel Modelleme Etkinlikleri Çalıştayı, Matematiksel Güç ve İnovatif Tasarım Derneği, 1 – 4 Nisan 2014, İzmir. Büyüköztürk, Ş., Kılıç-Çakmak, E., Erkan-Akgün, Ö., Karadeniz, Ş. & Demirel, F. (2016). Bilimsel araştırma yöntemleri (22th ed.). Ankara: PEGEM. 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. Chamberlin, S.A., & Moon, S.M. (2008). How does the problem based learning approach compare to the model-eliciting activity approach in mathematics?. International Journal of Mathematics Teaching and Learning, 9(3), 78-105. Çiltaş, A. (2015). Ortaokul matematik öğretmenlerinin matematiksel modelleme etkinliği oluşturma süreçlerinin incelenmesi. Route Educational and Social Science Journal. 2(4). Dede, A. T., Hidiroglu, Ç. N., & Güzel, E. B. (2017). Examining of model eliciting activities developed by mathematics student teachers. Journal on Mathematics Education, 8(2), 223-242. Deniz, D., & Akgün, 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. English, L.D. (2009). Promoting interdisciplinarity through mathematical modelling. Zentralblatt für Didaktik der Mathematik, 41, 161-181. Erbaş, A. K., Çetinkaya, B., Alacacı, C., Çakıroğlu, E., Aydoğan Yenmez, A., Şen, Lise matematik konuları için günlük hayattan modelleme soruları [Real-life modeling tasks for high school mathematics].. "Türkiye Bilimler Akademisi (TÜBA)", (2016). Ji, X. (2012). A quasi-experimental study of high school students‘ mathematics modelling competence. 12th International Congress On Mathematical Education Program. COEX, Seoul, Korea Kula-Unver, S., Hıdıroğlu,Ç., Tekin-Dede, A., & Bukova-Güzel, E. (2018). Factors revealed while posing mathematical modelling problems by mathematics student teachers. European Journal of Educational Research. 7(4), 941 – 952. Lesh, R., & Doerr, H.M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. . In R. Lesh & H. Doerr (Eds.), Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 3-33). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591-646). Mahwah, NJ: Lawrence Erlbaum. Lesh, R.A., & Zawojewski, J.S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics (pp. 763– 804). Charlotte, NC: Information Age Publishing. Lester, F.K. and Kehle, P.E., (2002). From problem solving to modeling: The Evolution of thinking about reseach on complex mathematical activity. Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning and teaching, Ed: R. Lesh ve H.M. Doerr. (501-517). Lawrance Erlbaum Associates Publishers Milli Eğitim Bakanlığı (MEB), (2013). Ortaöğretim matematik dersi (9-12. Sınıflar) Öğretim Programı. Ankara: MEB Basımevi. Mousoulides, N. G., and English, L. D. (2011). Engineering model eliciting activities for elementary school students. . In G. Kaiser, W. Blum, R. B. Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA 14 (pp. 221-230). Netherlands: Springer. Öztürk, F. (2016). İlköğretim matematik öğretmeni adaylarının etkinlik hazırlama ve uygulama süreçlerinin incelenmesi. Doktora Tezi, Atatürk Üniversitesi, Erzurum. Stohlmann, M., Maiorca, C., & Allen, C. (2017). A case study of teachers' development of well-structured mathematical modelling activities. Mathematics Teacher Education and Development, 19(2), 4-24. Tekin Dede, A. & Bukova Guzel, E. (2016). Matematik eğitiminde matematiksel modelleme. Ankara: Pegem. Urhan, S., & Dost, Ş. (2018). Analysis of ninth grade mathematics course book activities based on model-eliciting principles. International Journal of Science and Mathematics Education, 16(5), 985-1002. Voskoglou, M. (2007). A stochastic model for the modeling process. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 149-157). ICTMA12, Chichester: Horwood Pub. Yin,R.K. (2008). Case study research:Design and Methods (4th ed.). Thousand Oaks, CA: Sage. Yu, S., & Chang, C. (2009). What did Taiwan mathematics teachers think of model-eliciting activities and modeling? 14. International Conference on the Teaching of Mathematical Modeling and Applications, ICTMA-14. Hamburg: University of Hamburg.
Matematik Öğretmenlerinin Matematiksel Modelleme Etkinliklerini Oluşturma ve Çözme Süreçlerinin İncelenmesi
Öz
Bu araştırmada, matematik öğretmenleri tarafından oluşturulan ve çözümü yapılan matematiksel modelleme etkinliklerinin, uygunluğunun incelenmesi amaçlanmıştır. Oluşturulan etkinlikler model oluşturma prensiplerine göre değerlendirilmiş; yapılan çözümler ise modeli çözme basamaklarına göre incelenmiş ve veriler analiz edilerek raporlaştırılmıştır. Araştırmaya katılan toplam 17 matematik öğretmenine, üç haftası günde 3 saat olmak üzere 9 saat matematiksel modelleme etkinliklerine yönelik teorik bilgi içeren; toplam beş hafta matematiksel modelleme eğitimi verilmiş ve çalışma sonunda her birinden birer matematiksel modelleme etkinliği oluşturmaları istenmiştir. Özel durum çalışması yönteminin uygulandığı bu çalışmanın sonucunda, bir etkinlikte bulunması gereken özelliklerden “yapı belgelendirme” ve “model genelleme” prensipleri konusunda öğretmenlerdeki eksiklik göze çarpmaktadır. Matematiksel model etkinliği oluşturma sürecinde daha fazla deneyime sahip olmaları adına, uzun süreli bir proje, çalıştay ve hizmet içi seminerler verilerek matematiksel modelleme etkinliğinin doğasının anlatılması önerilmektedir. Bu sayede öğretmenlerin etkinlik hazırlama ve uygulama süreçlerine yönelik daha fazla tecrübe kazanmaları sağlanabilir.
Anahtar Kelimeler
Matematiksel modelleme matematiksel model oluşturma prensipleri matematik öğretmeni
Kaynakça
- Aydın-Güç, F. (2014). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi. Doktora tezi, Karadeniz Teknik Üniversitesi, Trabzon. Bilgili, S. & Çiltaş, A. (2018). A Multi-variable study of primary school pre-service teachers' abilities to generate and solve mathematical modelling activities. International Journal of Educational Studies in Mathematics. 5(2), 66-77. Blum, W. (1991). Applications and modelling in mathematics teaching - A review of arguments and instructional aspects. In M. Niss, W. Blum, and I. Huntley (Eds.), Teaching of Mathematical Modelling and Applications (S. 10-29). England: Ellis Horwood. Blum, W. & Kaiser, G. (1997). Vergleichende empirische Untersuchungen zu mathematischen Anwendungsfahigkeiten von englischen und deutschen Lernenden. Unpublished application for a DFG-sponsoship. Borromeo Ferri, R. (2014). Matematiksel modelleme öğrenimi ve öğretimi. 3. Matematik Eğitimi Uygulamaları Matematiksel Modelleme Etkinlikleri Çalıştayı, Matematiksel Güç ve İnovatif Tasarım Derneği, 1 – 4 Nisan 2014, İzmir. Büyüköztürk, Ş., Kılıç-Çakmak, E., Erkan-Akgün, Ö., Karadeniz, Ş. & Demirel, F. (2016). Bilimsel araştırma yöntemleri (22th ed.). Ankara: PEGEM. 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. Chamberlin, S.A., & Moon, S.M. (2008). How does the problem based learning approach compare to the model-eliciting activity approach in mathematics?. International Journal of Mathematics Teaching and Learning, 9(3), 78-105. Çiltaş, A. (2015). Ortaokul matematik öğretmenlerinin matematiksel modelleme etkinliği oluşturma süreçlerinin incelenmesi. Route Educational and Social Science Journal. 2(4). Dede, A. T., Hidiroglu, Ç. N., & Güzel, E. B. (2017). Examining of model eliciting activities developed by mathematics student teachers. Journal on Mathematics Education, 8(2), 223-242. Deniz, D., & Akgün, 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. English, L.D. (2009). Promoting interdisciplinarity through mathematical modelling. Zentralblatt für Didaktik der Mathematik, 41, 161-181. Erbaş, A. K., Çetinkaya, B., Alacacı, C., Çakıroğlu, E., Aydoğan Yenmez, A., Şen, Lise matematik konuları için günlük hayattan modelleme soruları [Real-life modeling tasks for high school mathematics].. "Türkiye Bilimler Akademisi (TÜBA)", (2016). Ji, X. (2012). A quasi-experimental study of high school students‘ mathematics modelling competence. 12th International Congress On Mathematical Education Program. COEX, Seoul, Korea Kula-Unver, S., Hıdıroğlu,Ç., Tekin-Dede, A., & Bukova-Güzel, E. (2018). Factors revealed while posing mathematical modelling problems by mathematics student teachers. European Journal of Educational Research. 7(4), 941 – 952. Lesh, R., & Doerr, H.M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. . In R. Lesh & H. Doerr (Eds.), Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 3-33). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591-646). Mahwah, NJ: Lawrence Erlbaum. Lesh, R.A., & Zawojewski, J.S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics (pp. 763– 804). Charlotte, NC: Information Age Publishing. Lester, F.K. and Kehle, P.E., (2002). From problem solving to modeling: The Evolution of thinking about reseach on complex mathematical activity. Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning and teaching, Ed: R. Lesh ve H.M. Doerr. (501-517). Lawrance Erlbaum Associates Publishers Milli Eğitim Bakanlığı (MEB), (2013). Ortaöğretim matematik dersi (9-12. Sınıflar) Öğretim Programı. Ankara: MEB Basımevi. Mousoulides, N. G., and English, L. D. (2011). Engineering model eliciting activities for elementary school students. . In G. Kaiser, W. Blum, R. B. Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA 14 (pp. 221-230). Netherlands: Springer. Öztürk, F. (2016). İlköğretim matematik öğretmeni adaylarının etkinlik hazırlama ve uygulama süreçlerinin incelenmesi. Doktora Tezi, Atatürk Üniversitesi, Erzurum. Stohlmann, M., Maiorca, C., & Allen, C. (2017). A case study of teachers' development of well-structured mathematical modelling activities. Mathematics Teacher Education and Development, 19(2), 4-24. Tekin Dede, A. & Bukova Guzel, E. (2016). Matematik eğitiminde matematiksel modelleme. Ankara: Pegem. Urhan, S., & Dost, Ş. (2018). Analysis of ninth grade mathematics course book activities based on model-eliciting principles. International Journal of Science and Mathematics Education, 16(5), 985-1002. Voskoglou, M. (2007). A stochastic model for the modeling process. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 149-157). ICTMA12, Chichester: Horwood Pub. Yin,R.K. (2008). Case study research:Design and Methods (4th ed.). Thousand Oaks, CA: Sage. Yu, S., & Chang, C. (2009). What did Taiwan mathematics teachers think of model-eliciting activities and modeling? 14. International Conference on the Teaching of Mathematical Modeling and Applications, ICTMA-14. Hamburg: University of Hamburg.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Eğitim Üzerine Çalışmalar |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Mart 2020 |
| Gönderilme Tarihi | 27 Ocak 2020 |
| Kabul Tarihi | 12 Mart 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 5 Sayı: 1 |
