FEN BİLGİSİ ÖĞRETMEN ADAYLARININ MATEMATİKSEL MODELLEME YAPABİLME BECERİLERİNİN GELİŞİMİ

Yıl 2015, Sayı: 24, 122 - 160, 01.04.2015

Zeynep Başkan Takaoğlu Nedim Alev

Öz

Bu çalışmada, matematiksel modelleme kullanılarak Doğrusal ve Düzlemde Hareket ünitelerinin öğretiminde fen bilgisi öğretmen adaylarının matematiksel modelleme yapabilme becerilerindeki gelişimleri incelenmiştir. Bu amaç doğrultusunda çalışmada Doğrusal ve Düzlemde Hareket ünitelerine yönelik geliştirilen öğretmen adayı ve öğretim elemanı rehber materyalleri 23 öğretmen adayına uygulanmış ve bu çalışma kapsamında bütün etkinliklere katılan 12 öğretmen adayının verileri içerik analizi ile analiz edilmiştir. Doğru, kısmen doğru, yanlış ve boş kategorilerilerinden oluşan bir rubrik ile incelenen öğretmen adayı materyalleri kendi içerisinde benzer kategoriler altında toplanmış, ardından rubrikte belirlenen kategoriler içerisine dahil edilmiş ve adaylar aldıkları toplam puanlar ve her bir aşama için verdikleri cevaplar açısından değerlendirilmiştir. Çalışma sonucunda öğretmen adaylarının etkinlikler ilerledikçe çalışmada kullanılan matematiksel modelleme etkinliklerinin tüm aşamalarında gelişim gösterdikleri belirlenmiş ve gerçek dünya problemi aşamasında başarılı olan adayların diğer aşamaları kolaylıkla yapabildikleri sonucuna ulaşılmıştır. Bunun yanında öğretmen adaylarının günlük yaşam- fizik bağını kurmalarında matematiksel modelleme çalışmalarının olumlu katkısı olduğu sonucuna varılmıştır.

Anahtar Kelimeler

Doğrusal hareket, düzlemde hareket, matematiksel modelleme, ilişkilendirme

Developing Prospective Science Teachers’ Mathematical Modelling Performances

Öz

In this study, prospective science teachers’ mathematical modelling performances were investigated at teaching one and two dimensional motion units with the help of mathematical modelling. For this aim, prospective science teachers and instructor’s guide materials developed for one and two dimensional motion units was applied to 23 prospective science teachers and data from 12 prospective science teachers attending all activities was analyzed for this research using content analysis. Prospective science teachers’ materials were examined using a rubric consisted of true, partially true, false and empty categories then incorporated into categories determined in rubric, and prospective science teachers’ performances were evaluated regarding the point they got from their answers at every stage of mathematical modelling. As a result of the study, it is determined that prospective science teachers showed improvements at all stages of mathematical modelling activities in the course of time, and it is concluded that those who were higher achievers at real world problem stage were performed well at the other stages. In addition, it is decided that mathematical modelling studies have positive contribution to prospective science teachers to make connection between real life and Physics.

Anahtar Kelimeler

One dimensional motion, two dimensional motion, mathematical modelling, integration

Kaynakça

• Ang, K.C. (2010). Teaching and learning mathematical modelling with technology, Proceedings of the 15th Asian Technology Conference in Mathematics, Kuala Lumpur, Malaysia.
• Ashmann, S., Zawojewski, J. & Bowman, K. (2006). Integrated mathematics and science teacher education courses: a modelling perspective, Canadian Journal of Science, Mathematics & Technology Education, 6, 2, 189-200.
• Bergman-Ärlebäck, J. (2009). On the use of realistic fermi problems for introducing mathematical modelling in school, The Montana Mathematics Enthusiast, 6, 3, 331-364.
• Barquero, B., Bosch, M. & Gascón, J. (2007). Using research and study courses for teaching modelling at university level, In M. Bosch (Ed.), Proceedings of the V Congress of the European Society for Research in Mathematics Education (CERME 5), 2050-2059, Barcelona.
• Biembengut, M., S. & Hein N. (2007). Mathematical modeling: implications for teaching, 13th Conference of the International Community of Teachers of Mathematical Modeling and Applications, Indiana University, Bloomington, USA.
• Blomhİj, M. (2007). Developing mathematical modelling competency through problem based project work - experiences from Roskilde University, Ninth International History, Philosophy & Science Teaching http://www.ucalgary.ca/ihpst07/proceedings/IHPST07%20paper s/125%20Blomhoj.pdf [09.05.2011] Conferance
• Blomhİj, M. & Jensen, T. H. (2003). Developing mathematical modelling competence: conceptual clarification and educational planning, Teaching Mathematics and its Applications, 22, 3, 123-139.
• Blomhoj, M. & Kjeldsen, T. (2007). Learning the integral concept through mathematical modelling. In: Pitta-Pantazi, D & Philippou, G. (Eds): CERME 5 – Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, 2070-2079.
• Blum, W. & Borromeo-Ferri, R. (2009). Mathematical modelling: can it be taught and learnt?, Journal of Mathematical Modelling and Application, 1, 1, 45-58.
• Bukova- Güzel, E. ve Uğurel, I. (2010). Matematik öğretmen adaylarının analiz dersi akademik başarıları ile matematiksel modelleme yaklaşımları arasındaki ilişki, Dokuz Eylül Üniversitesi Eğitim Fakültesi Dergisi, 29, 1, 69-90.
• Dervişoğlu S. ve Soran H. (2003). Orta öğretim biyoloji eğitiminde disiplinler arası öğretim yaklaşımının değerlendirilmesi, Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 25, 48-57.
• Diezmann, C. M. (2002). Enhancing students' problem solving through diagram use, Australian Primary Mathematics Classroom, 7, 3, 4-8.
• Doerr, H. M. & Tripp, J. S. (1999). Understanding how students develop mathematical models, Mathematical Thinking and Learning, 1, 3, 231 - 254.
• Doruk, B. K. (2010). Matematiği günlük yaşama transfer etmede matematiksel modellemenin etkisi, Doktora Tezi, Hacettepe Üniversitesi, Sosyal Bilimler Enstitüsü, Ankara.
• English, L. D. (2003). Mathematical modelling with young learners, In S. J. Lamon, W. A., Parker & S.K.Houston (Eds.), Mathematical modelling: a way of life (3-18). Chichester: Horwood Publishing.
• Friesel, A. & Nicolakis, G. A. (2006). Mathematical modeling as a tool to improve learning of mathematics, 9th International Conference on Engineering Education, July 23 – 28, http://icee.usm.edu/icee/conferences/icee2006/papers/3478.pdf [05.05.2011]
• Haynie, W.J. & Greenberg, D. (2001). Genetic disorders: an integrated curriculum project, The Technology Teacher, 60, 6, 10-13.
• Heck. A. (2010). Modelling in cross-disciplinary authentic student research projects, International Journal for Technology in Mathematics Education, 17, 3, 115-120.
• Hickman, F.R. (1986). Mathematical Modelling in Physics, Physics Education, 21, 173–180.
• Ikahata, S. (2007). How do novice students in mathematical modelling estimate assumptions?, 13th Conference of the International Community of Teachers of Mathematical Modeling and Applications. Indiana University Bloomington, USA.
• Klymchuk S., Zverkova T., Gruenwald N. & Sauerbier G. (2008). Increasing engineering students’ awareness to environment through innovative teaching of mathematical modelling, Teaching Mathematics and its Applications, 27, 3, 123- 130.
• Lin, F.L. & Yang, K.L. (2005). Distinctive characteristics of mathematical thinking in non-modelling friendly environment, Teaching Mathematics Applications, 24, 97-106.
• Maaß, K. (2005). Barriers and opportunities for the integration of modelling in mathematics classes: results of an empirical study, Teaching Mathematics and its Application, 24, 2-3, 61–74.
• Martinez-Luaces V. (2005). Engaging secondary school and university teachers in modelling: some experiences in South American Countries, International Journal of Mathematics Education and Science Technology, 36, 2–3, 193–205.
• Maull W. & Berry J. (2001). An investigation of student working styles in a mathematical modelling activity, Teaching Mathematics And its Applications, 20, 2, 78, 88.
• Michelsen, C. (2006). Functions: a modelling tool in mathematics and science, Zentralblatt für Didaktik der Mathematik, 38, 3, 269- 280.
• Munier, V. & Merle, H. (2009). Interdisciplinary Mathematics–Physics approaches to teaching the concept of angle in elementary school, International Journal of Science Education, 31, 14, 1857–1895.
• Nuokawa, K. (2006). Usıng drawings and generating ınformation in mathematical problem solving processes, Eurasia Journal of Mathematics, Science and Technology Education, 2, 3, 33-54.
• Ogunsola-Bandele, M. F. (1996). Mathematics in Physics - Which way forward: the influence of mathematics on students' attitudes to the teaching of Physics, Paper presented at the Annual Meeting of the National Science Teachers Association, Nigeria.
• Özer-Keskin, Ö. (2008). Ortaöğretim Matematik öğretmen adaylarının matematiksel modelleme yapabilme becerilerinin geliştirilmesi üzerine bir araştırma, Doktora Tezi, Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
• Özsevgeç, T. (2007). İlköğretim 5. sınıf kuvvet ve hareket ünitesine yönelik 5E modeline göre geliştirilen rehber materyallerin etkililiklerinin belirlenmesi, Doktora Tezi, Karadeniz Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Trabzon.
• Pantziara, M., Gagatsis, A. & Elia, I. (2009). Using diagrams as tools for the solution of non-routine Mathematical problems, Education Study of Mathematics, 72, 39–60.
• Parasuk, R. M. & Beyranedand, M. L. (2010). Algebra students' ability to recognize multiple representations and achievement, International Journal for Mathematics Teaching and Learning, http://www.cimt.plymouth.ac.uk/journal/panasuk.pdf [05.05.2011].
• Prins G., T., Bulte, A. M. W., Driel J. H. V. & Pilot, A. (2009). Students’ involvement in authentic modelling practices as contexts in Chemistry education, Research Science Education, 39, 681–700.
• Saastamoinen, K. (2005). Mathematical modelling course using the internet, Engineering/Electronics, Computer, Telecommunications and Information thailand.org/assets/papers/273_pub_24.pdf [14.03.2011] Technology, http://www.ecti
• Saglam-Arslan, A. & Arslan, S. (2010). Mathematical models in Physics: A study with prospective Physics teacher, Scientific Research and Essays 5, 7, 634-640.
• Taşkın-Can, B., Cantürk Günhan, B. ve Öngel E.S. (2005). Fen Bilgisi öğretmen adaylarının fen derslerinde matematiğin kullanımına yönelik özyeterlik inançlarının incelenmesi, Pamukkale Üniversitesi http://egitimdergi.pamukkale.edu.tr/makale/sayı17/5- FEN%20BİLGİSİ%20ÖĞRETMEN%20ADAYLARININ%20F EN%20DERSLERİNDE%20MATEMAT….pdf [7.03.2007]
• Tinker, M.H. & Thomson, J.J. (2003). Teaching mathematics to physicists in the UK – FLAP and PPLATO, Europhysics News, Vol. 34 No. 5 http://www.europhysicsnews.com/full/23/article4/article4.html [7.03.2008]
• Tipi, N. S. (2009). Teaching and assessing supply chain modelling modules in higher education, The International Journal of Learning, 16, 3, 283-292.
• Wallace, M. L. & Ellerton, N. F. (2004). Language & Belief Factors in Learning & Teaching Mathematics & Physics: a study of three teachers, Psychology of Mathematics & Education of North America; Annual Meeting, Toronto, CA, 1, 7.
• White, A. (2000). Mathematical modelling and the general mathematics syllabus, Curriculum Support for Teaching in Mathematics, 5, 3, 7-12.
• Yıldırım, A. (1996). Disiplinlerarası öğretim kavramı ve programlar açısından doğurduğu sonuçlar, Hacettepe Üniversitesi Eğitim Fakültesi Dergisi 12, 89-94.
• Zbiek, R. M. & Conner, A. (2006). Beyond motivation: exploring mathematical modeling as a context for deepening students’ understandings of curricular Mathematics, Educational Studies in Mathematics, 63, 1, 89-112.