İLKÖĞRETİM MATEMATİK ÖĞRETMEN ADAYLARININ MODEL OLUŞTURMA ETKİNLİĞİ TASARLAMA DENEYİMLERİNE İLİŞKİN GÖRÜŞLERİ
Author :
Abstract
Model oluşturma etkinlikleri matematiğin yoğun olarak kullanıldığı bilim dallarında ve ticaret, mühendislik, spor gibi çeşitli alanlarda karşılaşılan gerçek yaşam problemlerinden esinlenerek geliştirilmiştir. Bu etkinliklerin matematik sınıflarında kullanımıyla öğrencilerin matematik derslerinde bilim insanlarına benzer biçimde matematik yapmaları, gerçek yaşam problem durumlarının çözümünde matematikten yararlanmaları hedeflenmektedir. Ancak etkili model oluşturma etkinlikleri tasarlamak için dikkate alınması gereken bazı prensipler vardır. Bunlar gerçeklik, model oluşturma, öz değerlendirme, modeli belgelendirme, modeli genelleme ve etkili prototip prensipleridir. Bu prensipler doğrultusunda hazırlanan model oluşturma etkinlikleri öğrencilerin kendi düşünce yollarını ifade etme, test etme, revize etme aracılığıyla gerçeği matematikleştirmeye etmeye teşvik edildiği öğrenme etkinlikleridir. Çalışmamızda, bu altı özel prensibe uygun biçimde model oluşturma etkinliklerini tasarlama göreviyle meşgul olan öğretmen adaylarının bu deneyimlerine ilişkin görüşlerini incelemek amaçlanmıştır. Bu amaçla bir devlet üniversitesi eğitim fakültesinin ilköğretim matematik öğretmenliği 3.sınıfına devam etmekte olan 35 öğretmen adayına model oluşturma etkinlikleri hakkında verilen eğitim sonrasında bu prensiplere uygun olacak şekilde birer model oluşturma etkinliği tasarlama görevi verilmiştir. Görevin tamamlanmasının ardından gönüllü 11 öğretmen adayı ile görüşmeler düzenlenmiştir. Görüşmelerden elde edilen verilerin analizi sonucu öğretmen adaylarının etkinlik tasarımı sürecindeki önemli yaşantıları, zorlandıkları noktalar, bu görevin onlara sağladığı katkılar, tasarlanan etkinliklerin bağlamları gibi konular hakkında bilgiler sunan temalara ulaşılmış ve bu doğrultuda öğretmen yetiştirme üzerine bazı önerilerde bulunulmuştur.
Keywords
Abstract
Model eliciting activities have been developed by inspiring from real life problems encountered in science field where mathematics is used extensively and various fields such as trade, engineering, and sports. With the use of these activities in math classes, it is aimed that students do mathematics in mathematics lessons similar to scientists and benefit from mathematics in solving real life problem situations. However, there are some principles to consider when designing effective model eliciting activities. These are reality, modeling, self-evaluation, model certification, model generalization and effective prototype principles. Modeling eliciting activities prepared in line with these principles are learning activities in which students are encouraged to mathematize the reality through expressing, testing, revising their own ways of thinking. In our study, it was aimed to examine the opinions of pre-service teachers, who are deal in the task of designing model eliciting activities in accordance with these six special principles. Within the scope of the study, 35 pre-service mathematics teachers who continue their 3rd year, have been given the task of designing an activity in accordance with these principles after training on model eliciting activities. Following the completion of task, interviews were held with 11 volunteer pre-service teachers. As a result of the analysis of the data obtained from the interviews, the themes that provide information about the important experiences of prospective teachers in the activity design process, their difficulties, the task's contribution to them, the contexts of the designed activities were reached and some suggestions were made on teacher training in this direction.
Keywords
- Aldrich, J. E. and Thomas, K. R. (2005). Evaluating constructivist beliefs of teacher candidates. Journal of Early Childhood Teacher Education, 25(4), 339-347. http://dx.doi.org/10.1080/1090102050250408
- Bukova-Güzel, E. (2011). An examination of pre-service mathematics teachers’ approaches to construct and solve mathematical modelling problems. Teaching Mathematics and Its Applications. 30, 19-36.
- Cohen, L., Manion, L. and Morrison, K. (2007). Research methods in education (6th ed.).London: Routledge.
- Doruk, B.K. (2016). Realistic real world context: Model eliciting activities. International Journal for Mathematics Teaching and Learning. Vol. 17 (2).
- Doruk, B. K. (2014). The Educational Approaches of Turkish Pre-Service Elementary Mathematics Teachers in Their First Teaching Practices: Traditional or Constructivist? Australian Journal of Teacher Education, 39(10).113-134.
- Doruk, B.K. and Umay, A. (2011). The effect of mathematical modeling on transferring mathematics into daily life. H. U. Journal of Education. 41, 124-135.
- English, L. D. (2010). Young children’s early modelling with data. Mathematics Education Research Journal, Vol. 22, No. 2, 24-47.
- Eraslan, A. (2011). Prospective Elementary Mathematics Teachers’ Perceptions on Model Eliciting Activities and their Effects on Mathematics Learning. Elementary Education Online, 10(1), 364377.
- Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakiroğlu, E., Alacaci, C. and Baş, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory and Practice, 14(4), 1621-1627.Freudenthal, H. (1968). Why to teach mathematics so as to be useful? Educational Studies in Mathematics, 1(1/2), 3-8.
- Galbraith, P. (2012). Models of modelling: genres, purposes or perspectives. Journal of Mathematical Modeling and Application, 1(5), 3-16.
- Gall, M., Borg, W. and Gall, J. P. (1996). Educational research an introduction (6th ed.).White Plains: Longman.
- Haines, C. and Crouch, R. (2007). Mathematical modeling and applications: Ability and competence frameworks. In W. Blum, P. L. Galbraith, H. Henn, and M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 417-424). New York, NY: Springer.
- Johnson, T. and Lesh, R. (2003). A Models and Modeling Perspective on Technology-Based Representational Media. In R. Lesh and H. M. Doerr (Eds.), Beyond constructivism: A models & modelling perspective on mathematics problem solving, learning & teaching (pp. 297–316). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
- Kaiser, G. and Sriraman, B. (2006). A Global Survey of International Perspectives on Modelling in Mathematics Education. Zentralblatt für Didaktik der Mathematik, Vol. 38(3), 302-310.
- Kertil, M. (2008). Matematik Öğretmen Adaylarının Problem Çözme Becerilerinin Modelleme Sürecinde İncelenmesi. Yüksek Lisans Tezi, Marmara Üniversitesi, İstanbul.
- Lesh, R., Cramer, K., Doerr, H.M., Post, T. and Zawojewski, J.S. (2003). Model Development Sequences. In R. Lesh and H.M.Doerr (Eds.), Beyond constructivism: Models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 35-58). Mahwah, NJ: Erlbaum
- Lesh, R. and Doerr, H. M. (2003a). In what ways does a models and modeling perspective move beyond constructivism. In R. Lesh, and H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 519-556). Mahwah, NJ: Lawrence Erlbaum.
- Lesh, R. and Doerr, H. M. (2003b). Foundations of models and modeling perspective on mathematics teaching and learning. In R. Lesh and H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–34). Hillsdale, NJ: Lawrence Erlbaum and Associates.
- Lesh, R., Hoover, M., Hole, B., Kelly, A. and Post, T.(2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly and R. Lesh (Eds.), Handbook of research in mathematics and science education (pp. 113–149). Mahwah, NJ: Lawrence Erlbaum and Associates.
- Lesh, R. and Sriraman, B. (2005). John Dewey revisited – pragmatism and the models-modeling perspective on mathematical learning. In Beckmann, A., Michelsen, C., and Sriraman, B (Eds.). Proceedings of the 1st International Symposium of Mathematics and its Connections to the Arts and Sciences. The University of Education, Schwäbisch Gmünd, Germany, pp.7-31.
- McMillan, J. H. (2000). Educational research: Fundamentals for consumer (3th ed.). NewYork: Longman.
- Maaß, K. (2005). Barriers and opportunities for the integration of modelling in mathematic classes- results of an empirical study. Teaching Mathematics and Its Applications, 24(2-3), 61-74.
- Miles, M. B. and Huberman, M. A. (1994). An expanded sourcebook qualitative data analysis. London: Sage.
- Moore, T. and Diefes-Dux, H. (2004, October). Developing model-eliciting activities for undergraduate students based on advanced engineering content. In 34th Annual Frontiers in Education, 2004. FIE 2004. (pp. F1A-9). IEEE.
- Thomas, K. and Hart, J. (2013). Pre-service teacher perceptions of model eliciting activities. In R. Lesh et al. (Eds.), Modeling students’ mathematical modeling competencies (pp. 531-538). Dordrecht: Springer Science and Business Media.
- Toluk Uçar, Z. and Demirsoy, H. (2010). Tension between old and new: Mathematics teachers’ beliefs and practices. H. U. Journal of Education. 39: 321-332.
- Urhan, S. and 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), 9851002.
- Yoon, C., Dreyfus, T. and Thomas, O.J. (2010). How High is the Tramping Track? Mathematising and Applying in a Calculus Model-Eliciting Activity. Mathematics Education Research Journal. Vol. 22, No. 1, 141-157.
