Matematik Öğretmeni Adaylarının Matematiksel Modelleme Sürecinde Bilgisayar Kullanımları Üzerine Bir İnceleme

Year 2018, , 618 - 635, 17.12.2018

Ebru Saka , Derya Çelik

https://doi.org/10.16949/turkbilmat.409160

Abstract

Bu çalışmada ilköğretim
matematik öğretmeni adaylarının deneysel ve teorik modelleme problemlerini
çözme sürecinde yaşadıkları güçlükleri belirlemek ve bu güçlüklerin
giderilmesinde bilgisayar teknolojisinin nasıl bir etkisinin olduğunu ortaya
koymak amaçlanmıştır. Çalışmaya ilköğretim matematik öğretmenliği programı 4.
sınıfta bulunan 20 öğretmen adayı katılmıştır. Katılımcıların her biri
matematiksel modelleme ve GeoGebra yazılımını kullanma ile ilgili deneyime
sahiptir. Katılımcılar üçü deneysel, üçü teorik olmak üzere toplam altı
matematiksel modelleme problemi üzerinde dörder kişilik gruplar halinde
çalışmıştır. Araştırmanın verileri video kayıtları, odak grup görüşmeleri,
bilgisayar ekran çıktıları ve araştırmacının alan notları ile elde edilmiştir.
Verilerin analizinde nitel analiz teknikleri kullanılmıştır. Belirlenen kodlar
matematiksel modelleme sürecinin basamakları altında sınıflandırılmıştır.
Sonuçlar öğretmen adaylarının modelleme sürecinin her bir basamağında çeşitli
güçlüklerle karşılaştığını, teorik modelleme problemlerinde deneysel modelleme
problemlerine göre daha fazla zorlandıklarını, bilgisayar kullanımının ise bu
süreçte karşılaşılan güçlüklerin giderilmesine büyük ölçüde katkı sağladığını
ortaya koymuştur. Öğretmen adaylarının uygun modelleri oluşturma ve bu
modellemeyi doğrulama esnasında bilgisayar yardımıyla elde ettikleri sonuçlara
çok fazla güvenmesi ise olumsuzluk yaratan bir durum olarak ortaya çıkmıştır.

Keywords

Matematik öğretmeni adayları, matematiksel modelleme, güçlükler, bilgisayar teknolojisi

A Study on the Computer Usage in Mathematical Modeling of Pre-Service Mathematics Teachers

Abstract

The purpose of this
study is to identify the difficulties that preservice elementary mathematics
teachers have experienced in solving the experimental and theoretical modeling
problems and to show how the effect of computer usage is in eliminating these
difficulties. The study sample consisted of 20 preservice teachers in their
last year at the elementary mathematics education program. Each of the
preservice teachers has experience with mathematical modeling and using
GeoGebra software. The participants worked on six mathematical modeling
problems, three experimental and three theoretical problems, in groups of four.
The data were collected from the videos recorded during their work, the focus
group discussions, the screencasts of the groups on the computers and the
observation notes of the researcher. Qualitative analysis techniques were used
in the analysis of the data. The determined codes are classified under the
steps of the mathematical modeling process. The results show that preservice
teachers encountered a variety of difficulties in each phase of the modeling
process. They had more difficulty with theoretical modeling problems than with
experimental modeling problems and the use of computers significantly
contributed to the elimination of the difficulties. The fact that preservice
teachers had a lot of confidence in the results obtained through the use of
computer in modeling and verifying this model, has emerged as a negative effect
of computer technology.

Keywords

Preservice mathematics teachers, mathematical modeling, difficulties, computer technology

References

• Ang, K. C. (2010). Teaching and learning mathematical modelling with technology. Retrieved November 10, 2015 from http://atcm.mathandtech.org/ep2010/invited/3052010_18134.pdf
• Arzarello, F., Ferrara, F., & Robutti, O. (2012). Mathematical modelling with technology: The role of dynamic representations. Teaching Mathematics and its Applications, 31(1), 20-30.
• Aydın-Güç, F. (2015). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi (Yayınlanmamış doktora tezi). Karadeniz Teknik Üniversitesi, Eğitim Bilimleri Enstitüsü, Trabzon.
• Bal, A. P. ve Doğanay, A. (2014). Sınıf öğretmenliği adaylarının matematiksel modelleme sürecini anlamalarını geliştirmeye yönelik bir eylem araştırması. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1363-1384.
• Berry, J., & Houston, K. (1995). Mathematical modelling. Bristol: J. W.Arrowsmith Ltd.
• Blomhøj, M. (1993). Modelling of dynamical systems at O-level. In J. de Lange, C. Keitel, I. Huntley, & M. Niss (Eds.), Innovation in mathematics education by modelling and applications (pp. 257-268). Chichester: Ellis Horwood.
• Blomhøj, M. & Jensen, T. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and its Applications, 22(3), 123-139.
• Blum, W. (1996). Anwendungsbezüge im mathematikunterricht – trends und perspektiven. Schriftenreihe Didaktik der Mathematik, 23, 15-38.
• Blum, W., & Borromeo-Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
• Borromeo-Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86–95.
• Borromeo-Ferri, R., & Blum, W. (2013, February). Barriers and motivations of primary teachers for implementing modeling in mathematics lesson. Paper presented at 8th Congress of European Research in Mathematics Education, Antalya, Turkey.
• Borromeo-Ferri, R., & Blum, W. (2011). Are integrated thinkers better able to intervene adaptively? – A case study in a mathematical modelling environment. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (Vol.7, pp. 927-936). Rzesow, Poland: University of Rzeszow.
• Carreira, S., Amado, N., & Canário, F. (2013, February). Students’ modelling of lınear functıons: How geogebra stımulates a geometrıcal approach. Paper presented at CERME 8, Antalya, Turkey.
• Doruk, B. K. ve Umay, A. (2011). Matematiği günlük yaşama transfer etmede matematiksel modellemenin etkisi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41(41), 124-135.
• Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. The International Journal on Mathematics Education, 38(2), 143-162.
• Geiger, V. (2011). Factors affecting teachers’ adoption of innovative practices with technology and mathematical modeling. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modeling, (ICTMA 14) (pp. 305 – 314). New York: Springer.
• Ghosh, J. B. (2015). Learning mathematics in secondary school: The case of mathematical modelling enabled by technology. In S. J. Cho (Ed.), Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 203-222). Switzerland: Springer International Publishing.
• Hıdıroğlu, Ç. N. (2012). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analiz edilmesi: yaklaşım ve düşünme süreçleri üzerine bir açıklama (Yayınlanmamış yüksek lisans tezi). Dokuz Eylül Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir.
• Kadijevich, D., Haapasalo, L., & Hvorecky, J. (2005). Using technology in applications and modelling. Teaching Mathematics and its Applications, 24(2-3), 114-122.
• Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling education, engineering and economics (pp. 110-119). Chichester: Horwood.
• Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. The International Journal on Mathematics Education, 38(3), 302-310.
• Kant, S. (2011). İlköğretim 8. sınıf öğrencilerinin model oluşturma süreçleri ve karşılaşılan güçlükler (Yayınlanmamış yüksek lisans tezi). Ondokuz Mayıs Üniversitesi, Eğitim Bilimleri Enstitüsü, Samsun.
• Kapur, J. N. (1982). The art of teaching the art of mathematical modelling. International Journal of Mathematical Education in Science and Technology, 13(2), 185-192.
• Korkmaz, E. (2010). İlköğretim matematik ve sınıf öğretmeni adaylarının matematiksel modellemeye yönelik görüşleri ve matematiksel modelleme yeterlikleri (Yayınlanmamış doktora tezi). Balıkesir Üniversitesi, Fen Bilimleri Enstitüsü, Balıkesir.
• Köse, N., Uygan, C. ve Özen, D. (2014). Dinamik geometri yazılımlarındaki sürükleme ve çeşitlerinin geometri öğretimindeki rolü. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 3(1), 35-52.
• Lesh, R. A., & Doerr, H. (2003). Foundations of model and modelling perspectives on mathematic teaching and learning. In R. A. Lesh, & H. Doerr (Eds.), Beyond constructivism: Amodels and modelling perspectives on mathematics teaching, learning and problem solving (pp. 3-33). Mahwah, NJ: Lawrance Erlbauum.
• Lesh, R. A., & Zawojewski, J. (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. 763-802). Charlotte, NC: Information Age Publishing.
• Lingefjärd, T. (2000). Mathematical modeling by prospective teachers using technology (Unpublished doctoral dissertation). Univer¬sity of Georgia, USA.
• Lingefjärd, T. (2006). Faces of mathematical modeling. ZDM, 38(2), 96-112.
• Maaß, K. (2006). What are modelling competencies? The International Journal on Mathematics Education, 38(2), 113-142.
• Maaß, K. (2007). Modelling tasks for low achieving students – first results of an empirical study. In D. Pitta-Pantazi, & G. Philippou (Eds.), Proceedings of the Fifth Congress oftThe European Society for Research in Mathematics Education (pp. 2120-2129). Larnaca: University of Cyprus.
• Mousoulides, N. (2007). A modeling perspective in the teaching and learning of mathematical problem solving (Unpublished doctoral dissertation). University of Cyprus, Cyprus.
• Mousoulides, N., Chrysostomou, M., Pittalis, M., & Christou, C. (2009, February). Modeling with technology in elementary classrooms. Paper presented at CERME 6, Lyon, France.
• Mousoulides, N., Christou, C., & Sriraman, B. (2006). From problem solving to modelling- a meta analysis. Retrieved August 14, 2011 from http://www.umt.edu/math/reports/sriraman/mousoulideschristousriraman.pdf.
• Organisation for Economic Co-operation and Development [OECD]. (2007). PISA 2006: Science competencies for tomorrow's world (Vol. 1). Paris: OECD Publications.
• Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). Thousand Oaks, CA: Sage.
• Pollak, H. (1969). How can we teach applications of mathematics? Educational Studies in Mathematics, 2(2-3), 393-404.
• Santos-Trigo, M., & Reyes-Rodríguez, A. (2011). Teachers’ use of computational tools to construct and explore dynamic mathematical models. International Journal of Mathematical Education in Science and Technology, 42(3), 313-336.
• 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). Netherlands: Springer.
• Siller, H. S., & Greefrath, G. (2010). Mathematical modelling in class regarding to technology. In Durand-Guerrier, V., Soury-Lavergne, S., & Arzarello, F. (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 2136-2145). France: INRP.
• Sriraman, B. (2005). Conceptualizing the notion of model eliciting. Retrieved February 21, 2015 from http://www.umt.edu/math/reports/sriraman/mousoulideschristousriraman.pdf.
• Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. Mathematics: Essential Research, Essential Practice, 2, 688-697.
• Şahin, N. ve Eraslan, A. (2016). İlkokul öğrencilerinin modelleme süreçleri: Suç problemi. Eğitim ve Bilim, 41(183), 47-67.
• Tekin-Dede, A. ve Yılmaz, S. (2013). İlköğretim matematik öğretmeni adaylarının modelleme yeterliklerinin incelenmesi. Turkish Journal of Computer and Mathematics Education, 4(3), 185-206.
• Ural, A., & Ülper, H. (2013). The evaluation of the relationship between pre-service elementary mathematics teachers' mathematical modeling and reading comprehension skills. Kuramsal Eğitimbilim Dergisi, 6(2), 214-241.
• Yang, Z., & Yin, F. (2015). The interaction between mathematical modeling and computer. In Yang, L., & Zhao, M. (Eds.), International Industrial Informatics and Computer Engineering Conference (IIICEC 2015) (pp. 685-688). China: Atlantis Press.
• Yıldırım, A. ve Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (6. baskı). Ankara: Seçkin Yayıncılık.
• 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.