Matematiksel Modellemenin Öğretim Araçlarına Yansımaları: Ders Kitabı Analizi

Öz

Bu çalışmada son yıllarda birçok ülkenin öğretim programına girmiş olan matematiksel modellemeye ders kitaplarında ne derece kadar yer verildiği ve kitaplarda yer alan modelleme kavramının matematiksel modellemeyi ne ölçüde yansıttığı incelenmiştir. Doküman incelemesi yönteminden yararlanılan çalışmada, 2016-2017 eğitim-öğretim yılında uygulamada olan tüm ortaokul (5, 6, 7, 8) matematik ders kitaplarında yer alan model ve modelleme kavramları tespit edilerek öğrenme alanı, sınıf seviyesi, modelin kullanıldığı bölüm ve kullanılan model türü açısından içerik analizi yöntemiyle değerlendirilmiştir. Yapılan değerlendirmeler neticesinde, ders kitaplarında modelleme kavramının matematiksel modellemeden ziyade “matematiği modelleme” şeklinde ele alındığı ve modellerin bazı konularda yoğun bir şekilde kullanılırken bazı konularda model kavramına değinilmediği ve modellerin ise sadece somut ve görsel yapılarla sınırlı kaldığı söylenebilir. Ders kitaplarındaki modelleme anlayışı somutlaştırma ve görselleştirme şeklindedir. Programda matematiksel modellemeye yapılan vurgu da dikkate alındığında, söz konusu sınırlı algının değiştirilmesi için ders kitaplarında modelleme anlayışının revize edilmesi gerektiği önerilebilir.

Anahtar Kelimeler

• Matematiksel Modelleme,Matematiği Modelleme,Ders Kitabı

The Reflections of Mathematical Modeling in Teaching Tools: Textbook Analysis

Abstract

In this study, we investigate to what extent mathematical modelling, which has been included extensively in many countries' curriculum in recent years, is included in middle school textbooks in Turkey and how the concept  of modeling in textbooks reflects mathematical modeling. By conducting the document review, model and modeling concepts in all middle school (5, 6, 7, 8) mathematics textbooks in the 2016-2017 academic year were determined and evaluated, by means of content analysis method, in terms of the learning area, the class level, the section that model used, and the type of model used. The results show that the concept of modeling in middle school mathematics textbooks is used as a “modeling mathematics" rather than as means of mathematical modelling. Also, the concept of modelling is used intensively in some topics, but not mentioned in some topics and class levels at all. The concept of modelling used in the textbooks was limited only to concrete and visual structures.  Thus, the purpose of modelling in the textbooks was to model mathematical concepts into the concrete and visual forms rather than mathematizing the problem. Considering the emphasis on mathematical modeling in the current mathematics standards, we suggest that this limited and problematic understanding of modeling should be revised to reflect purpose of mathematical modelling in order to have better learning opportunities for both teachers and students. 

Keywords

• Mathematical Modeling,Modeling Mathematics,Textbook

References

1. Alacacı, C. (2015). Matematik Ders Kitabı Tasarımında Temel Unsurlar ve Matematiksel Modelleme. Türk Bilgisayar ve Matematik Eğitimi Sempozyumu-2 (s. 124). Adıyaman: Adıyaman Üniversitesi. http://www.bilmat.org/ adresinden alınmıştır.
2. Altun, M., Arslan, Ç., & Yazgan, Y. (2004). Lise matematik ders kitaplarının kullanım şekli ve sıklığı üzerine bir çalışma. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 17(2), 131-147.
3. Berry, J. (2002). Developing mathematical modelling skills: The role of CAS. The International Journal on Mathematics Education, 34(5), 212-220.
4. Berry, J., & Houston, K. (1995). Mathematical modelling. Butterworth-Heinemann.
5. Blomhøj, M. Jensen T.H. (2006). What’s all the fuss about competencies? Experiences with using a competence perspective on mathematics education to develop the teaching of mathematical modelling. In W. Blum, P.L. Galbraith and M. Niss: Modelling and applications in mathematics education
6. Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in the teaching and learning of mathematical modelling - Proceedings of ICTMA14. (pp. 15-30). New York: Springer.
7. Blum, W. (1993). Mathematical modelling in mathematics education and instruction. Teaching and learning mathematics in context, 3-14.
8. Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.

9. Blum, W., & Niss, M. (1989). Mathematical problem solving, modelling, applications, and links to other subjects-state, trends and issues in mathematics instruction. Roskilde universitetscenter.
10. Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—State, trends and issues in mathematics instruction. Educational studies in mathematics, 22(1), 37-68.
11. Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative research journal, 9(2), 27-40.
12. Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 3–16). Reston, VA: National Council of Teachers of Mathematics.
13. Common Core State Standards Initiative. (2011). Common core state standards for mathematics.
14. Corbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory.
15. Doerr, H. M. (1997). Experiment, Simulation And Analysis: An Integrated Instructional Approach To The Concept Of Force. International Journal Of Science Education. 19, 265-282.
16. English, L. D., & Watters, J. J. (2004). Mathematical modelling with young children. In Proceedings of the 28th International PME Conference (pp. 335-342).
17. Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95. Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38(2), 143-162.
18. Güç, F.A. (2015). Matematiksel Modelleme Yeterliklerinin Geliştirilmesine Yönelik Tasarlanan Öğrenme Ortamlarında Öğretmen Adaylarının Matematiksel Modelleme Yeterliklerinin Değerlendirilmesi (Doktora tezi). Karadeniz Teknik Üniversitesi, Eğitim Bilimleri Enstitüsü, Trabzon.
19. Güzel, E. B., Dede, A. T., Hıdıroğlu, Ç. N., Ünver, S. K., & Çelik, A. Ö. (2016). Matematik eğitiminde matematiksel modelleme: araştırmacılar, eğitimciler ve öğrenciler için. Pegem Atıf İndeksi, 001-146.
20. Harel, G., &Lesh, R. (2003). Local conceptual development of proof schemes in a cooperative learning setting. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, teaching, and learning (pp.359-382). New York: Routledge.
21. Haines, C., & Crouch, R. (2001). Recognizing constructs within mathematical modelling. Teaching Mathematics and its Applications, 20(3), 129-138.
22. Hıdıroğlu, Ç. N. (2012). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analiz edilmesi: Yaklaşım ve düşünme süreçleri üzerine bir açıklama (Doctoral dissertation, DEÜ Eğitim Bilimleri Enstitüsü).
23. Hıdıroğlu, Ç. N. (2015). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analizi: Bilişsel ve üst bilişsel yapılar üzerine bir açıklama. Doktora Tezi. Dokuz Eylül Üniversitesi, İzmir.
24. Hitt, F., & González-Martín, A. S. (2015). Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method. Educational studies in mathematics, 88(2), 201-219.
25. Kaiser, G. (2007). Modelling and modelling competencies in school. Mathematical modelling (ICTMA 12): Education, engineering and economics, 110-119.
26. Kaiser, G., & Maaß, K. (2007). Modelling in lower secondary mathematics classroom-problems and opportunities. NEW ICMI STUDIES SERIES, 10, 99.
27. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310.
28. 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.
29. Labuschagne, A. (2003). Qualitative research-airy fairy or fundamental?. The qualitative report, 8(1), 100-103.
30. Lesh,R., &Carmona, G. (2003). Piagetian conceptual systems and models for mathematizing everyday experiences. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, teaching, and learning (pp.71-96). New York: Routledge.
31. Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J. (2003). Model development sequences.
32. Lesh, R., Doerr, H. (2003). Foundation of a models and modeling perspective on mathematics teaching and learning. Beyond constructivism: A models and modeling perspective on mathematics teaching, learning, and problem solving, 9-34.
33. Lesh, R., &Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2&3), 157-189. http://dx.doi.org/10.1080/10986065.2003.9679998
34. Lesh, R., Landau, M., & Hamilton, E. (1983). Conceptual models and applied mathematical problem-solving research. Acquisition of mathematics concepts and processes, 263-343.
35. MaaB, K. (2006). Modelling in classrooms: What do we want the students to learn. Mathematical Modelling (ICTMA 12): Engineering and Economy. Chichester: Ellis Horwood.
36. MEB. (2017). İlköğretim ve Ortaöğretim Öğretim Programlarının Güncellenmesi. Erişim adresi: https://ttkb.meb.gov.tr/www/ilkogretim-ve-ortaogretim-ogretim-programlarinin güncellenmesi/icerik/289#
37. Milli Eğitim Bakanlığı, (2013). Ortaokul matematik dersi 5-8. sınıflar öğretim programı. Ankara: MEB.
38. Mousoulides, N. G., Christou, C., & Sriraman, B. (2008). A modeling perspective on the teaching and learning of mathematical problem solving. Mathematical Thinking and Learning, 10(3), 293-304.
39. National Council of Teachers of Mathematics (Ed.). (2000). Principles and standards for school mathematics (Vol. 1). National Council of Teachers of.
40. Ng, K.E.D. (2011). Mathematical knowledge application and student difficulties in a design-based interdisciplinary project. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling. (pp.107-116). New York: Springer. http://dx.doi.org/10.1007/978-94-007-0910-2_12
41. Niss, M., Blum, W., and Galbraith, P. L. (2007). Introduction. In M. Niss, W. Blum, H. Henn, and P. L. Galbraith (Eds.), Modelling and Applications in Mathematics Education (pp. 3-32). New York: Springer.
42. Park, J., Park, M.S., Park, M., Cho, J., & Lee, K.H. (2013). Mathematical modelling as a facilitator to conceptualization of the derivative and the integral in a spreadsheet environment.Teaching Mathematics and Its Applications, 32, 123-139.http://dx.doi.org/10.1093/teamat/hrt012
43. Pollak, H. O. (1969). How can we teach applications of mathematics?. Educational studies in mathematics, 2(2), 393-404.
44. Pollak, H. O. (1997). Solving problems in the real world (pp. 91-105). Why Nymbers Count: Quantitative Literacy for Tomorrow's America, New York: The College Board.
45. Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modeling activities at year 9. In Modeling students' mathematical modeling competencies (pp. 385-398). Springer US.
46. Stylianides, G. J. (2014). Textbook analyses on reasoning-and-proving: Significance and methodological challenges.
47. Şen-Zeytun, A. (2013). An ınvestigation of prospective teachers’ mathematical modeling processes and their views about factors affecting these processes. Unpublished Doctoral Dissertation. Middle East Tecnical University, Ankara.
48. Thompson, D. R. (2014). Reasoning-and-proving in the written curriculum: Lessons and implications for teachers, curriculum designers, and researchers. International Journal of Educational Research, 64, 141-148.