Seda ŞAHİN, Ramazan GÜRBÜZ, Muhammed Fatih DOĞAN

Matematik Öğretmenlerinin Matematiksel Modelleme Problemi Hazırlama Süreçlerinin İncelenmesi

Bu çalışmada bir mesleki gelişim programı kapsamında matematiksel modelleme eğitimi alan ortaokul matematik öğretmenlerinin matematiksel modelleme problemi hazırlama süreçleri incelenmiştir. Altı öğretmenin (ikisi kadın; dördü erkek) katılımıyla gerçekleştirilen ve çoklu durum çalışması niteliğindeki bu çalışmada öğretmenlerin matematiksel modelleme eğitimi boyunca kazandıkları teorik bilgileri problem hazırlama sürecinde nasıl ele aldıkları araştırılmıştır. Veriler, öğretmenlerin hazırladıkları problemler ve bireysel görüşme ses kayıtlarından oluşmaktadır. Bulgular, öğretmenlerin teorik bilgilerini problem hazırlama sürecine transfer ederken genel olarak başarılı olduklarını ancak birtakım zorluklar yaşadıklarını ortaya koymaktadır. Bununla birlikte süreç içinde bu zorlukların üstesinden gelerek matematiksel modelleme kriterlerine uygun problem hazırlama yeterliği kazandıkları söylenebilir. Elde edilen sonuçlar modelleme anlayışının gelişmesinde teori kadar uygulamanın da önemli bir role sahip olduğunu ve modelleme eğitiminde teori ile uygulama dengesinin sağlanması gerektiğini göstermektedir.

Anahtar Kelimeler:

Matematiksel Modelleme, Etkinlik Yeterliliği, Problem Hazırlama, Öğretmen Yeterlikleri

Investigating Mathematical Modeling Problem Designing Process of Inservice Mathematics Teachers

In this study, the mathematical modeling process of in-service middle school mathematics teachers who participated in a mathematical modeling workshop within the scope of a professional development program were examined. This study is a multi-case study with the participation of six teachers (two women; four men) and investigates how teachers handled the theoretical knowledge gained during the mathematical modeling workshop in the problem designing process. The data consists of problems designed by teachers and individual interviews. The findings show that teachers were generally successful in transferring their theoretical knowledge to the problem designing process, but had some difficulties. Besides, it can be said that they overcame these difficulties in the process and obtained the problem designing competence that is suitable for the mathematical modeling criteria. The results show that implementation has an important role in the development of a modeling point of view just like theory and that the balance of theory and application should be established in modeling education.

Keywords:

Mathematical Modelling, Problem Designing, Task Competency, Teacher Competencies,

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Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
Bliss, K., Libertini, J., Levy, R., Zbiek, R. M., Galluzzo, B., Long, M., ... & Giardano, F. (2016). GAIMME: Guidelines for assessment & instruction in mathematical modeling education. Philadelphia: COMAP & SIAM.
Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of Mathematical Modelling and Application, 1(1), 45-58.
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. https://doi.org/10.1007/BF00302716
Bonotto, C. (2007). How to replace word problems with activities of realistic mathematical modelling. In W. Blum, P.L. Galbraith, HW. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 185-192). Springer, Boston, MA.
Buhrman, D. (2017). The design and enactment of modeling tasks: a study on the development of modeling abilities in a secondary mathematics course [Unpublished doctoral dissertation]. University of Nebraska.
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. https://doi.org/10.4219/jsge-2005-393
Clement, J., Lochhead, J., & Monk, G. S. (1981). Translation difficulties in learning mathematics. The American Mathematical Monthly, 88(4), 286-290. https://doi.org/10.1080/00029890.1981.11995253
Deniz, D. (2014). Ortaöğretim matematik öğretmenlerinin matematiksel modelleme yöntemine uygun etkinlik oluşturabilme ve uygulayabilme yeterlikleri [The sufficiency of high school mathematics teachers' to elicit and apply activities apropriate to mathematical modelling method] [Unpublished doctoral dissertation]. Atatürk University.
Ellerton, N.F. (2015) Problem posing as an integral component of the mathematics curriculum: A study with prospective and practicing middle-school teachers. In F. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing: Research in mathematics education (pp. 513-543). Springer, New York.
English, L. D. (1997). The development of fifth-grade children's problem-posing abilities. Educational Studies in Mathematics, 34(3), 183-217. https://doi.org/10.1023/A:1002963618035
English, L. D. (2008). Mathematical modeling: Linking mathematics, science, and the arts in the elementary curriculum. In B. Sriraman, C. Michelsen, & A. Beckmann, & V. Freiman (Eds.), Proceedings of the second international symposium on mathematics and its connections to the arts and sciences. (MACAS2, pp. 5-36). University of Southern Denmark Press.
English, L., & Sriraman, B. (2010). Problem solving for the 21 st century. In G. Kaiser & B. Sriraman (Eds.), Theories of mathematics education (pp. 263-290). Springer, Berlin, Heidelberg.
Borromeo Ferri, R. B. (2014). Mathematical modeling-The teacher’s responsibility. In A. Sanfratello & B. Dickman (Eds.), Proceedings of conference on mathematical modeling at Teachers College of Columbia University (pp. 26–31). New York.
Ferri, R. B. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer.
Ferri, R. B., & Blum, W. (2009). Mathematical modelling in teacher education–experiences from a modelling seminar. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the sixth congress of the European society for research in mathematics education (pp. 2046-2055). Lyon, France: Institut National De Recherche Pédagogique.
Ferri, R. B., & Lesh, R. (2013). Should interpretation systems be considered to be models if they only function implicitly?. In G. Stillman et al. (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 57-66). Springer, Dordrecht.
Gainsburg, J. (2006). The mathematical modeling of structural engineers. Mathematical Thinking and Learning, 8(1), 3-36. https://doi.org/10.1207/s15327833mtl0801_2
Gainsburg, J. (2009). How and why secondary mathematics teachers make (or don’t make) real-world connections in teaching. In L. Verschaffel et. al. (Eds.), Words and worlds: Modelling verbal descriptions of situtations (pp. 265-281). Brill Sense.
Galbraith, P. (2007). Dreaming a ‘possible dream’: More windmills to conquer. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling education, engineering and economics (pp. 44–62). Chichester: Woodhead Publishing.
Galbraith, P. (2018). Beyond lip service: Sustaining modelling in curricula and coursework. In S. Schukajlow & W. Blum (Eds.), Evaluierte Lernumgebungen zum Modellieren (pp. 165-191). Springer Spektrum, Wiesbaden.
Güç, F.A. (2015). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi [Examining mathematical modeling competencies of teacher candidates in learning environments designed to improve mathematical modeling competencies] [Unpublished doctoral dissertation]. Karadeniz Technical University.
Hošpesová, A. & Tichá, M. (2015) Problem posing in primary school teacher training. In F.M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical Problem Posing (pp. 433-447). Springer, New York, NY.
Jupri, A. & Drijvers, P. H. M. (2016). Student difficulties in mathematizing word problems in algebra. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a
Kaiser, G., Schwarz, B., & Buchholtz, N. (2011). Authentic modelling problems in mathematics education. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 591-601). Springer, Dordrecht.
Lavy, I. & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st conference of the international group for the psychology of mathematics education (Vol. 3, pp. 129–136). Seoul, Korea: PME.
Lesh, R. & Zawojewski, J.S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763–804). Greenwich, CT: Information Age Publishing.
Lester, F. K. (1983). Trends and issues in mathematical problem-solving research. Acquisition of Mathematics Concepts and Processes, 229-261.
Ministry of National Education (2018). Ortaokul matematik dersi (1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) öğretim programı [National curriculum for secondary mathematics (Grades 1-8)]. Retrieved from http://mufredat.meb.gov.tr/Programlar.aspx
National Council of Teachers of Mathematics (Ed.). (2000). Principles and standards for school mathematics (Vol. 1). National Council of Teachers of.
National Research Council (2012). Discipline-based education research: Understanding and improving learning in undergraduate science and engineering. National Academies Press.
Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). New York: Springer Science + Business Media, LLC.
Reinke, L. T. (2019). Toward an analytical framework for contextual problem-based mathematics instruction. Mathematical Thinking and Learning, 21(4), 265-284. https://doi.org/10.1080/10986065.2019.1576004
Sahin, S. (2019). Matematik öğretmenlerinin matematiksel modelleme problemi hazırlama becerilerinin incelenmesi [Investıgatıon of mathematıcal modelıng problem posıng competencıes of mathematıcs teachers] [Unpublished doctoral dissertation]. Adıyaman University.
Sahin, S., Gürbüz, R., Çavuş Erdem, Z. & Doğan, F. (2017, May 18-20). Matematiksel modelleme problemi mi, değil mi?, II. Uluslararası Sosyal Bilimler Sempozyumu Özet Kitapçığı, 179. Alanya, Türkiye.
Sahin, S., Gürbüz, R., Doğan, M. F. & Çavuş Erdem, Z. (2018, June 27-29). Teachers’ mathematical mode¬ling competencies: Task dimension, International Conference on Mathematics and Mathe-matics Education (ICMME-2018), Ordu University, Ordu.
Senemoğlu, N. (2005). Gelişim, öğrenme ve öğretim [Development, learning and teaching] (12th ed.). Ankara: Gazi Kitabevi.
Sevinc, S., & Lesh, R. (2018). Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses. ZDM, 50(1), 301-314.
Yin, R. K. (2003). Case study research and applications: Design and methods (3rd ed.). Thousand Oaks, CA: Sage.
Zbiek, R. M. (2016). Supporting teachers’ development as modelers and teachers of modelers. In C. R. Hirsch (Ed), Annual perspectives in mathematics education (APME) 2016: Mathematical modeling and modeling mathematics (pp. 263–272). Reston, Va.: National Council of Teachers of Mathematics.