TY - JOUR T1 - İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Modelleme Sürecinde Matematiksel Becerilerinin İncelenmesi TT - Investigation of Preservice Elementary Mathematics Teachers’ Mathematical Skills in the Process of Mathematical Modelling AU - Demiray, Selin AU - Candan, Merve Nur AU - Gürsoy, Zeynep PY - 2025 DA - November Y2 - 2025 JF - Baskent University Journal of Education JO - BUJE PB - Başkent Üniversitesi WT - DergiPark SN - 2148-3272 SP - 217 EP - 232 VL - 12 IS - Özel Sayı LA - tr AB - Bu çalışma, disiplinler arası yaklaşımı benimseyen matematiksel modelleme süreci kapsamında, öğretmen adaylarının dört temel matematiksel beceriyi (problem çözme, iletişim, akıl yürütme ve ilişkilendirme) nasıl sergilediklerini incelemeyi amaçlamaktadır. Gerçek yaşam bağlamlı, açık uçlu bir problem üzerinden yürütülen modelleme etkinliğinde, bir üniversitede öğrenim gören dokuz ilköğretim matematik öğretmeni adayı, üç grup halinde çalışmıştır. Araştırmanın verileri, grupların çizimleri, yazılı raporları ve grup içi etkileşimlerine ait ses kayıtlarından elde edilmiştir. Veriler, Millî Eğitim Bakanlığı’nın matematiksel beceriler çerçevesi doğrultusunda içerik analiziyle değerlendirilmiştir. Bulgular, öğretmen adaylarının modelleme sürecinde dört temel matematiksel beceriyi süreç boyunca birbirini tamamlayacak biçimde ve farklı düzeylerde kullandıklarını ortaya koymuştur. Problem çözme ve akıl yürütme genellikle planlama ve değerlendirme aşamalarında öne çıkarken; iletişim, grup içi anlam üretimi ve karar verme süreçlerinde belirleyici rol oynamıştır. İlişkilendirme ise bazı gruplarda günlük yaşam bağlamlarıyla, bazı gruplarda ise mimarlık gibi farklı disiplinlerle kurulan bağlantılar üzerinden yapılmıştır. Bu beceriler yalnızca matematiksel düşünmeyi değil, aynı zamanda iş birliği, eleştirel düşünme ve karar verme gibi 21. yüzyıl becerilerini de desteklemiştir. Elde edilen bulgular, modelleme etkinliklerinin öğretmen yetiştirme sürecinde çok yönlü becerilerin gelişimini destekleyen önemli bir öğrenme alanı sunduğunu ortaya koymaktadır. KW - Matematiksel modelleme KW - Matematiksel beceriler KW - İlköğretim matematik öğretmeni adayları KW - 21. yüzyıl becerileri N2 - This study aims to examine how prospective mathematics teachers demonstrate four fundamental mathematical competencies—problem solving, reasoning, communication, and connections—within the interdisciplinary framework of the mathematical modelling process. The modelling activity was conducted using a real-world, open-ended problem and involved nine prospective elementary mathematics teachers studying at an university, working in three groups. The data were collected through students’ drawings, written reports, and audio recordings of their group interactions. The analysis was carried out through content analysis based on the mathematical competencies framework provided by the Ministry of National Education. The findings revealed that the prospective teachers utilized the four competencies at varying levels and in complementary ways throughout the modelling process. Problem Solving and reasoning typically emerged during the planning and evaluation phases, whereas communication played a decisive role in group meaning-making and decision-making processes. Connections were established in some groups through real-life contexts and in others through interdisciplinary associations such as architecture. These competencies supported not only mathematical thinking but also 21st-century skills such as collaboration, critical thinking, and decision-making. The findings indicate that modelling activities provide a rich learning environment that fosters the development of multidimensional skills in teacher education. CR - Binkley, M., Erstad, O., Herman, J., Raizen, S., Ripley, M., Miller-Ricci, M., & Rumble, M. (2012). Defining twenty-first century skills. In P. Griffin, B. McGaw, & E. Care (Eds.), Assessment and teaching of 21st century skills (pp. 17–66). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-2324-5_2 CR - Birgin, O., & Öztürk, F. N. (2021). Türkiye’de Matematik Eğitimi Alanında Matematiksel Modelleme Çalışmalarına İlişkin Eğilimler (2010-2020): Tematik İçerik Analizi. e-Uluslararası Eğitim Araştırmaları Dergisi, 12(5), 118-140. https://doi.org/10.19160/e-ijer.937654 CR - Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58. Retrieved from: https://www.researchgate.net/publication/279478754_Mathematical_Modelling_Can_It_Be_Taught_And_Learnt CR - Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics – ICTMA 12 (pp. 222–231). Cambridge, UK: Woodhead Publishing. https://doi.org/10.1533/9780857099419.5.221 CR - Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM – Mathematics Education, 38(2), 86–95. https://doi.org/10.1007/BF02655883 CR - Borromeo Ferri, R., & Blum, W. (2010). Mathematical modelling in teacher education – Experiences from a modelling seminar. In U. T. Jankvist, T. H. Kjeldsen, & C. Winsløw (Eds.), Proceedings of CERME 6 (pp. 2046–2055). Lyon, France. Retrieved from: https://scispace.com/pdf/mathematical-modelling-in-teacher-education-experiences-from-2jlmbefka7.pdf CR - Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2010). Bilimsel araştırma yöntemleri (5. Baskı). Pegem Akademi Yayınları. CR - Carreira, S. & Baioa, A. M. (2011). Students’ modelling routes in the context of object manipulation and experimentation in mathematics. In G. Kaiser, W. Blum, R. B. Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA 14 (pp. 211-220). Netherlands: Springer. https://doi.org/10.1007/978-94-007-0910-2_22 CR - Crompton, H., & Burke, D. (2024). The nexus of ISTE standards and academic progress: A mapping analysis of empirical studies. TechTrends, 68(4), 711–722. https://doi.org/10.1007/s11528-024-00973-y CR - Çakmak Gürel, Z., & Işık, A. (2018). İlköğretim matematik öğretmen adaylarının matematiksel modellemeye ilişkin yeterliklerinin incelenmesi. e-Uluslararası Eğitim Araştırmaları Dergisi, 9(3), 85–103. https://doi.org/10.19160/ijer.477651 CR - Çetinbaş, M. (2022). An investigation of pre-service mathematics teachers’ semiotic representations and modeling routes in a mathematical modeling activity (Unpublished master’s thesis). Middle East Technical University. CR - Delice, A., & Taşova, H. İ. (2011). Bireysel ve grup çalışmasının modelleme etkinliklerindeki sürece ve performansa etkisi. Marmara Üniversitesi Eğitim Bilimleri Dergisi, 34, 71–97. Erişim adresi: https://dergipark.org.tr/tr/pub/maruaebd/issue/376/2225 CR - Deniz, D., & Akgün, L. (2018). İlköğretim matematik öğretmeni adaylarının matematiksel modelleme becerilerinin incelenmesi. Akdeniz Eğitim Araştırmaları Dergisi, 12(24), 294–312. Erişim adresi: https://mjer.inased.org/makale/515 CR - 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. https://doi.org/10.1080/0950069970190302 CR - Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136. https://doi.org/10.2307/30034902 CR - Doerr, H. M., & Lesh, R. (2011). Models and modelling perspectives on teaching and learning mathematics in the twenty-first century. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 247–268). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-0910-2_26 CR - Doruk, B. K. (2012). Mathematical modelling activities as a useful tool for values education. Educational Sciences: Theory & Practice, 12(2), 1667–1672. Retrieved from: https://files.eric.ed.gov/fulltext/EJ987866.pdf CR - Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https://doi.org/10.1007/s10649-006-0400-z CR - Eli, J. A. (2009). An exploratory mixed methods study of prospective middle grades teachers’ mathematical connections while completing investigative tasks in geometry (Unpublished doctoral dissertation). University of Kentucky. Retrieved from: https://uknowledge.uky.edu/gradschool_diss/781/ CR - Eraslan, A. (2011). İlköğretim matematik öğretmen adaylarının model oluşturma etkinlikleri ve bunların matematik öğrenimine etkisi hakkındaki görüşleri. İlköğretim Online, 10(1), 368–388. Erişim adresi: https://dergipark.org.tr/tr/pub/ilkonline/issue/8593/106870 CR - English, L. D. (2006). Mathematical modeling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 62(3), 303–323. https://doi.org/10.1007/s10649-005-9013-1 CR - English, L. D. (2009). Promoting interdisciplinarity through mathematical modelling. ZDM – Mathematics Education, 41(1–2), 161–181. https://doi.org/10.1007/s11858-008-0106-z CR - English, L. D., & Walters, J. J. (2005). Mathematical modelling in the early school years. Mathematics Education Research Journal, 16(3), 58–79. https://doi.org/10.1007/BF03217401 CR - European Parliament & Council of the European Union. (2006). Recommendation of the European Parliament and of the Council of 18 December 2006 on key competences for lifelong learning (2006/962/EC). Official Journal of the European Union, L394, 10–18. Retrieved from: https://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:2006:394:0010:0018:en:PDF CR - Greer, B., Verschaffel, L., & Mukhopadhyay, S. (2007). Modelling for life: Mathematics and children’s experience. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 89–98). Boston, MA: Springer. https://doi.org/10.1007/978-0-387-29822-1_7 CR - Griffin, P., Care, E., & McGaw, B. (2012). The changing role of education and schools. In P. Griffin, B. McGaw, & E. Care (Eds.), Assessment and teaching of 21st century skills (pp. 1–16). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-2324-5_1 CR - Griffin, P., & Care, E. (2015). The ATC21S method. In P. Griffin & E. Care (Eds.), Assessment and teaching of 21st century skills: Methods and approaches (pp. 3–33). Dordrecht: Springer. https://doi.org/10.1007/978-94-017-9395-7 CR - Jamison, R. E. (2000). Learning the language of mathematics. Language and Learning Across The Disciplines, 4(1), 45-54. https://doi.org/10.37514/LLD-J.2000.4.1.06 CR - 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 – Proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA 12) (pp. 110–119). Chichester: Horwood. https://doi.org/10.1533/9780857099419.3.110 CR - Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM – Mathematics Education, 38, 302–310. https://doi.org/10.1007/BF02652813 CR - Lehrer, R. ve Schauble, L. (2007). A developmental approach for supporting the epistemology of modeling. W. Blum, P. L. Galbraith, H-W. Henn, and M. Niss (Eds.), Modeling and Applications in Mathematics Education içinde (ss. 153-160). New York, NY: Springer. https://doi.org/10.1007/978-0-387-29822-1_14 CR - Lesh, R., & Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum Associates. https://doi.org/10.4324/9781410607713 CR - Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591–645). Mahwah, NJ: Lawrence Erlbaum Associates. CR - Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2–3), 109–129. https://doi.org/10.1080/10986065.2003.9679996 CR - 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. CR - Lester, F. K. (2013). Thoughts about research on mathematical problem solving instruction. In K. Leatham (Ed.), Vital directions for mathematics education research (pp. 119–139). Springer. https://doi.org/10.54870/1551-3440.1267 CR - Lingefjärd, T. (2012). Learning mathematics through mathematical modelling. Journal of Mathematical Modelling and Application, 1(5), 41-49. Retrieved from: https://scispace.com/pdf/learning-mathematics-through-mathematical-modelling-47ppjd5ddv.pdf CR - Marshall, G. (1996). Problem solving about problem solving: Framing a research agenda. Retrieved from: https://files.eric.ed.gov/fulltext/ED398890.pdf CR - Mata Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186. https://doi.org/10.1007/s10649-017-9773-4 CR - Mercer, N., & Littleton, K. (2007). Dialogue and the development of children's thinking: A sociocultural approach. London: Routledge. https://doi.org/10.4324/9780203946657 CR - Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks, CA: Sage. CR - Milli Eğitim Bakanlığı [MEB]. (2009). İlköğretim matematik dersi 6–8. sınıflar öğretim programı ve kılavuzu. Ankara: MEB Yayınları. CR - Milli Eğitim Bakanlığı [MEB]. (2018). Ortaokul matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: MEB Yayınları. CR - National Research Council. (2010). Exploring the intersection of science education and 21st century skills: A workshop summary. Washington, DC: The National Academies Press. https://doi.org/10.17226/12771 CR - National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM. Retrieved from: https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/ CR - Niss, M., & Højgaard, T. (2011). Competencies and mathematical learning: Ideas and inspiration for developing mathematics teaching and learning in Denmark. Roskilde: Roskilde University. Retrieved from: https://www.researchgate.net/publication/270585013_Competencies_and_Mathematical_Learning_Ideas_and_inspiration_for_the_development_of_mathematics_teaching_and_learning_in_Denmark Organisation for Economic Co-operation and Development [OECD]. (2006). The new millennium learners: Challenging our views on ICT and learning. Paris: OECD Publishing. https://doi.org/10.18261/ISSN1891-943X-2007-04-04 CR - Organisation for Economic Co-operation and Development [OECD]. (2019). Education at a glance 2019: OECD indicators. Paris: OECD Publishing. https://doi.org/10.1787/f8d7880d-en CR - Organisation for Economic Co-operation and Development [OECD]. (2021). PISA 2018 mathematics framework (second draft). Retrieved from: https://one.oecd.org/document/EDU/PISA/GB(2018)19/en/pdf CR - Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton University Press. CR - Sahara, I., Darmawijoyo, & Hartono, Y. (2021). Learning mathematical modeling: Analysis of mathematical reasoning skills of junior high school students through a visual-formed problem. https://doi.org/10.2991/assehr.k.210508.081 CR - Sen Zeytun, A., Çetinkaya, B., & Erbaş, A. K. (2017). Understanding prospective teachers’ mathematical modeling processes in the context of a mathematical modeling course. Eurasia Journal of Mathematics, Science and Technology Education, 13(3), 691–722. https://doi.org/10.12973/eurasia.2017.00639a CR - Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press. CR - Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York, NY: Macmillan. CR - Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park, CA: Sage. CR - Şengil Akar, Ş. (2017). Üstün yetenekli öğrencilerin matematiksel yaratıcılıklarının matematiksel modelleme etkinlikleri sürecinde incelenmesi (Yayımlanmamış doktora tezi). Hacettepe Üniversitesi, Ankara. CR - Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289–321.Retrieved from: https://www.jstor.org/stable/pdf/30034869.pdf CR - Tekin Dede, A., & Yılmaz, S. (2013). İlköğretim matematik öğretmeni adaylarının modelleme yeterliliklerinin ı̇ncelenmesi. Turkish Journal of Computer and Mathematics Education, 4(3), 185-206. Erişim adresi: https://dergipark.org.tr/tr/pub/turkbilmat/issue/21571/231478 CR - Ural, A. (2014). Matematik öğretmen adaylarının matematiksel modelleme becerilerinin incelenmesi. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 23, 110–141. Erişim adresi: https://dergipark.org.tr/tr/pub/zgefd/issue/47938/606436 CR - Urhan, S., & Dost, Ş. (2016). Matematiksel modelleme etkinliklerinin derslerde kullanımı: Öğretmen görüşleri. Electronic Journal of Social Sciences, 15(59), 1412–1427. Erişim adresi: https://dergipark.org.tr/tr/pub/esosder/issue/24938/263231 CR - van De Walle, J., Karp, K. S., ve Bay-Williams, J. M. (2018). Matematik Yapmanın ve Bilmenin Ne Anlama Geldiğinin İncelenmesi (İ. Ö. Zembat, Çev.) S. Durmuş (Ed.), İlkokul ve Ortaokul Matematiği Gelişimsel Yaklaşımla Öğretim (ss. 13-29). Ankara: Nobel Yayıncılık. CR - Vorhölter, K., Krüger, A., & Wendt, L. (2019). Metacognition in mathematical modeling: An overview. In S. A. Chamberlin & B. Sriraman (Eds.), Affect in mathematical modeling (pp. 39–54). Cham: Springer. https://doi.org/10.1007/978-3-030-04432-9_3 CR - Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477. https://doi.org/10.2307/749877 CR - Yanagimoto, A., & Yoshimura, N. (2013). Mathematical modelling of a real-world problem: The decreasing number of bluefin tuna. In G. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 229–239). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-6540-5_20 CR - Yıldırım, A., & Şimşek, H. (2005). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara:Seçkin Yayıncılık. CR - Zawojewski, J., Lesh, R., & English, L. D. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics teaching, learning, and problem solving (pp. 337–359). Mahwah, NJ: Lawrence Erlbaum Associates. UR - https://dergipark.org.tr/tr/pub/bujoe/issue//1755885 L1 - https://dergipark.org.tr/tr/download/article-file/5112062 ER -