Matematiksel Modelleme Öğretiminde Öğretmen Müdahalelerinin İncelenmesi: Bir Ortaokul Öğretmeni Örneği

Year 2022, Volume: 5 Issue: 2, 60 - 79, 31.12.2022

Seda Şahin , Muhammed Fatih Doğan , Ramazan Gürbüz

https://doi.org/10.52134/ueader.1160828

Abstract

Matematiksel modelleme öğretiminde en önemli konulardan biri matematiksel modelleme uygulamalarında öğretmenin sahip olması gereken pedagojik bilgidir. Ders uygulaması sırasında öğretmenin kullandığı müdahaleler ise pedagojik bilgisinin dışavurumudur. Bu sebeple matematiksel modelleme öğretiminde öğretmen rolünün tanımlanmasında belirleyici etkiye sahip olan öğretmen müdahaleleri araştırılması gereken önemli bir faktördür. Bu çalışmada matematiksel modelleme eğitimine katılan bir ortaokul matematik öğretmeninin eğitimden sonra sınıf içi matematiksel modelleme uygulamalarının birinde kullandığı müdahale türleri incelenmiştir. Sekizinci sınıf öğrencilerinden oluşan 20 kişilik bir sınıfta “Kavşak Düzenleme” probleminin (2 ders saati) uygulamasına ait videolar transkript edilmiş, gözlemci notları ve öğrenci çalışma kağıtları ile desteklenerek içerik analizi yöntemi ile analiz edilmiştir. Elde edilen bulgular öğretmenin en çok duyuşsal müdahaleler ile ortam ve etkileşime yönelik müdahalelerde bulunduğunu göstermektedir. Öğretmenin içeriğe yönelik müdahalelerden kaçınması, stratejik müdahalelerde bulunmaması ya da müdahale etmemesi ise öğretmenin modelleme sürecini etkilemek istememesinden kaynaklandığı düşünülmektedir. Öte yandan sunum ve değerlendirme aşamasında daha etkin olması modelleme sürecinde nerede nasıl müdahale edeceği konusunda tereddütler ve zorluklar yaşadığını desteklemektedir. Yapılan çalışmalar ve bu araştırmanın sonuçları matematiksel modellemenin öğretiminde öğretmenlerin özel bir pedagojik bilgiye sahip olmaları gerektiğini ortaya koymaktadır.

Keywords

matematiksel modelleme, öğretmen müdahaleleri, sınıfiçi uygulamalar

Supporting Institution

TÜBİTAK-

Project Number

117K169

Examining Teacher Interventions in Teaching Mathematical Modeling: A Case of Middle School Teacher

Abstract

The teachers' pedagogical understanding of modeling applications is one of the most critical issues in teaching mathematical modeling. The interventions used by the teacher during the implementation of the tasks are the mirror of their pedagogical knowledge. For this reason, teacher interventions, which have a decisive effect on defining the teacher's role in teaching mathematical modeling, are a crucial issue to investigate. This study examines the types of interventions used by a middle school mathematics teacher who completed professional development in mathematical modeling. The data was collected in an eighth-grade classroom consisting of twenty students. The mathematical modeling task, called Intersection Arrangement, was implemented for 2 hours, and both video and audio recordings were used to collect data. All recordings were transcribed and analyzed using the content analysis method, supported by observer notes and student worksheets. The results revealed that the teacher mostly had effective environmental and classroom interaction interventions. The teacher avoided having content-oriented or strategic interventions or did not intervene during the modeling process. These intervention types might be because of the teacher's unwillingness to affect the modeling process. On the other hand, the fact that the teacher was more active in the presentation and evaluation stage supports his hesitations and difficulties about where and how to intervene in the modeling process. The relevant literature and the results of this research show that teachers must have unique pedagogical knowledge in teaching mathematical modeling.

Keywords

mathematical modeling, teacher intervention, classroom teaching

Project Number

117K169

References

• Berry, B. (2013). An investigation of teachers’ shared interpretations of their roles in supporting and enhancing group functioning. Modeling Students' Mathematical Modeling Competencies: ICTMA 13, (pp. 471-480). Dordrecht.
• Blum, W. (2005). Opportunities and problems for “Quality Mathematics Teaching” – the SINUS and DISUM Projects. In M. Niss et al. (Eds.), Regular Lectures at ICME-10.
• Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. Trends in teaching and learning of mathematical modelling (pp. 15-30). Springer.
• 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., & Leiss. D. (2003). Diagnose- und Interventionsformen für einen selbstständigkeitsorientierten Unterricht am Beispiel Mathematik – Vorstellung des Projekts DISUM. In H. W. Henn (Ed.), Beiträge zum Mathematikunterricht (pp. 129-132). Franzbecker.
• Blum, W., & Leiss, D. (2005). “Filling Up” -the problem of independence-preserving teacher interventions in lessons with demanding modelling tasks. CERME 4–Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 1623-1633).
• Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer.
• Borromeo Ferri, R. (2020). Make mathematical modeling marvelous! Follow teacher Mr. K. for your lesson tomorrow. The New Jersey Mathematics Teacher, 78(1), 44-53.
• Borromeo Ferri, R., & Blum, W. (2009). Mathematical modelling in teacher education–experiences from a modelling seminar. Proceedings of CERME, 6(2046-2055).
• Bozkurt, A., & Özbey, N. (2018). The effect of guided discovery process on gifted students' mathematical modeling skills. International Congress on Gifted and Talented Education Proceedings Book (pp. 44-53). Malatya, Turkey.
• Deci, E. L., Koestner, R., & Ryan, R. M. (1999). A meta-analytic review of experiments examining the effects of extrinsic rewards on intrinsic motivation. Psychological Bulletin, 125(6), 627.
• Denzin, N., & Lincoln, Y. (2005). Introduction: the discipline and practice of qualitative research. In N. Denzin, & Y. Lincoln (Eds.) Handbook of qualitative research (3rd ed.) (pp. 1-32). Sage.
• Didiş, M. G., Erbaş, A. K., & Çetinkaya, B. (2016). Investigating prospective mathematics teachers’ pedagogical approaches in response to students’ errors in the context of mathematical modeling activities. İlköğretim Online, 15(4), 1367-1384. http://dx.doi.org/10.17051/io.2016.75429
• Didiş Kabar, M. G., & Erbaş, A. K. (2021). Pre-service secondary mathematics teachers’ anticipation and identification of students’ thinking in the context of modelling problems. International Journal of Mathematical Education in Science and Technology, 52(2), 208-236.
• Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38(2), 143-162.
• Garfunkel, S. A., Montgomery, M., Bliss, K., Fowler, K., Galluzzo, B., Giordano, F., ... & Long, M. (2016). GAIMME: Guidelines for assessment & instruction in mathematical modeling education. Consortium for Mathematics and its Applications.
• Gürbüz, R., Doğan, M. F., Çalık, M., Çelı̇k, D., Şahı̇n, S., Çavuş Erdem, Z., Temurtaş, A., & Doğan C. (2018). Modelleme etkinlikleri hazırlama süreci [The process of completing the modeling operations]. In R. Gürbüz & M. F. Doğan (Eds.), Matematiksel modellemeye disiplinler arası bakış: Bir STEM yaklaşımı [An interdisciplinary perspective on mathematical modeling: A STEM approach] (pp. 97-159). Pegem Akademi.
• Hestenes, D. (2010). Modeling theory for math and science education. Modeling Students' Mathematical Modeling Competencies (pp. 13-41). Springer.
• Ikeda, T., Stephens, M., & Matsuzaki, A. (2007). A teaching experiment in mathematical modelling. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12). Education, engineering and economics (pp. 101–109). Horwood Publishing.
• Koellner-Clark, K., & Lesh, R. (2003). A modeling approach to describe teacher knowledge. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 159–173). Lawrence Erlbaum.
• Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716.
• Leavitt, D. R., & Ahn, C. M. (2013). A middle grade teacher’s guide to model eliciting activities. Modeling students' mathematical modeling competencies (pp. 353-364). Springer.
• Leiss, D. (2005). Teacher intervention versus self-regulated learning? Teaching Mathematics and Its Applications: International Journal of the IMA, 24(2-3), 75-89.
• Leiss, D. (2007). "Hilf mir, es selbst zu tun": Lehrerinterventionen beim mathematischen Modellieren. Franzbecker.
• Leiss, D., Schukajlow, S., Blum, W., Messner, R., & Pekrun, R. (2010). The role of the situation model in mathematical modelling—Task analyses, student competencies, and teacher interventions. Journal für Mathematik-Didaktik, 31(1), 119-141.
• Leiss, D., & Wiegand, B. (2005). A classification of teacher interventions in mathematics teaching. ZDM, 37(3), 240-245.
• Manouchehri, A., Bekdemir, M., & Yao, X. (2020). Facilitating modelling activities in a grade 5 classroom. Mathematical Modelling Education and Sense-making (pp. 187-197). Springer.
• Mayring, P. (2015). Qualitative content analysis: Theoretical background and procedures. Approaches to qualitative research in mathematics education (pp. 365-380). Springer.
• 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). Springer Science + Business Media, LLC.
• Sahin, S. (2019). Investigation of mathematical modeling problem posing competencies of mathematics teachers [Unpublished doctoral dissertation]. Adıyaman University, Adıyaman, Turkey.
• Sahin S., Cavus Erdem Z., & Gurbuz R. (2020). STEM eğitiminde disiplinlerarası matematiksel modelleme etkinliklerinin uygulanması [Application of interdisciplinary mathematical modeling activities in stem education]. In Y. Dede, M. F. Doğan, & F. Aslan Tutak (Eds.), Matematik eğitiminde etkinlikler ve uygulamaları [Activities and applications in mathematics education] (pp. 317-341). Pegem Akademi.
• Sahin, S., Dogan, M. F., Cavus Erdem, Z., Gurbuz, R., & Temurtas, A. (2019). Prospective Teachers' Criteria for Evaluating Mathematical Modeling Problems. International Journal of Research in Education and Science, 5(2), 730-743.
• Schukajlow, S., Leiss, D., Pekrun, R., Blum, W., Müller, M., & Messner, R. (2012). Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations. Educational Studies in Mathematics, 79(2), 215-237.
• Stender, P. (2018). The use of heuristic strategies in modelling activities. ZDM, 50(1-2), 315-326.
• Stender, P. (2019). Heuristic strategies as a toolbox in complex modelling problems. Lines of inquiry in mathematical modelling research in education (pp. 197-212). Springer.
• Stender, P., & Kaiser, G. (2015). Scaffolding in complex modelling situations. ZDM, 47(7), 1255-1267.
• Stender, P. & Kaiser, G. (2016). Fostering modeling competencies for complex situations. In C. Hirsch (Ed.), Mathematical modeling and modeling mathematics: Annual perspectives in mathematics education (pp.107-115). NCTM.
• Temurtas A., Sahin S., Cavus Erdem Z., Gurbuz R., & Dogan M. F. (2021). Ortaokul seviyesinde matematiksel modelleme uygulamaları [Mathematical modeling applications at secondary school level]. In E. Bukova Güzel, M. F. Doğan, & A. Özaltun Çelik), Matematiksel modelleme: Teoriden uygulamaya bütünsel bakış [Mathematical modeling: a holistic view from theory to practice] (pp. 229-246). Pegem Akademi.
• Tropper, N., Leiss, D., & Hänze, M. (2015). Teachers’ temporary support and worked-out examples as elements of scaffolding in mathematical modeling. ZDM, 47(7), 1225-1240.
• Van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in teacher-student interaction: A decade of research. Educational Psychology Review, 22(3), 271-296.