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Research Article
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Investigation of Middle School Students' Interdisciplinary Mathematical Modeling Skills

Year 2021, Volume: 10 Issue: 4, 1763 - 1788, 30.12.2021

Zeynep Çavuş Erdem , Muhammed Fatih Doğan , Ramazan Gürbüz

https://doi.org/10.30703/cije.927243
Cited By: 4

Abstract

The contextual aspect of mathematical modeling might provide an opportunity to address different disciplines in solving a real-life problem. Interdisciplinary Mathematical Modeling (IMM) can be expressed as a reinterpretation of mathematical modeling with an interdisciplinary dimension. The IMM approach focuses on integrating at least two different disciplines, such as mathematics and science, to solve real-life problems. For this purpose, this study aims to examine middle school students' IMM skills. In total, six IMM activities were implemented in two 8 grade middle school classrooms. The data consisted of student solution papers, video and audio recordings of the implications, and researcher notes from classrooms. To analyze the data IMM Skill Assessment Rubric developed by researchers and were coded by using the content analysis method. The results showed that students experience some difficulties arising from the nature of the IMM activities. In the modeling process, students were successful at the level of understanding the problem, while had difficulties at the level of evaluation. The students' IMM skills were affected by their problem-solving habits as well as their knowledge of mathematics and science concepts that required to solve the problem. The results also showed that students' IMM kills improved significantly during the implication process. The results suggest that the necessity of giving more place to modeling activities in teaching mathematics.

Project Number

117K169

References

  • Aydın-Güç, F. (2015). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi. (Yayınlanmış doktora tezi). Karadeniz Teknik Üniversitesi/Eğitim Bilimleri Enstitüsü, Trabzon.
  • Baki, A., ve Güç, F. A. (2014). Dokuzuncu sınıf öğrencilerinin devirli ondalık gösterimle ilgili kavram yanılgıları. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 5(2), 176-206.
  • Blomhøj, M., and Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching mathematics and its applications, 22(3), 123-139.
  • Blomhøj, M. and Jensen, T. H. (2007). What’s all the fuss about competencies? In W. Blum, P. L. Galbraith, H. Henn, and M. Niss (Eds.), Modelling and applications in mathematics educati¬on. The 14th ICMI study (pp. 45-56). New York, NY: Springer.
  • Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. B. Ferri, and G.A. Stillman (Eds.), In Trends in teaching and learning of mathematical modelling (pp. 15-30). Springer, Dordrecht.
  • Blum, W., and Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.
  • Blum, W., and Leiß, D. (2007). Investigating quality mathematics teaching: The DISUM project. Developing and researching quality in mathematics teaching and learning, proceedings of MADIF, 5, 3-16.
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2017). Bilimsel araştırma yöntemleri. Pegem Akademi, Ankara.
  • Çavuş-Erdem, Z. (2018). Matematiksel modelleme etkinliklerine dayalı öğrenme sürecinin alan ölçme konusu bağlamında incelenmesi. (Yayınlanmış doktora tezi). Adıyaman Üniversitesi/Fen Bilimleri Enstitüsü, Adıyaman.
  • Dede, C. (2010). Comparing frameworks for 21st century skills. In J. Bellance, & R. Brandt (Eds.), “21st century skills: Rethinking how students learn”(pp. 51-76). Bloomington, IN: Solution Tree Press.
  • Doğan, M. F., Gürbüz, R., Çavuş-Erdem, Z., and Şahin, S. (2019). Using mathematical modeling for integrating STEM disciplines: A theoretical framework. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 10(3), 628-653. https://doi.org/10.16949/turkbilmat.502007.
  • Doerr, H. M. (1997). Experiment, simulation and analysis: An integrated instructional approach to the concept of force. International Journal of Science Education, 19(3), 265-282.
  • Dogan, M. F. (2020). Evaluating Pre-Service Teachers’ Design of Mathematical Modelling Tasks. International Journal of Innovation in Science and Mathematics Education, 28(1), 44-59.
  • Dunne, T., and Galbraith, P. (2003). Mathematical modelling as pedagogy–impact of an immersion program. In Q. X. Ye, W. Blum, K. Houston, and Q.Y. Jiang (Eds.), Mathematical modelling in education and culture (pp-16-30). Horwood Publishing Chichester, England.
  • English, Lyn D. (2008). Mathematical modeling: linking mathematics, science and artsin the primary curriculum. In: 2nd International Symposium on Mathematics and its Connections to the Arts and Sciences (MACAS2) (pp. 187-194), 29 - 31 May 2007, Odense, Denmark.
  • Englısh L. D. (2009). Promoting interdisciplinarity through mathematical modelling. ZDM, 41, 161-181. doi 10.1007/s11858-008-0106-z.
  • English, L. D. (2015). STEM: Challenges and opportunities for mathematics education. In Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 4-18). PME.
  • Erbaş, A.K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C. ve Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: temel kavramlar ve farklı yaklaşımlar. Kuram ve Uy¬gulamada Eğitim Bilimleri, 14(4), 1607-1627. doi: 10.12738/estp.2014.4.2039.
  • Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95.
  • Galbraith, P. (2012). Models of modelling: Genres, purposes or perspectives. Journal of Mathematical Modelling and application, 1(5), 3-16.
  • Gonzalez, H. B., and Kuenzi, J. J. (2012). Science, technology, engineering, and mathematics (STEM) education: A primer. Washington, DC: Congressional Research Service, Library of Congress.
  • Gürbüz, R., and Doğan, M.F. (2019). Giriş: Matematiksel modellemeye disiplinler arası bakış: Bir STEM yaklaşımı. R. Gürbüz ve M. F Doğan (Eds) (2.baskı). Matematiksel modellemeye disiplinler arası bakış: Bir STEM yaklaşımı, (pp.1-5). Ankara, Pegem Akademi.
  • Ehri, L. C. (2005). Learning to read words: Theory, findings, and issues. Scientific Studies of Reading, 9(2), 167-188. https://doi.org/10.1207/s1532799xssr0902_4.
  • Hamilton, E., Lesh, R., Lester, F.,and Brilleslyper, M. (2008). Model-Eliciting Activities (MEAs) as a Bridge between Engineering Education Research and Mathematics Education Research. Advances in Engineering Education, 1(2), 1-25.
  • Hıdıroğlu, Ç. N., Tekin Dede, A., Kula, S., ve Bukova Güzel, E. (2014). Öğrencilerin kuyruklu yıldız problemi’ne ilişkin çözüm yaklaşımlarının matematiksel modelleme süreci çerçevesinde incelenmesi. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 31, 1-17.
  • Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi. Marmara Üniversitesi, Eğitim Bilimleri Enstitüsü, İstanbul.
  • Lesh, R., and Doerr, H. M. (2003a). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, and H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., Galbraith, P. L., Haines, C. R., and Hurford, A. (2010). Modeling students’ mathematical modeling competencies (ICTMA13). Springer, Dordrecht.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., and Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly and R. Lesh (Eds.), Hand book of reseacrh design in mathematics and science education (pp. 591-646). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Lesh, R., and Yoon, C. (2007). What is Distinctive in (Our Views about) Models and Modelling Perspectives on Mathematics Problem Solving, Learning, and Teaching?. In W. Blum, P. L. Galbraith, H.W. Henn, and M. Niss (Eds.), Modelling and applications in mathematics education (pp. 161-170). Springer, Boston, MA.
  • Lesh, R., and Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teac hing and learning (pp. 763–804). Greenwich, CT: Information Age Publishing.
  • Ludwig, M., and Xu, B. (2010). A Comparative Study of Modelling Competencies Among Chinese and German Students. Journal fur Mathematik-Didaktik, 31(1), 77-97.
  • Maaß, K. (2006). What are modelling competencies?. ZDM, 38(2), 113-142.
  • Maaß, K. (2007a). Modelling taks for low achieving students. First results of an empirical study. In CERME 5–Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 2120-2129).
  • Maaß, K., and Mischo, C. (2011). Implementing modelling into day-to-day teaching practice–The project STRATUM and its framework. Journal Für Mathematik-Didaktik, 32(1), 103-131. Doi: 10.1007/s13138-010-0015-x
  • Milli Eğitim Bakanlığı [MEB], (2018). Talim Terbiye Kurulu. Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı, Erişim Tarihi 20 Şubat 2018, http://mufredat.meb.gov.tr/Programlar.aspx.
  • Michelsen, C. (2005). Expanding the domain: Variables and functions in an interdisciplinary context between mathematics and physics. In Beckmann, A., Michelsen, C., and Sriraman, B (Eds.), Proceedings of the 1st International Symposium of Mathematics and its Connections to the Arts and Sciences (pp. 201-214).
  • Michelsen, C. (2015). Mathematical modeling is also physics—interdisciplinary teaching between mathematics and physics in Danish upper secondary education. Physics Education, 50(4), 489. https://doi.org/10.1088/0031-9120/50/4/489.
  • Polya, G. (1945). How to solve it: A new aspect of mathematical model. Princeton, New Jersey.
  • Sahin, S. (2019). Matematik öğretmenlerinin matematiksel modelleme problemi hazırlama becerilerinin incelenmesi [Doktora tezi], Adıyaman Üniversitesi, Adıyaman.
  • Tekin Dede, A. (2015). Matematik derslerinde öğrencilerin modelleme yeterliklerinin geliştirilmesi: bir eylem araştırması. (Yayınlanmış doktora tezi). Dokuz Eylül Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir.
  • Williams, J., Roth, W. M., Swanson, D., Doig, B., Groves, S., Omuvwie, M., Borromeo Ferri, R., and Mousoulides, N. (2016). Interdisciplinary mathematics education. Springer Nature.
  • Zawojewski, J. (2010). Problem solving versus modeling. In Lesh, R., Galbraith P. L., Haines C. R. ve Hurford A., (Ed.). Modeling Students’ Mathematical Modeling Competencies. ICTMA 13, Springer New York Dordrecht Heidelberg London.

Ortaokul Öğrencilerinin Disiplinler Arası Matematiksel Modelleme Becerilerinin İncelenmesi

Year 2021, Volume: 10 Issue: 4, 1763 - 1788, 30.12.2021

Zeynep Çavuş Erdem , Muhammed Fatih Doğan , Ramazan Gürbüz

https://doi.org/10.30703/cije.927243
Cited By: 4

Abstract

Matematiksel modellemenin disiplinler arası boyutuyla yeniden yorumlanması olan Disiplinler arası Matematiksel Modellemede (DMM) gerçek yaşam problemi, matematik ve fen bilimlerine ait bilgi ve yöntemlerle çözülmeye çalışılır. Bu araştırmada ortaokul öğrencilerinin DMM becerilerinin incelenmesi amaçlanmıştır. Kapsamlı bir projenin bir bölümünü kapsayan araştırmada, projeye katılan öğretmenler tarafından geliştirilen altı (6) adet DMM etkinliği, katılımcı öğretmenler tarafından iki farklı sınıf ortamında uygulanmıştır. Uygulamalar 4 kişilik öğrenci grupları üzerinden yürütülmüş ve her sınıftan bir grup seçilerek DMM becerileri iki grup üzerinden incelenmiştir. Öğrenci çözüm kağıtları, uygulama sürecinin video ve ses kayıtları ile araştırmacıların notlarından oluşan verilerin analizinde, içerik analizi yönteminden faydalanılmış ve veriler “DMM Beceri Değerlendirme Rubriği” ile analiz edilmiştir. Yapılan analizler, öğrencilerin DMM etkinliklerinin doğasından kaynaklı bazı zorluklar yaşadığını göstermektedir. Modelleme sürecinde öğrencilerin en yüksek ve en düşük performansı gösterdikleri basamaklar sırasıyla problemi anlama ve değerlendirme basamağı olmuştur. Öğrencilerin DMM becerilerinin, problem çözme alışkanlıklarından, etkinliğin gerektirdiği matematik ve fen kazanımlarından etkilendiği sonucuna ulaşılmıştır. Grup performanslarının birbirine benzediği ve uygulama süreci ilerledikçe öğrenci becerilerinin geliştiği sonucuna ulaşılmıştır. Sonuçlar, modelleme uygulamalarına öğretim sahasında daha çok yer verilmesinin gerekliliğini göstermektedir.

Keywords

Disiplinler arası matematiksel modelleme disiplinler arası matematiksel modelleme becerisi disiplinler arası matematiksel modelleme süreci matematiksel modelleme ortaokul öğrencisi

Supporting Institution

TÜBİTAK

Project Number

117K169

References

  • Aydın-Güç, F. (2015). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi. (Yayınlanmış doktora tezi). Karadeniz Teknik Üniversitesi/Eğitim Bilimleri Enstitüsü, Trabzon.
  • Baki, A., ve Güç, F. A. (2014). Dokuzuncu sınıf öğrencilerinin devirli ondalık gösterimle ilgili kavram yanılgıları. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 5(2), 176-206.
  • Blomhøj, M., and Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching mathematics and its applications, 22(3), 123-139.
  • Blomhøj, M. and Jensen, T. H. (2007). What’s all the fuss about competencies? In W. Blum, P. L. Galbraith, H. Henn, and M. Niss (Eds.), Modelling and applications in mathematics educati¬on. The 14th ICMI study (pp. 45-56). New York, NY: Springer.
  • Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. B. Ferri, and G.A. Stillman (Eds.), In Trends in teaching and learning of mathematical modelling (pp. 15-30). Springer, Dordrecht.
  • Blum, W., and Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.
  • Blum, W., and Leiß, D. (2007). Investigating quality mathematics teaching: The DISUM project. Developing and researching quality in mathematics teaching and learning, proceedings of MADIF, 5, 3-16.
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2017). Bilimsel araştırma yöntemleri. Pegem Akademi, Ankara.
  • Çavuş-Erdem, Z. (2018). Matematiksel modelleme etkinliklerine dayalı öğrenme sürecinin alan ölçme konusu bağlamında incelenmesi. (Yayınlanmış doktora tezi). Adıyaman Üniversitesi/Fen Bilimleri Enstitüsü, Adıyaman.
  • Dede, C. (2010). Comparing frameworks for 21st century skills. In J. Bellance, & R. Brandt (Eds.), “21st century skills: Rethinking how students learn”(pp. 51-76). Bloomington, IN: Solution Tree Press.
  • Doğan, M. F., Gürbüz, R., Çavuş-Erdem, Z., and Şahin, S. (2019). Using mathematical modeling for integrating STEM disciplines: A theoretical framework. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 10(3), 628-653. https://doi.org/10.16949/turkbilmat.502007.
  • Doerr, H. M. (1997). Experiment, simulation and analysis: An integrated instructional approach to the concept of force. International Journal of Science Education, 19(3), 265-282.
  • Dogan, M. F. (2020). Evaluating Pre-Service Teachers’ Design of Mathematical Modelling Tasks. International Journal of Innovation in Science and Mathematics Education, 28(1), 44-59.
  • Dunne, T., and Galbraith, P. (2003). Mathematical modelling as pedagogy–impact of an immersion program. In Q. X. Ye, W. Blum, K. Houston, and Q.Y. Jiang (Eds.), Mathematical modelling in education and culture (pp-16-30). Horwood Publishing Chichester, England.
  • English, Lyn D. (2008). Mathematical modeling: linking mathematics, science and artsin the primary curriculum. In: 2nd International Symposium on Mathematics and its Connections to the Arts and Sciences (MACAS2) (pp. 187-194), 29 - 31 May 2007, Odense, Denmark.
  • Englısh L. D. (2009). Promoting interdisciplinarity through mathematical modelling. ZDM, 41, 161-181. doi 10.1007/s11858-008-0106-z.
  • English, L. D. (2015). STEM: Challenges and opportunities for mathematics education. In Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 4-18). PME.
  • Erbaş, A.K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C. ve Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: temel kavramlar ve farklı yaklaşımlar. Kuram ve Uy¬gulamada Eğitim Bilimleri, 14(4), 1607-1627. doi: 10.12738/estp.2014.4.2039.
  • Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95.
  • Galbraith, P. (2012). Models of modelling: Genres, purposes or perspectives. Journal of Mathematical Modelling and application, 1(5), 3-16.
  • Gonzalez, H. B., and Kuenzi, J. J. (2012). Science, technology, engineering, and mathematics (STEM) education: A primer. Washington, DC: Congressional Research Service, Library of Congress.
  • Gürbüz, R., and Doğan, M.F. (2019). Giriş: Matematiksel modellemeye disiplinler arası bakış: Bir STEM yaklaşımı. R. Gürbüz ve M. F Doğan (Eds) (2.baskı). Matematiksel modellemeye disiplinler arası bakış: Bir STEM yaklaşımı, (pp.1-5). Ankara, Pegem Akademi.
  • Ehri, L. C. (2005). Learning to read words: Theory, findings, and issues. Scientific Studies of Reading, 9(2), 167-188. https://doi.org/10.1207/s1532799xssr0902_4.
  • Hamilton, E., Lesh, R., Lester, F.,and Brilleslyper, M. (2008). Model-Eliciting Activities (MEAs) as a Bridge between Engineering Education Research and Mathematics Education Research. Advances in Engineering Education, 1(2), 1-25.
  • Hıdıroğlu, Ç. N., Tekin Dede, A., Kula, S., ve Bukova Güzel, E. (2014). Öğrencilerin kuyruklu yıldız problemi’ne ilişkin çözüm yaklaşımlarının matematiksel modelleme süreci çerçevesinde incelenmesi. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 31, 1-17.
  • Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi. Marmara Üniversitesi, Eğitim Bilimleri Enstitüsü, İstanbul.
  • Lesh, R., and Doerr, H. M. (2003a). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, and H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Mahwah, NJ: Lawrence Erlbaum.
  • Lesh, R., Galbraith, P. L., Haines, C. R., and Hurford, A. (2010). Modeling students’ mathematical modeling competencies (ICTMA13). Springer, Dordrecht.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., and Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly and R. Lesh (Eds.), Hand book of reseacrh design in mathematics and science education (pp. 591-646). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Lesh, R., and Yoon, C. (2007). What is Distinctive in (Our Views about) Models and Modelling Perspectives on Mathematics Problem Solving, Learning, and Teaching?. In W. Blum, P. L. Galbraith, H.W. Henn, and M. Niss (Eds.), Modelling and applications in mathematics education (pp. 161-170). Springer, Boston, MA.
  • Lesh, R., and Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teac hing and learning (pp. 763–804). Greenwich, CT: Information Age Publishing.
  • Ludwig, M., and Xu, B. (2010). A Comparative Study of Modelling Competencies Among Chinese and German Students. Journal fur Mathematik-Didaktik, 31(1), 77-97.
  • Maaß, K. (2006). What are modelling competencies?. ZDM, 38(2), 113-142.
  • Maaß, K. (2007a). Modelling taks for low achieving students. First results of an empirical study. In CERME 5–Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 2120-2129).
  • Maaß, K., and Mischo, C. (2011). Implementing modelling into day-to-day teaching practice–The project STRATUM and its framework. Journal Für Mathematik-Didaktik, 32(1), 103-131. Doi: 10.1007/s13138-010-0015-x
  • Milli Eğitim Bakanlığı [MEB], (2018). Talim Terbiye Kurulu. Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı, Erişim Tarihi 20 Şubat 2018, http://mufredat.meb.gov.tr/Programlar.aspx.
  • Michelsen, C. (2005). Expanding the domain: Variables and functions in an interdisciplinary context between mathematics and physics. In Beckmann, A., Michelsen, C., and Sriraman, B (Eds.), Proceedings of the 1st International Symposium of Mathematics and its Connections to the Arts and Sciences (pp. 201-214).
  • Michelsen, C. (2015). Mathematical modeling is also physics—interdisciplinary teaching between mathematics and physics in Danish upper secondary education. Physics Education, 50(4), 489. https://doi.org/10.1088/0031-9120/50/4/489.
  • Polya, G. (1945). How to solve it: A new aspect of mathematical model. Princeton, New Jersey.
  • Sahin, S. (2019). Matematik öğretmenlerinin matematiksel modelleme problemi hazırlama becerilerinin incelenmesi [Doktora tezi], Adıyaman Üniversitesi, Adıyaman.
  • Tekin Dede, A. (2015). Matematik derslerinde öğrencilerin modelleme yeterliklerinin geliştirilmesi: bir eylem araştırması. (Yayınlanmış doktora tezi). Dokuz Eylül Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir.
  • Williams, J., Roth, W. M., Swanson, D., Doig, B., Groves, S., Omuvwie, M., Borromeo Ferri, R., and Mousoulides, N. (2016). Interdisciplinary mathematics education. Springer Nature.
  • Zawojewski, J. (2010). Problem solving versus modeling. In Lesh, R., Galbraith P. L., Haines C. R. ve Hurford A., (Ed.). Modeling Students’ Mathematical Modeling Competencies. ICTMA 13, Springer New York Dordrecht Heidelberg London.
There are 43 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Zeynep Çavuş Erdem 0000-0002-7448-2722

Muhammed Fatih Doğan 0000-0002-5301-9034

Ramazan Gürbüz 0000-0002-2412-5882

Project Number 117K169
Publication Date December 30, 2021
Published in Issue Year 2021 Volume: 10 Issue: 4

Cite

APA Çavuş Erdem, Z., Doğan, M. F., & Gürbüz, R. (2021). Ortaokul Öğrencilerinin Disiplinler Arası Matematiksel Modelleme Becerilerinin İncelenmesi. Cumhuriyet Uluslararası Eğitim Dergisi, 10(4), 1763-1788. https://doi.org/10.30703/cije.927243

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