Araştırma Makalesi
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Matematiksel Modelleme Uygulamalarında Ortaokul Öğrencilerinin Sembol, İşlem, Kavram ve Kuralları Kullanma Becerilerinin İncelenmesi

Yıl 2024, , 422 - 462, 15.11.2024
https://doi.org/10.29250/sead.1508427

Öz

Bu çalışma, altıncı sınıf öğrencilerinin matematiksel modelleme süreçlerinde kullandıkları sembollerin, işlemlerin, kuralların ve genellemelerin incelenmesini amaçlamaktadır. Öğretim Deneyi yöntemi kullanılarak veriler öğrenci çalışma kağıtları ve video kayıtları ile toplanmıştır. Analizler, öğrencilerin +, =, / gibi daha önce öğrendikleri sembolleri doğru bir şekilde kullandıklarını, yeni semboller keşfettiklerini ve modelleme sırasında kendi stratejilerini uyguladıklarını göstermiştir. Matematiksel modelleme etkinlikleri, öğrencilerin disiplinler arası bağlantılar kurmalarına ve kavramları günlük yaşamla ilişkilendirmelerine yardımcı olmuştur. Öğrenciler, daha önce öğrendikleri kavramları doğru bir şekilde kullanmış ve yeni kavramlar keşfetmişlerdir, ancak genelleme yapabilmek için daha fazla zamana ve uygulamaya ihtiyaç duydukları belirlenmiştir. Çalışma, matematiksel modelleme etkinliklerinin sık ve çeşitli konularla uygulanmasının önemini vurgulamaktadır.

Kaynakça

  • Abel, T., Searcy, M. E., & Salinas, T. M. L. (2020). Sense-making with the mathematical modelling process: Developing a framework for faculty practice. In Stillman, G. A., Kaiser, G., & Lampen, C. E. (eds), Mathematical modelling education and sense-making. International perspectives on the teaching and learning of mathematical modelling (pp. 119-128). Springer, Cham. https://doi.org/10.1007/978-3-030-37673-4_11
  • Akgün, L., Çiltaş, A., Deniz, D., & Çiftçi, Z. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi (12), 1-34. https://doi.org/10.14520/adyusbd.410
  • Aydın, E., & Derin, G. (2020). Matematik öğretmeni eğitiminde STEM - matematiksel modelleme birlikteliğinin problem çözme ve modelleme becerilerine etkisi. Bogazici University Journal of Education, 37, 93-121.
  • Anhalt, C. O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation. Journal of Mathematics Teacher Education, 19, 523-545. https://doi.org/10.1007/s10857-015-9309-8
  • Biccard, P. (2024). Productive struggle in mathematical modelling. The Mathematics Enthusiast, 21(1), 99-112. https://doi.org/10.54870/1551-3440.1620
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. Zentralblatt für Didaktik der Mathematik, 38(2), 163-177. https://doi.org/10.1007/BF02655887
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
  • Blum, W., & Leiß, D. (2007). How do teachers deal with modeling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 222-231). Horwood Publishing.
  • Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modeling behavior. Journal of Mathematics Didactics, 31, 99–118. https://doi.org/10.1007/s13138-010-0009-8
  • Carreira, S., & Baioa, A. M. (2018). Mathematical modelling with hands-on experimental tasks: On the student’s sense of credibility. ZDM - Mathematics Education, 50(1-2), 201-215. https://doi.org/10.1007/s11858-017-0905-1
  • Çakmak Gürel, Z. (2018). Matematik öğretmeni adaylarının matematiksel modelleme süreçlerinin bilişsel açıdan incelenmesi [Yayımlanmamış doktora tezi]. Atatürk Üniversitesi.
  • Çakmak Gürel, Z., & Bekdemir, M. (2022). The teacher and peer intervention for preservice mathematics teachers on the validity of mathematical models. Pedagogical Research, 7(2), em0120. https://doi.org/10.29333/pr/11800
  • Cheng, A. K. (2001). Teaching mathematical modelling in Singapore school. The Mathematics Educator, 6(1), 63-75.
  • Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modelling in school mathematics. In C. R. Hirsch & A. R. McDuffie (Eds.), Annual perspectives in mathematics education 2016: Mathematical modelling and modelling mathematics (pp. 3-16). NCTM.
  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13.
  • Czocher, J. A. (2017). How can emphasizing mathematical modeling principles benefit students in a traditionally taught differential equations course? The Journal of Mathematical Behavior, 45, 78-94. https://doi.org/10.1016/j.jmathb.2016.10.006
  • Czocher, J. A. (2018). Etkinliği doğrulamak modelleme sürecine nasıl katkıda bulunur? Matematikte Eğitim Çalışmaları, 99(3), 137-159.
  • Chamberlın, S.A & Moon, S.M (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. The Journal of Secondary Gifted Education, 17(1), 37-47. https://doi.org/10.4219/jsge-2005-393
  • Durandt, R., & Lautenbach, G. (2020). Strategic support to students’ competency development in the mathematical modelling process: A qualitative study. Perspectives in Education, 38(1), 211-223. https://doi.org/10.18820/2519593X/pie.v38i1.15
  • Frejd, P., & Vos, P. (2024). The spirit of mathematical modeling–a philosophical study on the occasion of 50 years of mathematical modeling education. The Mathematics Enthusiast, 21(1), 269-300. https://doi.org/10.54870/1551-3440.1626
  • Geiger, V., & Frejd, P. (2015). A reflection on mathematical modelling and applications as a field of research: Theoretical orientation and diversity. In Stillman, G., Blum, W., & Salett Biembengut, M. (eds) Mathematical modelling in education research and practice. International perspectives on the teaching and learning of mathematical modelling (pp. 161-171). Springer. https://doi.org/10.1007/978-3-319-18272-8_12
  • Geiger, V., Galbraith, P., Niss, M., & Delzoppo, C. (2021). Developing a task design and implementation framework for fostering mathematical modelling competencies. Educational Studies in Mathematics, 109, 313–336. https://doi.org/10.1007/s10649-021-10039-y
  • Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modelling: Approaches and developments from German speaking countries. In Teaching and learning mathematical modelling. ICME-13 topical surveys (pp. 1-42). Springer. https://doi.org/10.1007/978-3-319-45004-9_1
  • Gürbüz, R., & Çalik, M. (2021). Intertwining mathematical modeling with environmental issues. Problems of Education in the 21st Century, 79(3), 412-424. https://doi.org/10.33225/pec/21.79.412
  • Kal, F. M. (2013). Matematiksel modelleme etkinliklerinin ilköğretim 6. sınıf öğrencilerinin matematik problemi çözme tutumlarına etkisi [Yayımlanmamış yüksek lisans tezi]. Kocaeli Üniversitesi.
  • Karalı, D. (2013). İlköğretim matematik öğretmen adaylarının matematiksel modelleme hakkındaki görüşlerinin ortaya çıkarılması [Yayımlanmamış yüksek lisans tezi]. Abant İzzet Baysal Üniversitesi
  • Kaiser, G. (2020). Mathematical modelling and applications in education. In Lerman, S. (eds) Encyclopedia of mathematics education (pp. 553-561). Springer. https://doi.org/10.1007/978-3-030-15789-0_101
  • Kutluca, T., & Kaya, D. (2023). Mathematical Modelling: A Retrospective Overview. Journal of Computer and Education Research, 11(21), 240-274. https://doi.org/10.18009/jcer.1242785
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Lawrence Erlbaum Associates.
  • Manouchehri, A., Bekdemir, M., & Yao, X. (2020). Facilitating modelling activities in a grade 5 classroom. In Stillman, G.A., Kaiser, G., & Lampen, C.E. (eds), Mathematical modelling education and sense-making. International perspectives on the teaching and learning of mathematical modelling. Springer. https://doi.org/10.1007/978-3-030-37673-4_17
  • Maass, K. (2006). What are modelling competencies? ZDM, 38, 113-142.
  • Milli Eğitim Bakanlığı (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Talim ve Terbiye Kurulu Başkanlığı
  • Milli Eğitim Bakanlığı (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Talim ve Terbiye Kurulu Başkanlığı, Ankara
  • Miles, M, B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. (2nd ed). Sage.
  • Muşlu, M., & Çiltaş, A. (2016). Doğal sayılarda işlemler konusunun öğretiminde matematiksel modelleme yönteminin öğrenci başarısına etkisi. Bayburt Eğitim Fakültesi Dergisi, 11(2), 330-343
  • National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: ensuring mathematical success for all. NCTM.
  • 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.
  • Olkun, S. & Uçar, T. Z. (2007). İlköğretimde etkinlik temelli matematik öğretimi. Maya Akademi Yayın Dağıtım.
  • Özkaya, A., Bulut, S., & Şahin, G. (2023). Disiplinler arası matematiksel modelleme etkinliklerinin öğretmen adaylarının matematiksel düşünme becerileri ve matematik okuryazarlığına etkisi. Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 25(4), 634-650. https://doi.org/10.17556/erziefd.1312400
  • Pollak, H. (2003). A history of the teaching of modelling. In G. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (pp. 647-671). NCTM.
  • Rosa, M., & Orey, D. C. (2015). Social-critical dimension of mathematical modelling. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in educational research and practice (pp. 385-395). Springer.
  • Schleicher, A. (2007). PISA 2006: Science competencies for tomorrow’s World. OECD briefing note for The United States. OECD Directorate for Education. Sokolowski, A. (2015). The effects of mathematical modelling on students’ achievement: Meta-analysis of research. The IAFOR Journal of Education, 3(1), 93-114.
  • Solar, H., Ortiz, A., Arriagada, V., & Deulofeu, J. (2022). Argumentative orchestration in the mathematical modelling cycle in the classroom. EURASIA Journal of Mathematics, Science and Technology Education, 18(8), 1-15. https://doi.org/10.29333/ejmste/12245
  • Steffe, L. P., & Olive, J. (2010). Children’s fractional knowledge. Springer.
  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. A. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267-306). Lawrence Erlbaum Associates.
  • Stillman, G., Kaiser, G., & Lampen, C. E. (Eds.). (2020). Mathematical modelling education and sense-making. Pringer Publishing. https://doi.org/10.1007/978-3-030-37673-4
  • Stillman, G. A., Blum, W., & Kaiser, G. (Eds.). (2017). Mathematical modelling and applications: Crossing and researching boundaries in mathematics education. Springer.
  • 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. https://doi.org/10.1007/s11858-015-0718-
  • Vorhölter, K., Greefrath, G., Borromeo Ferri, R., Leiß, D., & Schukajlow, S. (2019). Mathematical modelling. In H. N. Jahnke & L. Hefendehl-Hebeker (Eds.), Traditions in German-speaking mathematics education research (pp. 91-114). Springer Publishing. https://doi.org/10.1007/978-3-030-11069-7_4
  • Widjaja, W. (2013). The use of contextual problems to support mathematical learning. Indonesian Mathematical Society Journal on Mathematics Education, 4(2), 157-168. https://files.eric.ed.gov/fulltext/EJ1078956.pdf
  • Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9 bs.). Seçkin Yayıncılık.

An Investigation into Secondary School Students' Skills in Using Symbols, Operations, Concepts and Rules in Mathematical Modeling Applications

Yıl 2024, , 422 - 462, 15.11.2024
https://doi.org/10.29250/sead.1508427

Öz

This study aims to examine the symbols, operations, rules and generalizations used by sixth grade students in mathematical modeling processes. Using the Teaching Experiment method, data was collected through student worksheets and video recordings. Analyzes showed that students correctly used previously learned symbols such as +, =, /, discovered new symbols, and applied their own strategies during modelling. Mathematical modeling activities helped students make interdisciplinary connections and relate concepts to daily life. The students correctly used the concepts they had previously learned and discovered new concepts, but it was determined that they needed more time and practice to generalize. The study emphasizes the importance of applying mathematical modeling activities frequently and with a variety of topics.

Kaynakça

  • Abel, T., Searcy, M. E., & Salinas, T. M. L. (2020). Sense-making with the mathematical modelling process: Developing a framework for faculty practice. In Stillman, G. A., Kaiser, G., & Lampen, C. E. (eds), Mathematical modelling education and sense-making. International perspectives on the teaching and learning of mathematical modelling (pp. 119-128). Springer, Cham. https://doi.org/10.1007/978-3-030-37673-4_11
  • Akgün, L., Çiltaş, A., Deniz, D., & Çiftçi, Z. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi (12), 1-34. https://doi.org/10.14520/adyusbd.410
  • Aydın, E., & Derin, G. (2020). Matematik öğretmeni eğitiminde STEM - matematiksel modelleme birlikteliğinin problem çözme ve modelleme becerilerine etkisi. Bogazici University Journal of Education, 37, 93-121.
  • Anhalt, C. O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation. Journal of Mathematics Teacher Education, 19, 523-545. https://doi.org/10.1007/s10857-015-9309-8
  • Biccard, P. (2024). Productive struggle in mathematical modelling. The Mathematics Enthusiast, 21(1), 99-112. https://doi.org/10.54870/1551-3440.1620
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. Zentralblatt für Didaktik der Mathematik, 38(2), 163-177. https://doi.org/10.1007/BF02655887
  • Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45-58.
  • Blum, W., & Leiß, D. (2007). How do teachers deal with modeling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 222-231). Horwood Publishing.
  • Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modeling behavior. Journal of Mathematics Didactics, 31, 99–118. https://doi.org/10.1007/s13138-010-0009-8
  • Carreira, S., & Baioa, A. M. (2018). Mathematical modelling with hands-on experimental tasks: On the student’s sense of credibility. ZDM - Mathematics Education, 50(1-2), 201-215. https://doi.org/10.1007/s11858-017-0905-1
  • Çakmak Gürel, Z. (2018). Matematik öğretmeni adaylarının matematiksel modelleme süreçlerinin bilişsel açıdan incelenmesi [Yayımlanmamış doktora tezi]. Atatürk Üniversitesi.
  • Çakmak Gürel, Z., & Bekdemir, M. (2022). The teacher and peer intervention for preservice mathematics teachers on the validity of mathematical models. Pedagogical Research, 7(2), em0120. https://doi.org/10.29333/pr/11800
  • Cheng, A. K. (2001). Teaching mathematical modelling in Singapore school. The Mathematics Educator, 6(1), 63-75.
  • Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modelling in school mathematics. In C. R. Hirsch & A. R. McDuffie (Eds.), Annual perspectives in mathematics education 2016: Mathematical modelling and modelling mathematics (pp. 3-16). NCTM.
  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13.
  • Czocher, J. A. (2017). How can emphasizing mathematical modeling principles benefit students in a traditionally taught differential equations course? The Journal of Mathematical Behavior, 45, 78-94. https://doi.org/10.1016/j.jmathb.2016.10.006
  • Czocher, J. A. (2018). Etkinliği doğrulamak modelleme sürecine nasıl katkıda bulunur? Matematikte Eğitim Çalışmaları, 99(3), 137-159.
  • Chamberlın, S.A & Moon, S.M (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. The Journal of Secondary Gifted Education, 17(1), 37-47. https://doi.org/10.4219/jsge-2005-393
  • Durandt, R., & Lautenbach, G. (2020). Strategic support to students’ competency development in the mathematical modelling process: A qualitative study. Perspectives in Education, 38(1), 211-223. https://doi.org/10.18820/2519593X/pie.v38i1.15
  • Frejd, P., & Vos, P. (2024). The spirit of mathematical modeling–a philosophical study on the occasion of 50 years of mathematical modeling education. The Mathematics Enthusiast, 21(1), 269-300. https://doi.org/10.54870/1551-3440.1626
  • Geiger, V., & Frejd, P. (2015). A reflection on mathematical modelling and applications as a field of research: Theoretical orientation and diversity. In Stillman, G., Blum, W., & Salett Biembengut, M. (eds) Mathematical modelling in education research and practice. International perspectives on the teaching and learning of mathematical modelling (pp. 161-171). Springer. https://doi.org/10.1007/978-3-319-18272-8_12
  • Geiger, V., Galbraith, P., Niss, M., & Delzoppo, C. (2021). Developing a task design and implementation framework for fostering mathematical modelling competencies. Educational Studies in Mathematics, 109, 313–336. https://doi.org/10.1007/s10649-021-10039-y
  • Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modelling: Approaches and developments from German speaking countries. In Teaching and learning mathematical modelling. ICME-13 topical surveys (pp. 1-42). Springer. https://doi.org/10.1007/978-3-319-45004-9_1
  • Gürbüz, R., & Çalik, M. (2021). Intertwining mathematical modeling with environmental issues. Problems of Education in the 21st Century, 79(3), 412-424. https://doi.org/10.33225/pec/21.79.412
  • Kal, F. M. (2013). Matematiksel modelleme etkinliklerinin ilköğretim 6. sınıf öğrencilerinin matematik problemi çözme tutumlarına etkisi [Yayımlanmamış yüksek lisans tezi]. Kocaeli Üniversitesi.
  • Karalı, D. (2013). İlköğretim matematik öğretmen adaylarının matematiksel modelleme hakkındaki görüşlerinin ortaya çıkarılması [Yayımlanmamış yüksek lisans tezi]. Abant İzzet Baysal Üniversitesi
  • Kaiser, G. (2020). Mathematical modelling and applications in education. In Lerman, S. (eds) Encyclopedia of mathematics education (pp. 553-561). Springer. https://doi.org/10.1007/978-3-030-15789-0_101
  • Kutluca, T., & Kaya, D. (2023). Mathematical Modelling: A Retrospective Overview. Journal of Computer and Education Research, 11(21), 240-274. https://doi.org/10.18009/jcer.1242785
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Lawrence Erlbaum Associates.
  • Manouchehri, A., Bekdemir, M., & Yao, X. (2020). Facilitating modelling activities in a grade 5 classroom. In Stillman, G.A., Kaiser, G., & Lampen, C.E. (eds), Mathematical modelling education and sense-making. International perspectives on the teaching and learning of mathematical modelling. Springer. https://doi.org/10.1007/978-3-030-37673-4_17
  • Maass, K. (2006). What are modelling competencies? ZDM, 38, 113-142.
  • Milli Eğitim Bakanlığı (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Talim ve Terbiye Kurulu Başkanlığı
  • Milli Eğitim Bakanlığı (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Talim ve Terbiye Kurulu Başkanlığı, Ankara
  • Miles, M, B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. (2nd ed). Sage.
  • Muşlu, M., & Çiltaş, A. (2016). Doğal sayılarda işlemler konusunun öğretiminde matematiksel modelleme yönteminin öğrenci başarısına etkisi. Bayburt Eğitim Fakültesi Dergisi, 11(2), 330-343
  • National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: ensuring mathematical success for all. NCTM.
  • 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.
  • Olkun, S. & Uçar, T. Z. (2007). İlköğretimde etkinlik temelli matematik öğretimi. Maya Akademi Yayın Dağıtım.
  • Özkaya, A., Bulut, S., & Şahin, G. (2023). Disiplinler arası matematiksel modelleme etkinliklerinin öğretmen adaylarının matematiksel düşünme becerileri ve matematik okuryazarlığına etkisi. Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 25(4), 634-650. https://doi.org/10.17556/erziefd.1312400
  • Pollak, H. (2003). A history of the teaching of modelling. In G. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (pp. 647-671). NCTM.
  • Rosa, M., & Orey, D. C. (2015). Social-critical dimension of mathematical modelling. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in educational research and practice (pp. 385-395). Springer.
  • Schleicher, A. (2007). PISA 2006: Science competencies for tomorrow’s World. OECD briefing note for The United States. OECD Directorate for Education. Sokolowski, A. (2015). The effects of mathematical modelling on students’ achievement: Meta-analysis of research. The IAFOR Journal of Education, 3(1), 93-114.
  • Solar, H., Ortiz, A., Arriagada, V., & Deulofeu, J. (2022). Argumentative orchestration in the mathematical modelling cycle in the classroom. EURASIA Journal of Mathematics, Science and Technology Education, 18(8), 1-15. https://doi.org/10.29333/ejmste/12245
  • Steffe, L. P., & Olive, J. (2010). Children’s fractional knowledge. Springer.
  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. A. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267-306). Lawrence Erlbaum Associates.
  • Stillman, G., Kaiser, G., & Lampen, C. E. (Eds.). (2020). Mathematical modelling education and sense-making. Pringer Publishing. https://doi.org/10.1007/978-3-030-37673-4
  • Stillman, G. A., Blum, W., & Kaiser, G. (Eds.). (2017). Mathematical modelling and applications: Crossing and researching boundaries in mathematics education. Springer.
  • 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. https://doi.org/10.1007/s11858-015-0718-
  • Vorhölter, K., Greefrath, G., Borromeo Ferri, R., Leiß, D., & Schukajlow, S. (2019). Mathematical modelling. In H. N. Jahnke & L. Hefendehl-Hebeker (Eds.), Traditions in German-speaking mathematics education research (pp. 91-114). Springer Publishing. https://doi.org/10.1007/978-3-030-11069-7_4
  • Widjaja, W. (2013). The use of contextual problems to support mathematical learning. Indonesian Mathematical Society Journal on Mathematics Education, 4(2), 157-168. https://files.eric.ed.gov/fulltext/EJ1078956.pdf
  • Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9 bs.). Seçkin Yayıncılık.
Toplam 51 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik Eğitimi
Bölüm Makaleler
Yazarlar

Uğur Yıldırım 0000-0001-8437-6272

Mehmet Bekdemir 0000-0003-1884-2938

Yayımlanma Tarihi 15 Kasım 2024
Gönderilme Tarihi 1 Temmuz 2024
Kabul Tarihi 27 Ekim 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

APA Yıldırım, U., & Bekdemir, M. (2024). An Investigation into Secondary School Students’ Skills in Using Symbols, Operations, Concepts and Rules in Mathematical Modeling Applications. The Journal of Limitless Education and Research, 9(3), 422-462. https://doi.org/10.29250/sead.1508427

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