Araştırma Makalesi
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INTERACTIONS BETWEEN PROSPECTIVE MATHEMATICS TEACHERS' SOLUTION APPROACHES IN INDIVIDUAL AND GROUP MATHEMATICAL MODELING PROCESSES

Yıl 2024, Cilt: 14 Sayı: 1, 408 - 426, 31.01.2024
https://doi.org/10.24315/tred.1377278

Öz

This study aimed to understand the mathematical approaches that prospective teachers produced individually and as a group during their mathematical modeling experience, and the interactions between these approaches. For this purpose, the case study method was adopted. Forty prospective middle school mathematics teachers participated in the study. The prospective teachers first worked individually and then in groups of four on a mathematical modeling activity. The data were obtained through written individual solutions for the modeling problem, group solutions, audio recordings of the group work process, and reflective reports after the group work. In data analysis, mathematical solutions produced individually and as a group were considered as two separate cases and comparative analyzes were made. The results regarding the individual solution approaches produced for the modeling problem indicated that the prospective teachers, when considering a modeling activity individually, resorted to the classical ways that came to their minds geometrically, instead of examining the given situation in a real-world context. However, the individual solutions of the prospective teachers became different when they worked with the group. In particular, the variation in the solution approaches of the individuals in the group or the existence of a more reasonable solution caused a change of opinion in all group members together with the final decision of the group.

Kaynakça

  • Abramovich, S. (2013). Modeling as isomorphism: The case of teacher education. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 501–510). New York, NY: Springer.
  • Akgün, L., Çiltaş, A., Deniz, D., Çiftçi, Z., & Ahmet, I. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 12, 1-34.
  • Anhalt, C. O., & Cortez, R. (2015). Mathematical modeling: A structured process. The Mathematics Teacher, 108(6), 446-452.
  • Aydin-Güç, F., & Baki, A. (2019). Evaluation of the learning environment designed to develop student mathematics teachers’ mathematical modelling competencies. Teaching Mathematics and its Applications: An International Journal of the IMA, 38(4), 191-215.
  • Aydogan-Yenmez, A., Erbas, A. K., Cakiroglu, E., Alacaci, C., & Cetinkaya, B. (2017). Developing teachers' models for assessing students' competence in mathematical modelling through lesson study. International Journal of Mathematical Education in Science and Technology, 48(6), 895-912.
  • Aydogan-Yenmez, A., Erbas, A. K., Cakiroglu, E., Cetinkaya, B., & Alacaci, C. (2018). Mathematics teachers’ knowledge and skills about questioning in the context of modeling activities. Teacher Development, 22(4), 497-518.
  • Berry, J. (2002). Developing mathematical modeling skills: The role of CAS. Zentralblatt für Didaktik der Mathematik, 34(5), 212–220.
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. ZDM, 38(2), 163-177.
  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and attitudinal challenges (pp. 73-96). New York, NY: 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., & 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.
  • Borromeo-Ferri, R. (2018). Task Competency: For Your Instructional Flexibility. In Learning How to Teach Mathematical Modeling in School and Teacher Education (pp. 41-75). Springer, Cham.
  • Borromeo-Ferri, R., & Blum, W. (2013, February). Barriers and motivations of primary teachers for implementing modelling in mathematics lessons. In Eighth Congress of European Research in Mathematics Education (CERME 8), Antalya, Turkey.
  • Burkhardt, H. (2006). Modelling in mathematics classrooms: Reflections on past developments and the future. ZDM, 38(2), 178-195.
  • Chan, E. C. M. (2008). Using model-eliciting activities for primary mathematics classrooms. The Mathematics Educator, 11(1), 47-66.
  • Cheng, A. K. (2001). Teaching mathematical modeling in Singapore schools. The Mathematics Educator, 6(1), 63–75.
  • Dede, A. T. (2019). Arguments constructed within the mathematical modelling cycle. International Journal of Mathematical Education in Science and Technology, 50(2), 292-314.
  • Deniz, D., & Akgün, L. (2017). Ortaöğretim matematik öğretmenlerinin matematiksel modelleme yöntemi ve uygulamalarına yönelik görüşleri. Anemon Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi, 5(1), 95-117.
  • English, L. D. (2006). Mathematical modeling in the primary school: Children's construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303-323.
  • English, L. D., & Watters, J. (2004). Mathematical modeling with young children. In M. J. Høines & A. B. Fuglestad (Eds.), Proceeding of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 335–342). Bergen: IGPME.
  • Erbaş, A. K., Çetinkaya, B., Alacacı, C., Çakıroğlu, E., Aydoğan Yenmez, A., Şen Zeytun, A., & Şahin, Z. (2016). Nasıl Depolayalım?. Lise matematik konuları için günlük hayattan modelleme soruları (s. 26). Ankara: Türkiye Bilimler Akademisi.
  • Ferri, R. B. (2007). Modelling problems from a cognitive perspective. In Mathematical Modelling (pp. 260-270). Woodhead Publishing.
  • Figazzolo, L. (2009). Impact of PISA 2006 on the education policy debate. Paper presented at the Education International Research Network Fifth Annual Meeting, Brussels, Belgium.
  • Fox, J. (2006). A justification for mathematical modeling experiences in the preparatory classroom. Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia 1,21–228.
  • Greefrath, G., Hertleif, C., & Siller, H. S. (2018). Mathematical modelling with digital tools—a quantitative study on mathematising with dynamic geometry software. ZDM, 50(1), 233-244.
  • Haines, C. & Crouch, R. (2010). Remarks on a modeling cycle and interpretation of behaviours. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (ICTMA 13) (pp. 145–154). New York: Springer.
  • Henn, H.-W. (2007). Modeling in school: Chances and obstacles. The Montana Mathematics Enthusiast, Monograph, 3, 125–138.
  • Hıdıroğlu, Ç. N., & Özkan Hıdıroğlu, Y. (2017). Altıncı sınıf öğrencilerinin matematiksel modellemede oluşturdukları gerçek yaşam problem durumu modelleri. Ilkogretim Online, 16(4), 1702-1734.
  • Jung, H., Stehr, E. M., & He, J. (2019). Mathematical modeling opportunities reported by secondary mathematics preservice teachers and instructors. School Science and Mathematics, 119(6), 353-365.
  • Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi [Investigation of problem-solving skills of mathematics teacher candidates during modeling process]. İstanbul: Yüksek Lisans Tezi, Marmara Üniversitesi.
  • Ledezma, C., Font, V., & Sala, G. (2022). Analysing the mathematical activity in a modelling process from the cognitive and onto-semiotic perspectives. Mathematics Education Research Journal, 1-27.
  • Lesh R. & Yoon C. (2007) What is Distinctive in (Our Views about) Models & Modelling Perspectives on Mathematics Problem Solving, Learning, and Teaching?. In: Blum W., Galbraith P.L., Henn HW., Niss M. (Eds.) Modelling and Applications in Mathematics Education. New ICMI Study Series, vol 10. Springer, Boston, MA.
  • Lesh, R. & Doerr, H. M. (2003). Foundations of a Models and Modeling Perspective on Mathematics Teaching, Learning, and Problem Solving. Lesh, R. & Doerr, H. M. (Eds.), Beyond Constructivism Models and modeling perspectives on mathematics problem solving, learning, and teaching (ss. 3-33). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Lesh, R. & Fennewald, T. (2010). Modeling: What is it? Why do it. Lesh, R., Galbraith, P. L., Haines, C. R., & Hurford, A. (Eds.), Modeling students’ mathematical modeling competencies (ss.5-15). Boston, MA: Springer US. Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. Corwin Press.
  • Lingefjärd, T. (2006). Faces of mathematical modeling. ZDM, 38(2), 96-112.
  • Lingefjärd, T., & Meier, S. (2010). Teachers as managers of the modelling process. Mathematics Education Research Journal, 22(2), 92-107.
  • Maaß, K. (2006). What are modelling competencies?. ZDM, 38(2), 113-142.
  • Milli Eğitim Bakanlığı [MEB] (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). MEB Yayıncılık. https://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
  • Sevinç, Ş., & Melek, Z. (2020). Modelleme etkinliğinde matematik öğretmen adaylarının bireysel ve grup gelişiminin incelenmesi. Başkent University Journal of Education, 7(1), 1-19.
  • Stillman, G., Brown, J., & Czocher, J. (2020). Yes, mathematicians do X so students should do X, but it’s not the X you think!. ZDM, 52(6), 1211-1222.
  • Swetz, F., & Hartzler, J. S. (1991). Mathematical modeling in the secondary school curriculum: A resource guide of classroom exercises. Reston, VA: NCTM.
  • 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.
  • Türker, B., Sağlam, Y., & Umay, A. (2010). Preservice teachers’ performances at mathematical modeling process and views on mathematical modeling. Procedia-Social and Behavioral Sciences, 2(2), 4622-4628.
  • Vygotsky, L. S. (1978). Mind in society: the development of higher psychological processes (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, Eds.) Harvard University Press.
  • Yin, R. (1984). Case study research: Design and methods (1st ed.). Sage Publishing.
  • Yu, S. Y., & Chang, C. K. (2011). What did taiwan mathematics teachers think of modeleliciting activities and modelling teaching?. In G. Kaiser, W. Blum, R. B. Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA 14 (pp. 147-156). Netherlands: Springer.
  • Yüksek Öğretim Kurulu [YÖK] (2018a). Öğretmen yetiştirme lisans programları. https://www.yok.gov.tr/Documents/Kurumsal/egitim_ogretim_dairesi/Yeni-Ogretmen-Yetistirme-Lisans-Programlari/AA_Sunus_%20Onsoz_Uygulama_Yonergesi.pdf.
  • Yüksek Öğretim Kurulu [YÖK] (2018b). İlköğretim matematik öğretmenliği lisans programı. https://www.yok.gov.tr/Documents/Kurumsal/egitim_ogretim_dairesi/Yeni-Ogretmen-Yetistirme-Lisans-Programlari/Ilkogretim_Matematik_Lisans_Programi.pdf.
  • Zawojewski, J., Lesh, R., & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving; learning and teaching (ss. 337–358). Mahwah, New Jersey: Lawrence Erlbaum.

MATEMATİK ÖĞRETMENİ ADAYLARININ BİREYSEL VE GRUP İLE MATEMATİKSEL MODELLEME SÜREÇLERİNDEKİ ÇÖZÜM YAKLAŞIMLARI ARASINDAKİ ETKİLEŞİMLER

Yıl 2024, Cilt: 14 Sayı: 1, 408 - 426, 31.01.2024
https://doi.org/10.24315/tred.1377278

Öz

Bu çalışma, öğretmen adaylarının matematiksel modelleme deneyimi sürecinde bireysel ve grupça ürettikleri matematiksel yaklaşımları ve bu yaklaşımlar arasındaki etkileşimleri anlamayı amaçlamıştır. Bu amaç doğrultusunda, çalışmada nitel bir araştırma deseni olan durum çalışması yöntemi benimsenmiştir. Çalışmaya 40 ilköğretim matematik öğretmeni adayı katılmıştır. Öğretmen adayları ilk olarak bireysel ardından dörder kişilik gruplarda çalışmıştır. Veriler, modelleme problemi için yapılan yazılı bireysel çözümler, grup çözümleri, grup çalışma süreci ses kayıtları, grup çalışması sonrası yansıtıcı raporlar aracılığıyla elde edilmiştir. Veri analizinde bireysel ve grupça üretilen matematiksel çözümler iki ayrı durum olarak düşünülerek karşılaştırmalı analizler yapılmıştır. Elde edilen sonuçlar, öğretmen adaylarının bireysel olarak bir modelleme etkinliğini düşünürken verilen durumu verilen gerçek yaşam bağlamı içinde incelemek yerine geometrik olarak akıllarına gelen klasik yollara başvurduklarına işaret etmiştir. Diğer taraftan, öğretmen adaylarının bireysel çözümleri grup ile birlikte çalıştıklarında farklı hale gelmiştir. Özellikle gruptaki bireylerin çözüm yaklaşımlarındaki varyasyon ya da daha makul çözümün varlığı grubun nihai kararı ile birlikte tüm grup üyelerinde fikir değişimlerine neden olmuştur.

Kaynakça

  • Abramovich, S. (2013). Modeling as isomorphism: The case of teacher education. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 501–510). New York, NY: Springer.
  • Akgün, L., Çiltaş, A., Deniz, D., Çiftçi, Z., & Ahmet, I. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 12, 1-34.
  • Anhalt, C. O., & Cortez, R. (2015). Mathematical modeling: A structured process. The Mathematics Teacher, 108(6), 446-452.
  • Aydin-Güç, F., & Baki, A. (2019). Evaluation of the learning environment designed to develop student mathematics teachers’ mathematical modelling competencies. Teaching Mathematics and its Applications: An International Journal of the IMA, 38(4), 191-215.
  • Aydogan-Yenmez, A., Erbas, A. K., Cakiroglu, E., Alacaci, C., & Cetinkaya, B. (2017). Developing teachers' models for assessing students' competence in mathematical modelling through lesson study. International Journal of Mathematical Education in Science and Technology, 48(6), 895-912.
  • Aydogan-Yenmez, A., Erbas, A. K., Cakiroglu, E., Cetinkaya, B., & Alacaci, C. (2018). Mathematics teachers’ knowledge and skills about questioning in the context of modeling activities. Teacher Development, 22(4), 497-518.
  • Berry, J. (2002). Developing mathematical modeling skills: The role of CAS. Zentralblatt für Didaktik der Mathematik, 34(5), 212–220.
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. ZDM, 38(2), 163-177.
  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education: Intellectual and attitudinal challenges (pp. 73-96). New York, NY: 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., & 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.
  • Borromeo-Ferri, R. (2018). Task Competency: For Your Instructional Flexibility. In Learning How to Teach Mathematical Modeling in School and Teacher Education (pp. 41-75). Springer, Cham.
  • Borromeo-Ferri, R., & Blum, W. (2013, February). Barriers and motivations of primary teachers for implementing modelling in mathematics lessons. In Eighth Congress of European Research in Mathematics Education (CERME 8), Antalya, Turkey.
  • Burkhardt, H. (2006). Modelling in mathematics classrooms: Reflections on past developments and the future. ZDM, 38(2), 178-195.
  • Chan, E. C. M. (2008). Using model-eliciting activities for primary mathematics classrooms. The Mathematics Educator, 11(1), 47-66.
  • Cheng, A. K. (2001). Teaching mathematical modeling in Singapore schools. The Mathematics Educator, 6(1), 63–75.
  • Dede, A. T. (2019). Arguments constructed within the mathematical modelling cycle. International Journal of Mathematical Education in Science and Technology, 50(2), 292-314.
  • Deniz, D., & Akgün, L. (2017). Ortaöğretim matematik öğretmenlerinin matematiksel modelleme yöntemi ve uygulamalarına yönelik görüşleri. Anemon Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi, 5(1), 95-117.
  • English, L. D. (2006). Mathematical modeling in the primary school: Children's construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303-323.
  • English, L. D., & Watters, J. (2004). Mathematical modeling with young children. In M. J. Høines & A. B. Fuglestad (Eds.), Proceeding of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 335–342). Bergen: IGPME.
  • Erbaş, A. K., Çetinkaya, B., Alacacı, C., Çakıroğlu, E., Aydoğan Yenmez, A., Şen Zeytun, A., & Şahin, Z. (2016). Nasıl Depolayalım?. Lise matematik konuları için günlük hayattan modelleme soruları (s. 26). Ankara: Türkiye Bilimler Akademisi.
  • Ferri, R. B. (2007). Modelling problems from a cognitive perspective. In Mathematical Modelling (pp. 260-270). Woodhead Publishing.
  • Figazzolo, L. (2009). Impact of PISA 2006 on the education policy debate. Paper presented at the Education International Research Network Fifth Annual Meeting, Brussels, Belgium.
  • Fox, J. (2006). A justification for mathematical modeling experiences in the preparatory classroom. Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia 1,21–228.
  • Greefrath, G., Hertleif, C., & Siller, H. S. (2018). Mathematical modelling with digital tools—a quantitative study on mathematising with dynamic geometry software. ZDM, 50(1), 233-244.
  • Haines, C. & Crouch, R. (2010). Remarks on a modeling cycle and interpretation of behaviours. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (ICTMA 13) (pp. 145–154). New York: Springer.
  • Henn, H.-W. (2007). Modeling in school: Chances and obstacles. The Montana Mathematics Enthusiast, Monograph, 3, 125–138.
  • Hıdıroğlu, Ç. N., & Özkan Hıdıroğlu, Y. (2017). Altıncı sınıf öğrencilerinin matematiksel modellemede oluşturdukları gerçek yaşam problem durumu modelleri. Ilkogretim Online, 16(4), 1702-1734.
  • Jung, H., Stehr, E. M., & He, J. (2019). Mathematical modeling opportunities reported by secondary mathematics preservice teachers and instructors. School Science and Mathematics, 119(6), 353-365.
  • Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi [Investigation of problem-solving skills of mathematics teacher candidates during modeling process]. İstanbul: Yüksek Lisans Tezi, Marmara Üniversitesi.
  • Ledezma, C., Font, V., & Sala, G. (2022). Analysing the mathematical activity in a modelling process from the cognitive and onto-semiotic perspectives. Mathematics Education Research Journal, 1-27.
  • Lesh R. & Yoon C. (2007) What is Distinctive in (Our Views about) Models & Modelling Perspectives on Mathematics Problem Solving, Learning, and Teaching?. In: Blum W., Galbraith P.L., Henn HW., Niss M. (Eds.) Modelling and Applications in Mathematics Education. New ICMI Study Series, vol 10. Springer, Boston, MA.
  • Lesh, R. & Doerr, H. M. (2003). Foundations of a Models and Modeling Perspective on Mathematics Teaching, Learning, and Problem Solving. Lesh, R. & Doerr, H. M. (Eds.), Beyond Constructivism Models and modeling perspectives on mathematics problem solving, learning, and teaching (ss. 3-33). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Lesh, R. & Fennewald, T. (2010). Modeling: What is it? Why do it. Lesh, R., Galbraith, P. L., Haines, C. R., & Hurford, A. (Eds.), Modeling students’ mathematical modeling competencies (ss.5-15). Boston, MA: Springer US. Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. Corwin Press.
  • Lingefjärd, T. (2006). Faces of mathematical modeling. ZDM, 38(2), 96-112.
  • Lingefjärd, T., & Meier, S. (2010). Teachers as managers of the modelling process. Mathematics Education Research Journal, 22(2), 92-107.
  • Maaß, K. (2006). What are modelling competencies?. ZDM, 38(2), 113-142.
  • Milli Eğitim Bakanlığı [MEB] (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). MEB Yayıncılık. https://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
  • Sevinç, Ş., & Melek, Z. (2020). Modelleme etkinliğinde matematik öğretmen adaylarının bireysel ve grup gelişiminin incelenmesi. Başkent University Journal of Education, 7(1), 1-19.
  • Stillman, G., Brown, J., & Czocher, J. (2020). Yes, mathematicians do X so students should do X, but it’s not the X you think!. ZDM, 52(6), 1211-1222.
  • Swetz, F., & Hartzler, J. S. (1991). Mathematical modeling in the secondary school curriculum: A resource guide of classroom exercises. Reston, VA: NCTM.
  • 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.
  • Türker, B., Sağlam, Y., & Umay, A. (2010). Preservice teachers’ performances at mathematical modeling process and views on mathematical modeling. Procedia-Social and Behavioral Sciences, 2(2), 4622-4628.
  • Vygotsky, L. S. (1978). Mind in society: the development of higher psychological processes (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, Eds.) Harvard University Press.
  • Yin, R. (1984). Case study research: Design and methods (1st ed.). Sage Publishing.
  • Yu, S. Y., & Chang, C. K. (2011). What did taiwan mathematics teachers think of modeleliciting activities and modelling teaching?. In G. Kaiser, W. Blum, R. B. Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA 14 (pp. 147-156). Netherlands: Springer.
  • Yüksek Öğretim Kurulu [YÖK] (2018a). Öğretmen yetiştirme lisans programları. https://www.yok.gov.tr/Documents/Kurumsal/egitim_ogretim_dairesi/Yeni-Ogretmen-Yetistirme-Lisans-Programlari/AA_Sunus_%20Onsoz_Uygulama_Yonergesi.pdf.
  • Yüksek Öğretim Kurulu [YÖK] (2018b). İlköğretim matematik öğretmenliği lisans programı. https://www.yok.gov.tr/Documents/Kurumsal/egitim_ogretim_dairesi/Yeni-Ogretmen-Yetistirme-Lisans-Programlari/Ilkogretim_Matematik_Lisans_Programi.pdf.
  • Zawojewski, J., Lesh, R., & English, L. (2003). A models and modeling perspective on the role of small group learning activities. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving; learning and teaching (ss. 337–358). Mahwah, New Jersey: Lawrence Erlbaum.
Toplam 49 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Matematik Eğitimi
Bölüm Makaleler
Yazarlar

Fadime Ulusoy 0000-0003-3393-8778

Seda Nur Bingöl 0009-0004-6811-6541

Nurşen Olgun 0009-0006-4763-4563

Erken Görünüm Tarihi 26 Ocak 2024
Yayımlanma Tarihi 31 Ocak 2024
Gönderilme Tarihi 17 Ekim 2023
Kabul Tarihi 10 Kasım 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 14 Sayı: 1

Kaynak Göster

APA Ulusoy, F., Bingöl, S. N., & Olgun, N. (2024). MATEMATİK ÖĞRETMENİ ADAYLARININ BİREYSEL VE GRUP İLE MATEMATİKSEL MODELLEME SÜREÇLERİNDEKİ ÇÖZÜM YAKLAŞIMLARI ARASINDAKİ ETKİLEŞİMLER. Trakya Eğitim Dergisi, 14(1), 408-426. https://doi.org/10.24315/tred.1377278