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Kısmi Destekli Bütüncül Yaklaşıma Dayalı Uygulamaların Matematik Öğretmeni Adaylarının Modelleme Yeterliklerini Desteklemesi

Year 2022, Volume: 11 Issue: 1, 177 - 192, 28.03.2022

Zeynep Çakmak Gürel , Ahmet Işık

https://doi.org/10.30703/cije.978001

Abstract

Bu çalışmanın amacı, kısmi destekli bütüncül yaklaşıma dayalı matematiksel modelleme uygulamalarını içeren öğrenme ortamının matematik öğretmeni adaylarının modelleme yeterliklerini nasıl desteklediğinin ortaya konulmasıdır. Çalışmada eylem araştırması yöntemi kullanılmıştır. Çalışma grubu, ortama katılan 17 ve katılmayan 15 olmak üzere, toplamda 32 matematik öğretmen adayından oluşmaktadır. Ön ve son görüşmede olmak üzere iki modelleme probleminin yer aldığı görüşme formları veri toplama aracı olarak kullanılmıştır. Veriler içerik analizine tabi tutulmuştur. Meydana gelen gelişimin öğrenme ortamından kaynaklı olup olmadığını belirlemek amacıyla, ortama katılan ve katılmayan öğretmen adaylarının modelleme yeterlikleri nitel olarak karşılaştırılmıştır. Kısmi destekli bütüncül yaklaşıma dayalı öğrenme ortamına katılan öğretmen adaylarının matematiksel modelleme yeterliklerinde artış gözlemlenmiştir. Bu artışın en fazla model oluşturma, modeli çözme ve yorumlama yeterliklerinde olduğu tespit edilmiştir. Öğrenme ortamının doğrulama yeterliğine ise katkı sağlamadığı ortaya konulmuştur.

Keywords

Bütüncül yaklaşım Kısmi yaklaşım Matematiksel modelleme Matematik öğretmen adayları Yeterlikler

References

  • Bal, A. P., ve Doğanay, A. (2014). Sınıf öğretmenliği adaylarının matematiksel modelleme sürecini anlamalarını geliştirmeye yönelik bir eylem araştırması. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1363-1384.
  • Berry, J. S., and Houstan, S. K. (1995). Mathematical modelling. London: Edward Arnold.
  • Biccard, P., and Wessels D. C. J. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. In G. Kaiser, W. Blum, R. B. Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 375-383). New York: Springer. doi: 10.1007/978-94-007-0910-2_37
  • 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. doi: 10.1093/teamat/22.3.123
  • Blomhøj, M., and Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. Zentralblatt für Didaktik der Mathematik, 38(2), 163-177.
  • Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education Discussion document. Educational Studies in Mathematics, 51, 149-171.
  • Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15-30). New York: Springer. doi: 10.1007/978-94-007-0910-2_3
  • Blum, W., and Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1) 45-58.
  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86-95. doi: 10.1007/BF02655883.
  • Brand, S. (2014). Effects of a holistic versus an atomistic modelling approach on students’mathematical modelling competencies. In C. Nicol, P. Liljedahl, S. Oesterle, and D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36, Vol. 2 (pp. 185-191). Vancouver, Canada: PME.
  • Bukova Güzel, E. (2011). An examination of pre-service mathematics teachers’approaches to construct and solve mathematical modeling problems. Teaching Mathematics and Its Applications, 30(1), 19-36. doi: 10.1093/teamat/hrq015.
  • Bukova Güzel, E., ve Uğurel, I. (2010). Matematik öğretmen adaylarının analiz dersi akademik başarıları ile matematiksel modelleme yaklaşımları arasındaki ilişki. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 29(1), 69-90.
  • Carr, W., and Kemmis, S. (2003). Becoming Critical: Education, Knowledge And Action Research. New York: RoutledgeFarmer, Taylor & Francis.
  • Çiltaş, A. ve Işık, A. (2013). The effect of instruction through mathematical modelling on modelling skills of prospective elementary mathematics teachers. Educational Sciences: Theory & Practice, 13(2), 1187-1192.,
  • Dede, A. T. (2017). Modelleme yeterlikleri ile sınıf düzeyi ve matematik başarısı arasındaki ilişkilerin incelenmesi. İlköğretim Online, 16(3), 1201-1219. doi: 10.17051/ilkonline.2017.330251
  • Dede, A. T. ve Yılmaz, S. (2013). İlköğretim matematik öğretmeni adaylarının modelleme yeterliliklerinin incelenmesi. Turkish Journal of Computer and Mathematics Education, 4(3), 185-206.
  • Doerr, H. M., and Tripp, J. S. (1999). Understanding how students develop mathematical models. Mathematical Thinking and Learning, 1(3), 231–254
  • Elliott, J. (1991). Action research for educational change. Philadelphia: Open University Press.
  • Frejd, P., and Ärlebäck, J. B. (2011). First results from a study investigating Swedish upper secondary students’mathematical modelling competencies. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 407–416). Springer: New York.
  • Galbraith, P., and Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM. 38(2), 143-162. doi: 10.1007/BF02655886.
  • Gatabi, A. R., and Abdolahpour, K. (2013). Investigating students’modeling competency through grade, gender, and location. In B. Ubuz, C. Haser and M. A. Mariotti (Eds.), Proceedings of the 8th congress of the european society for research in mathematics education CERME 8 (pp. 1070-1077). Turkey: Middle East Technical University.
  • Grünewald, S. (2012, July). Acquirement of modelling competencies – first results of an empirical comparison of the effectiveness of a holistic respectively an atomistic approach to the development of (metacognitive) modelling competencies of students. Paper presented at the meeting of the 12. International Congress on Mathematical Education. Korea: Seoul.
  • Güç, F. A. (2015). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi (Yayınlanmamış Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 381105)
  • Güç, F. A. ve Baki, A. (2016). Matematiksel modelleme yeterliklerini geliştirme ve değerlendirme yaklaşımlarının sınıflandırılması. Turkish Journal of Computer and Mathematics Education, 7(3), 621-645.
  • Ji, X. (2012, July). A quasi-experimental study of high school students’mathematics modelling competence. Paper presented at the meeting of the 12. International Congress on Mathematical Education. Korea: Seoul.
  • Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum and S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 110–119). Chichester: Horwood.
  • Kaiser, G., and Brand, S. (2015). Modelling competencies: Past development and further perspectives. In G. A. Stillman, W. Blum and M. S. Biembengut (Eds.), Mathematical modelling in education research and practice (pp. 129–149). Cham: Springer International Publishing.
  • Kaplan, T. (2011). Lineer denklem sistemleri ve uygulama alanları (Yüksek lisans tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 299752)
  • Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi (Yüksek lisans tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 221516)
  • Korkmaz, E. (2010). İlköğretim matematik ve sınıf öğretmeni adaylarının matematiksel modellemeye yönelik görüşleri ve matematiksel modelleme yeterlikleri (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 275237)
  • Lesh, R., and Doerr, H. M. (2003). Foundations of a models and modelling perspective on mathematics teaching, learning and problem solving. In R. Lesh and H. M. Doerr (Eds.), Beyond constructivism: models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 3-33). Mahwah N. J.:Lawrance Erlbaum Associates Publishers.
  • Lingefjärd, T. (2006). Faces of mathematical modelling. Zentralblatt Für Didactik Der Mathematic, 38(2), 96 -112. doi: 10.1007/BF02655884
  • Maaß, K. (2006). What are modelling competencies? Zentralblatt Für Didactik Der Mathematic, 38(2), 113-142. doi: 10.1007/BF0265588
  • Maaß, K. (2007). Modelling in class: What do we want the students to learn? In C. Haines, P. Galbraith, W. Blum and S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 63–78). Chichester: Horwood.
  • Miles, M.B and Huberman, A.M. (1994). Qualitative data analysis, Thousand Oaks, CA: Sage.
  • Niss, M., Blum, W., and Galbraith, P. (2007). How to replace the word problems. In W. Blum, P. Galbraith, H-W. Henn and M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). New York: Springer.
  • Schaap, S., Vos, P., and Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: Exploring a framework. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (ICTMA 14) (pp. 137-146). New York: Springer.
  • Swetz, F., and Hartzler, J. S. (1991). Mathematical Modelling İn The Secondary School Curriculum: A Resource Guide Of Classroom Exercises. Reston, VA: NCTM.
  • Türker, B., Sağlam, Y. ve Umay, A. (2010). Preservice teachers’performances at mathematical modeling process and views on mathematical modeling. Procedia Social and Behavioral Sciences, 2, 4622–4628. doi: 10.1016/j.sbspro.2010.03.740.
  • Yıldırım, A. ve Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (6. Baskı). Ankara: Seçkin.
  • Zawojewski, J. S., and Lesh, R. (2003). A models and modeling perspective on problem solving. In R. Lesh and H. M. Doerr (Ed.). Beyond constructivism: models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 317-336). Mahwah N. J.:Lawrance Erlbaum Associates Publishers.
  • Zeytun, A. Ş. (2013). An investigation of prospective teachers’mathematical modelling processes and their views about factors affecting these processes (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 341056)

Applications Based on Atomic Supported Holistic Approach Fostering The Modeling Competencies of Preservice Mathematics Teachers

Year 2022, Volume: 11 Issue: 1, 177 - 192, 28.03.2022

Zeynep Çakmak Gürel , Ahmet Işık

https://doi.org/10.30703/cije.978001

Abstract

The aim of this study is to reveal how the learning environment, which includes mathematical modelling applications based on the atomic supported holistic approach, fosters the modelling competencies of mathematics pre-service teachers. The action research method was used in the study. The study group consists of a total of 32 preservice mathematics teachers, 17 of whom attended the learning environment and 15 not participating. As the data collection tools, two modelling situations were applied to the pre-service teachers individually before and after attending the environment. The data is examined with the content analysis method. The modelling competencies of the preservice teacher who participated and did not participate in the environment were qualitatively compared to determine whether the development occurred due to the learning environment. It was determined that the mathematical modelling competencies of preservice teachers participating in the learning environment improved. It has been determined that this increase is mostly in model creation, model solving, and interpretation competencies. On the contrary, it was revealed that the learning environment did not contribute to the validation competence.

Keywords

Holistic approach Atomic approach Mathematical modelling Preservice Mathematics Teachers Competencies

References

  • Bal, A. P., ve Doğanay, A. (2014). Sınıf öğretmenliği adaylarının matematiksel modelleme sürecini anlamalarını geliştirmeye yönelik bir eylem araştırması. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1363-1384.
  • Berry, J. S., and Houstan, S. K. (1995). Mathematical modelling. London: Edward Arnold.
  • Biccard, P., and Wessels D. C. J. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. In G. Kaiser, W. Blum, R. B. Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 375-383). New York: Springer. doi: 10.1007/978-94-007-0910-2_37
  • 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. doi: 10.1093/teamat/22.3.123
  • Blomhøj, M., and Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. Zentralblatt für Didaktik der Mathematik, 38(2), 163-177.
  • Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education Discussion document. Educational Studies in Mathematics, 51, 149-171.
  • Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15-30). New York: Springer. doi: 10.1007/978-94-007-0910-2_3
  • Blum, W., and Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1) 45-58.
  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86-95. doi: 10.1007/BF02655883.
  • Brand, S. (2014). Effects of a holistic versus an atomistic modelling approach on students’mathematical modelling competencies. In C. Nicol, P. Liljedahl, S. Oesterle, and D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36, Vol. 2 (pp. 185-191). Vancouver, Canada: PME.
  • Bukova Güzel, E. (2011). An examination of pre-service mathematics teachers’approaches to construct and solve mathematical modeling problems. Teaching Mathematics and Its Applications, 30(1), 19-36. doi: 10.1093/teamat/hrq015.
  • Bukova Güzel, E., ve Uğurel, I. (2010). Matematik öğretmen adaylarının analiz dersi akademik başarıları ile matematiksel modelleme yaklaşımları arasındaki ilişki. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 29(1), 69-90.
  • Carr, W., and Kemmis, S. (2003). Becoming Critical: Education, Knowledge And Action Research. New York: RoutledgeFarmer, Taylor & Francis.
  • Çiltaş, A. ve Işık, A. (2013). The effect of instruction through mathematical modelling on modelling skills of prospective elementary mathematics teachers. Educational Sciences: Theory & Practice, 13(2), 1187-1192.,
  • Dede, A. T. (2017). Modelleme yeterlikleri ile sınıf düzeyi ve matematik başarısı arasındaki ilişkilerin incelenmesi. İlköğretim Online, 16(3), 1201-1219. doi: 10.17051/ilkonline.2017.330251
  • Dede, A. T. ve Yılmaz, S. (2013). İlköğretim matematik öğretmeni adaylarının modelleme yeterliliklerinin incelenmesi. Turkish Journal of Computer and Mathematics Education, 4(3), 185-206.
  • Doerr, H. M., and Tripp, J. S. (1999). Understanding how students develop mathematical models. Mathematical Thinking and Learning, 1(3), 231–254
  • Elliott, J. (1991). Action research for educational change. Philadelphia: Open University Press.
  • Frejd, P., and Ärlebäck, J. B. (2011). First results from a study investigating Swedish upper secondary students’mathematical modelling competencies. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 407–416). Springer: New York.
  • Galbraith, P., and Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM. 38(2), 143-162. doi: 10.1007/BF02655886.
  • Gatabi, A. R., and Abdolahpour, K. (2013). Investigating students’modeling competency through grade, gender, and location. In B. Ubuz, C. Haser and M. A. Mariotti (Eds.), Proceedings of the 8th congress of the european society for research in mathematics education CERME 8 (pp. 1070-1077). Turkey: Middle East Technical University.
  • Grünewald, S. (2012, July). Acquirement of modelling competencies – first results of an empirical comparison of the effectiveness of a holistic respectively an atomistic approach to the development of (metacognitive) modelling competencies of students. Paper presented at the meeting of the 12. International Congress on Mathematical Education. Korea: Seoul.
  • Güç, F. A. (2015). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi (Yayınlanmamış Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 381105)
  • Güç, F. A. ve Baki, A. (2016). Matematiksel modelleme yeterliklerini geliştirme ve değerlendirme yaklaşımlarının sınıflandırılması. Turkish Journal of Computer and Mathematics Education, 7(3), 621-645.
  • Ji, X. (2012, July). A quasi-experimental study of high school students’mathematics modelling competence. Paper presented at the meeting of the 12. International Congress on Mathematical Education. Korea: Seoul.
  • Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum and S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 110–119). Chichester: Horwood.
  • Kaiser, G., and Brand, S. (2015). Modelling competencies: Past development and further perspectives. In G. A. Stillman, W. Blum and M. S. Biembengut (Eds.), Mathematical modelling in education research and practice (pp. 129–149). Cham: Springer International Publishing.
  • Kaplan, T. (2011). Lineer denklem sistemleri ve uygulama alanları (Yüksek lisans tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 299752)
  • Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi (Yüksek lisans tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 221516)
  • Korkmaz, E. (2010). İlköğretim matematik ve sınıf öğretmeni adaylarının matematiksel modellemeye yönelik görüşleri ve matematiksel modelleme yeterlikleri (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 275237)
  • Lesh, R., and Doerr, H. M. (2003). Foundations of a models and modelling perspective on mathematics teaching, learning and problem solving. In R. Lesh and H. M. Doerr (Eds.), Beyond constructivism: models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 3-33). Mahwah N. J.:Lawrance Erlbaum Associates Publishers.
  • Lingefjärd, T. (2006). Faces of mathematical modelling. Zentralblatt Für Didactik Der Mathematic, 38(2), 96 -112. doi: 10.1007/BF02655884
  • Maaß, K. (2006). What are modelling competencies? Zentralblatt Für Didactik Der Mathematic, 38(2), 113-142. doi: 10.1007/BF0265588
  • Maaß, K. (2007). Modelling in class: What do we want the students to learn? In C. Haines, P. Galbraith, W. Blum and S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 63–78). Chichester: Horwood.
  • Miles, M.B and Huberman, A.M. (1994). Qualitative data analysis, Thousand Oaks, CA: Sage.
  • Niss, M., Blum, W., and Galbraith, P. (2007). How to replace the word problems. In W. Blum, P. Galbraith, H-W. Henn and M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). New York: Springer.
  • Schaap, S., Vos, P., and Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: Exploring a framework. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (ICTMA 14) (pp. 137-146). New York: Springer.
  • Swetz, F., and Hartzler, J. S. (1991). Mathematical Modelling İn The Secondary School Curriculum: A Resource Guide Of Classroom Exercises. Reston, VA: NCTM.
  • Türker, B., Sağlam, Y. ve Umay, A. (2010). Preservice teachers’performances at mathematical modeling process and views on mathematical modeling. Procedia Social and Behavioral Sciences, 2, 4622–4628. doi: 10.1016/j.sbspro.2010.03.740.
  • Yıldırım, A. ve Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (6. Baskı). Ankara: Seçkin.
  • Zawojewski, J. S., and Lesh, R. (2003). A models and modeling perspective on problem solving. In R. Lesh and H. M. Doerr (Ed.). Beyond constructivism: models and modelling perspectives on mathematics problem solving, learning and teaching (pp. 317-336). Mahwah N. J.:Lawrance Erlbaum Associates Publishers.
  • Zeytun, A. Ş. (2013). An investigation of prospective teachers’mathematical modelling processes and their views about factors affecting these processes (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 341056)
There are 42 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Zeynep Çakmak Gürel 0000-0003-0913-3291

Ahmet Işık 0000-0002-1599-2570

Publication Date March 28, 2022
Published in Issue Year 2022Volume: 11 Issue: 1

Cite

APA Çakmak Gürel, Z., & Işık, A. (2022). Kısmi Destekli Bütüncül Yaklaşıma Dayalı Uygulamaların Matematik Öğretmeni Adaylarının Modelleme Yeterliklerini Desteklemesi. Cumhuriyet Uluslararası Eğitim Dergisi, 11(1), 177-192. https://doi.org/10.30703/cije.978001
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