İlköğretim Matematik Öğretmen Adaylarının Matematiksel Modellemeye İlişkin Yeterliklerinin İncelenmesi
Öz
Bu araştırmada bütüncül yaklaşıma göre tasarlanan
matematiksel modellemeyi öğrenme ortamına katılan ve katılmayan ilköğretim
matematik öğretmen adaylarının matematiksel modellemeye ilişkin yeterliklerinin
incelenmesi amaçlanmıştır. Çalışmada nicel araştırma yöntemlerinden deneysel
desen kullanılmıştır. Araştırmanın örneklemini, tasarlanan öğrenme ortamına
katılan 35 ve katılmayan 32 olmak üzere toplamda 67 öğretmen adayı
oluşturmaktadır. Öğrenme ortamı bütüncül yaklaşıma göre oluşturulmuş ve
öğretmen adayları 12 hafta boyunca söz konusu öğrenme ortamına katılmışlardır.
Veriler, matematiksel modelleme ile ilgili 12 adet soru içeren çoktan seçmeli
çok cevaplı test yardımıyla toplanmıştır. Birinci alt probleme ilişkin
verilerin analizinde betimsel analiz kullanılırken, ikinci alt problemde tek
yönlü MANOVA kullanılmıştır. Yapılan veri analizinde, öğrenme ortamına katılan
öğretmen adayları ile katılmayan öğretmen adayları arasında
basitleştirme/yapılandırma, matematikselleştirme ve yorumlama yeterlikleri
açısından anlamlı farklılıklar olduğu tespit edilmiştir. Bu durum, tasarlanan
öğrenme ortamının öğretmen adaylarının matematiksel modelleme yeterlikleri
üzerinde olumlu bir etkisi olduğunu göstermektedir. Ayrıca oluşturulan öğrenme
ortamının yorumlama yeterliğini desteklediği görülse de etki düzeyinin diğer
yeterliklere göre düşük olduğu belirlenmiştir. Bu bulgulardan hareketle
matematiksel modellemeyi öğrenme ortamlarının tasarlanması modelleme
yeterliklerinin gelişimi açısından önemli olup; tasarlanan öğrenme ortamının da
geliştirilerek yorumlama yeterliğinin de önemli ölçüde öğretmen adaylarına
kazandırılması önerilmektedir.
Anahtar Kelimeler
Matematiksel modelleme modelleme yeterliliği Bütüncül yaklaşım
Kaynakça
- Biccard, P., & Wessels D. C. J. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. In G. Kaiser, W. Blum, R. B. Ferri & 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., & 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., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. Zentralblatt für Didaktik der Mathematik, 38(2), 163-177. doi: 10.1007/BF02655887.
- Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education - Discussion document. Educational Studies in Mathematics, 51, 149-171. doi: 10.1023/A:1022435827400
- Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1) 45-58.
- Brand, S. (2014). Effects of a holistic versus an atomistic modelling approach on students’ mathematical modelling competencies. In C. Nicol, P. Liljedahl, S. Oesterle, & 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.
- Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2013). Bilimsel araştırma yöntemleri (15. baskı). Ankara: Pegem.
- Çiltaş, A. (2011). Dizi ve seriler konusunun matematiksel modelleme yoluyla öğretiminin ilköğretim matematik öğretmeni adaylarının öğrenme ve modelleme becerileri üzerine etkisi (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 301126)
- 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
- Frejd, P., & 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 & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 407–416). Springer: New York.
- Fu, J., & Xie, J. (2013). Comparison of mathematical modelling skills of secondary and tertiary students. In G. A. Stillman, G. Kaiser, W.
- Blum & J. P. Brown (Eds.), Teaching mathematical modelling: connecting to research and practice. ınternational perspectives on the teaching and learning of mathematical modelling (pp. 165-173). New York: Springer. doi: 10.1007/978-94-007-6540-5_14.
- Galbraith, P., & 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., & Abdolahpour, K. (2013). Investigating students’ modeling competency through grade, gender, and location. In B. Ubuz, C.
- Haser & 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.
- Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modelling: approaches and developments from German speaking countries. ICME-13 Topical Surveys, 1-42, Switzerland: Springer International Publishing. doi: 10.1007/978-3-319-45004-9_1.
- 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.
- Grünewald, S. (2013). The development of modelling competencies by year 9 students: Effects of a modelling project. In G. A. Stillman, G.
- Kaiser, W. Blum & J. P. Brown (Eds.), Teaching mathematical modelling: connecting to research and practice: International perspectives on the teaching and learning of mathematical modelling (pp. 185-194). New York: Springer.
- Güç, F. A. (2015). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 381105)
- Güç, F. A., & Baki, A. (2016). Matematiksel modelleme yeterliklerini geliştirme ve değerlendirme yaklaşımlarının sınıflandırılması. Turkish Journal of Computer and Mathematics Education, 7(3), 621-645.
- Haines C. R., Crouch, R. & Davis, J. (2001). Understanding Students' Modelling Skills. In J. Matos, W. Blum, K. Houston & S. Carreira (Eds.), Modelling and mathematics education, ICTMA 9: Applications in science and technology (pp. 366-380). Chichester: Horwood Publishing.
- Houston, K. (2007). Assessing the "phases" of mathematical modelling. In W. Blum, P.L. Galbraith, H. W. Henn & M. Niss (Eds.), Modeling and applications in mathematics education (ICMI 14) (pp. 249–256). New York: Springer.
- Huang, C. H. (2011). Assessing the modelling competencies of engineering students. World Transactions on Engineering and Technology Education, 9(3), 172-177.
- 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 & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 110–119). Chichester: Horwood.
- Kaiser, G., & Brand, S. (2015). Modelling competencies: Past development and further perspectives. In G. A. Stillman, W. Blum & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice (pp. 129–149). Cham: Springer International Publishing.
- Kalaycı, Ş. (2010). SPSS uygulamalı çok değişkenli istatistik teknikleri (5. bs.). Ankara: Asil Yayın Dağıtım.
- 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)
- Lingefjärd, T. (2004). Assessing engineering student’s modeling skills. Retrieved from http://wvvw.cdio.org/files/document/file/assess_model_skls.pdf
- 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/BF02655885
- Pallant, J. (2015). SPSS survival manual a step by step guide to data analysis using IBM SPSS (6. Ed.). USA: Open University Press.
- Tabachnick, B. G. & Fidell, L.S. (2007). Using multivariate statistics (5. Ed.). Boston: Pearson Education.
- Tabachnick, B. G. & Fidell, L.S. (2013). Using multivariate statistics (6. Ed.). Boston: Pearson Education.
- Taşpınar, M. (2017). Sosyal bilimlerde SPSS uygulamalı nicel veri analizi (1. Bs). Ankara: Pegem Akademi
- 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, 4622–4628. doi: 10.1016/j.sbspro.2010.03.740.
Investigation of the Competences of Pre-Service Secondary School Mathematics Teachers Related to the Mathematical Modelling
Öz
In this research, it
was aimed to investigate the mathematical modelling competences of the
pre-service secondary school mathematics teachers who included and not included
in the mathematical modelling designed according to the holistic approach in
the learning environment. Among the quantitative research methods, the
experimental pattern was employed in the research. The sampling of the research
consisted of totally 67 pre-service teachers-35 of whom included and 32 not
included in the learning environment. The learning environment was created
considering the holistic approach and the pre-service teachers attended to this
learning environment throughout 12 weeks. Data, were collected with
multiple-answer multiple choice test including 12 mathematical modelling
questions. The descriptive analysis was used in the analysis of data related to
the first sub-problem; on the other hand, the one-way MANOVA was used for the
second sub-problem. In the data analysis, meaningful differences were found
between the pre-service teacher included in the learning environment and those
not included in terms of the competences of simplifying/structuring,
mathematizing and interpretation. This case demonstrates that the designed
learning environment has positive effect on the mathematical modelling
competences of the pre-service teachers. In addition, although the created
learning environment was realized to support the interpretation competence, its
effect level was determined to be low compared with the other competences.
Considering these results, the designing mathematical modelling learning
environments are significant in terms of the development of the modelling
competences; in addition, it is recommended that the pre-service teachers
should substantially gain the interpretation competence by developing the
designed learning environment.
Anahtar Kelimeler
Mathematical modelling modelling competence Holistic approach
Kaynakça
- Biccard, P., & Wessels D. C. J. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. In G. Kaiser, W. Blum, R. B. Ferri & 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., & 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., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. Zentralblatt für Didaktik der Mathematik, 38(2), 163-177. doi: 10.1007/BF02655887.
- Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education - Discussion document. Educational Studies in Mathematics, 51, 149-171. doi: 10.1023/A:1022435827400
- Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1) 45-58.
- Brand, S. (2014). Effects of a holistic versus an atomistic modelling approach on students’ mathematical modelling competencies. In C. Nicol, P. Liljedahl, S. Oesterle, & 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.
- Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2013). Bilimsel araştırma yöntemleri (15. baskı). Ankara: Pegem.
- Çiltaş, A. (2011). Dizi ve seriler konusunun matematiksel modelleme yoluyla öğretiminin ilköğretim matematik öğretmeni adaylarının öğrenme ve modelleme becerileri üzerine etkisi (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 301126)
- 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
- Frejd, P., & 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 & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 407–416). Springer: New York.
- Fu, J., & Xie, J. (2013). Comparison of mathematical modelling skills of secondary and tertiary students. In G. A. Stillman, G. Kaiser, W.
- Blum & J. P. Brown (Eds.), Teaching mathematical modelling: connecting to research and practice. ınternational perspectives on the teaching and learning of mathematical modelling (pp. 165-173). New York: Springer. doi: 10.1007/978-94-007-6540-5_14.
- Galbraith, P., & 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., & Abdolahpour, K. (2013). Investigating students’ modeling competency through grade, gender, and location. In B. Ubuz, C.
- Haser & 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.
- Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modelling: approaches and developments from German speaking countries. ICME-13 Topical Surveys, 1-42, Switzerland: Springer International Publishing. doi: 10.1007/978-3-319-45004-9_1.
- 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.
- Grünewald, S. (2013). The development of modelling competencies by year 9 students: Effects of a modelling project. In G. A. Stillman, G.
- Kaiser, W. Blum & J. P. Brown (Eds.), Teaching mathematical modelling: connecting to research and practice: International perspectives on the teaching and learning of mathematical modelling (pp. 185-194). New York: Springer.
- Güç, F. A. (2015). Matematiksel modelleme yeterliklerinin geliştirilmesine yönelik tasarlanan öğrenme ortamlarında öğretmen adaylarının matematiksel modelleme yeterliklerinin değerlendirilmesi (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi’nden edinilmiştir. (Tez No. 381105)
- Güç, F. A., & Baki, A. (2016). Matematiksel modelleme yeterliklerini geliştirme ve değerlendirme yaklaşımlarının sınıflandırılması. Turkish Journal of Computer and Mathematics Education, 7(3), 621-645.
- Haines C. R., Crouch, R. & Davis, J. (2001). Understanding Students' Modelling Skills. In J. Matos, W. Blum, K. Houston & S. Carreira (Eds.), Modelling and mathematics education, ICTMA 9: Applications in science and technology (pp. 366-380). Chichester: Horwood Publishing.
- Houston, K. (2007). Assessing the "phases" of mathematical modelling. In W. Blum, P.L. Galbraith, H. W. Henn & M. Niss (Eds.), Modeling and applications in mathematics education (ICMI 14) (pp. 249–256). New York: Springer.
- Huang, C. H. (2011). Assessing the modelling competencies of engineering students. World Transactions on Engineering and Technology Education, 9(3), 172-177.
- 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 & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 110–119). Chichester: Horwood.
- Kaiser, G., & Brand, S. (2015). Modelling competencies: Past development and further perspectives. In G. A. Stillman, W. Blum & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice (pp. 129–149). Cham: Springer International Publishing.
- Kalaycı, Ş. (2010). SPSS uygulamalı çok değişkenli istatistik teknikleri (5. bs.). Ankara: Asil Yayın Dağıtım.
- 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)
- Lingefjärd, T. (2004). Assessing engineering student’s modeling skills. Retrieved from http://wvvw.cdio.org/files/document/file/assess_model_skls.pdf
- 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/BF02655885
- Pallant, J. (2015). SPSS survival manual a step by step guide to data analysis using IBM SPSS (6. Ed.). USA: Open University Press.
- Tabachnick, B. G. & Fidell, L.S. (2007). Using multivariate statistics (5. Ed.). Boston: Pearson Education.
- Tabachnick, B. G. & Fidell, L.S. (2013). Using multivariate statistics (6. Ed.). Boston: Pearson Education.
- Taşpınar, M. (2017). Sosyal bilimlerde SPSS uygulamalı nicel veri analizi (1. Bs). Ankara: Pegem Akademi
- 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, 4622–4628. doi: 10.1016/j.sbspro.2010.03.740.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Eğitim Üzerine Çalışmalar |
| Bölüm | Eğitim Bilimleri ve Alan Eğitimi Bilimleri |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Aralık 2018 |
| Yayımlandığı Sayı | Yıl 2018 |
Cited By
İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Modelleme Süreçleri: Su İsrafı Örneği
Yuzunci Yil Universitesi Egitim Fakultesi Dergisi
https://doi.org/10.33711/yyuefd.1177845
[email protected] http://www.e-ijer.com Adres: Ege Üniversitesi Eğitim Fakültesi Bornova/İzmir