Araştırma Makalesi
PDF Zotero Mendeley EndNote BibTex Kaynak Göster

Matematiksel Modelleme Eğitiminin İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Modellemenin Doğasına İlişkin Bilgilerine Katkısı: Bir Eylem Araştırması

Yıl 2021, Cilt 6, Sayı 1, 124 - 145, 25.06.2021

Öz

Matematiksel modelleme gerçek yaşamla matematik arasındaki ilişkileri kurmada öne çıkan araştırma alanlarından biridir. Öğrencilerin matematiksel dünya ile gerçek dünya arasında geçiş yapmalarına olanak sağlayacak öğrenme ortamlarına girmeleri için geleceğin öğretmenlerinin matematiksel modelleme ile ilgili yetkinlik kazanmaları gerekir. Öğretmen adayları, uygulamadan önce matematiksel model ve modellemenin doğasına ilişkin temel bilgilere hâkim olmalıdır. Bu bağlamda eylem araştırması kapsamında bir teorik eğitim planı hazırlanmış ve on dokuzu pilot uygulamada, yirmi biri asıl uygulamada olmak üzere kırk ilköğretim matematik öğretmeni adayı ile çalışma yürütülmüştür. Veriler açık uçlu anket, gözlem ve eğitim sürecindeki video kayıtlar aracılığıyla toplanarak içerik analizine tabi tutulmuştur. Katılımcıların eğitim süreci öncesinde model ve modelleme kavramlarına ilişkin somut öğretim materyali, maket ve rol model gibi algılara sahip olduğu görülürken; eğitim süreci sonunda literatürde yer alan matematiksel model ve modelleme kavramlarının tanımlarına yakın cevaplar verdikleri tespit edilmiştir. Çalışmada yürütülen eğitim sürecinin öğretmen adaylarının matematiksel modellemenin doğasına ilişkin bilgilerini geliştirmelerine olanak sağladığı sonucuna ulaşılmıştır.

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. https://doi.org/10.1007/978-94-007-6271-8_43
  • Akgün, L., Çiltaş, A., Deniz, D., Çiftçi Z., & Işık, A. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 6(12), 1-34.
  • Ang, K.C. (2006). Mathematical modelling, technology and H3 mathematics. The Mathematics Educator, 9(2), 33-47.
  • Anhalt, C.O., & Cortez, R. (2015). Developing understanding of mathematical modeling in secondary teacher preparation. J Math Teacher Educ, 19, 523–545. https://doi.org/10.1007/s10857-015-9309-8
  • Aydın 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. https://doi.org/10.1093/teamat/hry002
  • Aztekin, S., & Taşpınar Şener, Z. (2015). Türkiye’de Matematik Eğitimi Alanındaki Matematiksel Modelleme Araştırmalarının İçerik Analizi: Bir Meta-Sentez Çalışması. Eğitim ve Bilim, 179(40), 139-161. http://dx.doi.org/10.15390/EB.2015.4125
  • Berry, J. (2002). Developing mathematical modelling skills: the role of CAS. Zentralblatt für Didaktik der Nathematik-ZDM, 34(5), 212-220.
  • Berry, J. S., & Houston, S. K. (1995). Mathematical modelling. London: Edward Arnold.
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. Zentralblatt für Didaktik der Mathematik-ZDM, 38(2), 163-177.
  • Blum, W. (1993). Mathematical modelling in mathematics education and instruction. In T. Breiteig, I. Huntley & G. Kaiser-Messmer (Eds.), Teaching and learning mathematics in context (pp. 3-14). New York: Ellis Horwood.
  • 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 students and 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). Chichester: Horwood Publishing.
  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM, 38(2), 86-95.
  • Borromeo Ferri, R. (2018). Learning How to Teach Mathematical Modeling in School and Teacher Education. Cham: Springer.
  • Cetinkaya, B., Kertil, M., Erbas, A. K., Korkmaz, H., Alacaci, C., & Cakiroglu, E. (2016). Pre-service teachers’ developing conceptions about the nature and pedagogy of mathematical modeling in the context of a mathematical modeling course. Mathematical Thinking and Learning, 18(4), 287-314. https://doi.org/10.1080/10986065.2016.1219932
  • Chamberlin, 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.
  • Chang, Y. P., Krawitz, J., Schukajlow, S., & Yang, K. L. (2019). Comparing German and Taiwanese secondary school students’ knowledge in solving mathematical modelling tasks requiring their assumptions. ZDM Mathematics Education, 52, 59-72. https://doi.org/10.1007/s11858-019-01090-4
  • Cohen, L., Manion, L., & Morrison, K., (2007). Research Methods in Education, Research methods in education (Sixth Edition). London: Routledge.
  • Common Core State Standards Initiative (CCSSI) (2010). Common Core State Standards for Mathematics.Washington, DC: National Governors Association Center for Best Practices and the Council of ChiefState School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf
  • Çiltaş, A., & 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.
  • Deniz, D., & Akgün, L. (2016). Ortaöğretim Matematik Öğretmenlerinin Model Oluşturma Etkinliği Tasarım Prensiplerine Uygun Etkinlik Tasarlayabilme Yeterlikleri. Karaelmas Journal of Educational Sciences, 4, 1-14.
  • Deniz, D., & Akgün, L. (2017). Ortaöğretim matematik öğretmenlerinin matematiksel modelleme yöntemi ve uygulamalarına yönelik görüşleri. Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi, 5(1), 95-117. http://doi.org/10.18506/anemon.272677
  • Doerr, H., & English, L. (2006). Middle Grade Teachers’ Learning through Students’ Engagement with Modeling Tasks. Journal of Mathematics Teacher Education, 9(1), 5–32. http://doi.org/10.1007/s10857-006-9004-x
  • Durandt, R., & Jacobs, G. J. (2017). Mathematical modelling strategies and attitudes of third year pre-service teachers. In G. A. Stillman, W. Blum & G. Kaiser (Eds.), Mathematical modelling and applications: Crossing and researchng boundaries in mathematics education (pp. 243–254). New York: Springer.
  • English, L. D., Fox, J. L., & Watters, J. J. (2005). Problem posing and solving with mathematical modeling. Teaching Children Mathematics, 12(3), 156–163. https://doi.org/10.5951/TCM.12.3.0156
  • Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Matematik Eğitiminde Matematiksel Modelleme: Temel Kavramlar ve Farklı Yaklaşımlar. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1607-1627. https://doi.org/10.12738/estp.2014.4.2039
  • Ferrance, E. (2000). Action research. Providence, RI: Northeast and Islands Regional Education Laboratory.
  • Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155–177.
  • Gravemeijer, K. (2002). Preamble: From models to modeling. In K. Gravemeijer, R. Lehrer, B. Oers, ve L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 7-22). Dordrecht: Kluwer Academic Publish.
  • Johnson, A. P. (2012). A short guide to action research (4th ed.). New Jersey: Pearson Education.
  • Julie, C. (2002). Making relevance in mathematics teacher education. In I. Vakalis, D. Hughes Hallett, D. Quinney ve C. Kourouniotis (Compilers). Proceedings of 2nd International Conference on the Teaching of Mathematics. New York: Wiley.
  • Julie, C. (2020). Modelling competencies of school learners in the beginning and final year of secondary school mathematics. International Journal of Mathematical Education in Science and Technology, 51(8), 1181-1195. https://doi.org/10.1080/0020739X.2020.1725165
  • Jung, H., Stehr, E. M., & He, J. (2019). Mathematical modeling opportunities reported by secondary mathematics preservice teachers and instructors. School Sience and Mathematics, 119(6), 353-365. https://doi.org/10.1111/ssm.12359
  • Kaiser, G., & Maaß, K. (2007). Modelling in Lower Secondary Mathematics Classroom — Problems and Opportunities. In: Blum, W., Galbraith, P.L., Henn, HW. & Niss M. (Eds), Modelling and Applications in Mathematics Education New ICMI Study Series, vol 10 (pp. 99-108). Boston MA: Springer. https://doi.org/10.1007/978-0-387-29822-1
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310.
  • Karalı, D., & Durmuş, S. (2015). Primary school pre-service mathematics teachers’ views on mathematical modeling. Eurasia Journal of Mathematics, Science & Technology Education, 11(4), 803– 815. https://doi.org/10.12973/eurasia.2015.1440a
  • Kemmis, S., & McTaggart, R. (2005). Communicative action and public sphere. In N. K. Denzin & Y. S. Lincoln (Eds.), The Sage handbook of qualitative research (pp. 559–603). Thousand Oaks, CA: Sage.
  • Korkmaz, H. (2014). An ınvestıgatıon of prospectıve secondary mathematıcs teachers’ thınkıng about mathematıcal modelıng and pedagogy of modelıng throughout a modelıng course. Yayımlanmamış Doktora Tezi: Ortadoğu Teknik Üniversitesi.
  • Köklü, N. (2001). Eğitim eylem araştırması-öğretmen araştırması. Anakara Üniversitesi Eğitim Bilimleri Fakültesi Dergisi, 34(1), 35-43. https://doi.org/10.1501/Egifak_0000000040
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modelling perspective on mathematics teaching, learning and problem solving. In R. Lesh & 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.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. Lesh & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591-645). Hillsdale, NJ: Lawrence Erlbaum.
  • Lingefjärd, T. (2007). Mathematical modelling in teacher education – necessity or unnecessarily. In W. Blum, P. Galbraith, H. Henn, and M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 333-340). New York: Springer.
  • Maaß, K. (2006). What are modelling competencies? The International Journal on Mathematics Education, 38(2), 113-142.
  • Maaß, K. (2010). Classification scheme for modelling tasks. J Math Didakt, 31, 285-311.
  • McKernan, J. (2008). Curriculum and imagination: Process theory, pedagogy and action research. London: Routledge.
  • McTaggart, R. (1997). Participatory action research: International contexts and consequences. Albany: State University of New York Press.
  • MEB, (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: MEB Talim Terbiye Kurulu Başkanlığı.
  • Merrill, S. J. (2003). Solving problems: Perchance to dream. In S. J. Lamon, W.A. Parker, & S. K. Houston (Eds.), Mathematical modelling: A way of life (pp. 97—105). Chichester: Horwood.
  • Mertler, C. A. (2016). Action Research Improving Schools and Empowering Educators (Fifth Edition). Thousand Oaks, California: SAGE Publications.
  • NCTM (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical competencies (pp. 43-59). New York: Springer.
  • Niss, M., Blum, W., & Galbraith, P. (2007). How to replace the word problems. In W. Blum, P. Galbraith, H-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). New York: Springer.
  • Oliveira, A. M. P., & Barbosa, J. C. (2009). The teachers’ tensions in mathematical modelling practice. In Blomhøj, M. & Carreira, S. (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics : 461. Proceedings from Topic Study Group 21 at the 11th International Congress on Mathematics Education (pp. 61–71).
  • Oliveira, A. M. P., & Barbosa, J.C. (2013). Mathematical modelling, mathematical content and tensions in discourses. In Stillman, G. A., Kaiser, G., Blum, W. & Brown J. P. (Eds.), Teaching Mathematical Modelling: Connecting to Research and Practice, International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 67 – 76). Dordrecht: Springer.
  • Özdemir, E. (2014). Matematik eğitiminde modelleme üzerine öğrenme-öğretme uygulamaları. Yayımlanmamış Doktora Tezi: Balıkesir Üniversitesi Fen Bilimleri Enstitüsü.
  • Özturan Sağırlı, M. (2010). Türev konusunda matematiksel modelleme yönteminin ortaöğretim öğrencilerinin akademik başarıları ve öz-düzenleme becerilerine etkisi. Yayımlanmamış Doktora Tezi. Atatürk Üniversitesi Eğitim Bilimleri Enstitüsü. Patton, M. Q. (2002). Qualitative research & evaluation methods (3rd ed.). Thousand Oaks, CA: Sage.
  • Sevinc, S., & Lesh, R. (2017). Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses. ZDM, 50, 301–314. https://doi.org/10.1007/s11858-017-0898-9
  • Simon, L. H., & Cox, D. C. (2019). The role of prototyping in mathematical design thinking. The Journal of Mathematical Behavior, 56, 100724. https://doi.org/10.1016/j.jmathb.2019.100724
  • Sriraman, B. (2006). Conceptualizing the model-eliciting perspective of mathematical problem solving. In M. Bosch (Ed.), Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (CERME 4) (pp. 1686-1695). Sant Feliu de Guíxols, Spain: FUNDEMI IQS, Universitat Ramon Llull.
  • Steen, L. A. (1999). Twenty question about mathematical reasoning. In L. V. Stiff, F. R. Curcio. (Ed.), Developing mathematical reasoning in grades K-12. 1999 yearbook (pp. 270-285). Reston, VA: National Council of Teachers of Mathematics.
  • Stillman, G.A. (2015). Applications and modelling research in secondary classrooms: What have we learnt?. In Cho, S. (Eds), Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 791-805). Cham: Springer. https://doi.org/10.1007/978-3-319-17187-6_44
  • Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in ımplementing mathematical modelling in the secondary classroom. In J. Watson & K. Beswick, (Eds.). Mathematics: Essential research, essential practice (pp. 691-700). Australia: Merga.
  • Superfine, A. C., & Wagreich, P. (2010). Developing mathematics knowledge for teaching in a content course: A “Design Experiment” involving mathematics educators and mathematicians. In D. Mewborn (Eds.), Scholarly practices and inquiry in the preparation of mathematics teachers (pp. 15–27). San Diego, CA: Association of Mathematics Teacher Educators.
  • Şahin, N., & Eraslan, A. (2016). İlkokul öğrencilerinin modelleme süreçleri: Suç problemi. Eğitim ve Bilim, 41(183), 47-67. http://dx.doi.org/10.15390/EB.2016.6011
  • Taşpınar Şener, Z. (2017). Ortaokul matematik öğretmen adaylarının tasarladıkları model oluşturma etkinliklerinin incelenmesi ve bu etkinliklerin öğretim sürecinde kullanımlarına ilişkin görüşleri. Yayımlanmamış Doktora Tezi: Gazi Üniversitesi Eğitim Bilimleri Enstitüsü.
  • TDK (2018). Türk Dil Kurumu. Erişim adresi: https://sozluk.gov.tr/
  • 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.
  • Wagner, T. (2008). Rigor redefined. Educational Leadership, 66(2), 20-24.
  • Weber, R. P. (1990). Basic content analysis. Beverly Hills, CA: Sage.
  • Zawojewski, J. (2010). Problem solving versus modeling. In R. Lesh, P. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 237-244). New

The Contribution of Mathematical Modeling Course to Pre-service Mathematics Teachers’ Knowledge about the Nature of Mathematical Modeling: An Action Research

Yıl 2021, Cilt 6, Sayı 1, 124 - 145, 25.06.2021

Öz

Mathematical modeling is the one of the prominent research areas in establishing connections between real life and mathematics. Future teachers need to be competent about mathematical modeling so that their students experience the learning environments that enable them to move between mathematical world and real-world. Before practicing, pre-service teachers ought to have a grasp of basic knowledge about nature of mathematical modeling. In this context, a theoretical program was developed within the scope of action research and forty pre-service secondary mathematics teachers, nineteen of them in the pilot study and twenty one of them in the main study, participated to the study. Data was collected through open-ended questionnaire, observation notes and video recordings and analyzed by content analysis. While it was found that the participants had perceptions about model and modeling concepts relating to concrete teaching materials, mock-up and role model at the beginning of the study; it was reached that their answers were close to the definitions of mathematical model and modeling concepts in the literature at the end of the study. It was concluded that the program carried out in the study enabled pre-service teachers to enhance their knowledge about the nature of mathematical modeling.

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. https://doi.org/10.1007/978-94-007-6271-8_43
  • Akgün, L., Çiltaş, A., Deniz, D., Çiftçi Z., & Işık, A. (2013). İlköğretim matematik öğretmenlerinin matematiksel modelleme ile ilgili farkındalıkları. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 6(12), 1-34.
  • Ang, K.C. (2006). Mathematical modelling, technology and H3 mathematics. The Mathematics Educator, 9(2), 33-47.
  • Anhalt, C.O., & Cortez, R. (2015). Developing understanding of mathematical modeling in secondary teacher preparation. J Math Teacher Educ, 19, 523–545. https://doi.org/10.1007/s10857-015-9309-8
  • Aydın 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. https://doi.org/10.1093/teamat/hry002
  • Aztekin, S., & Taşpınar Şener, Z. (2015). Türkiye’de Matematik Eğitimi Alanındaki Matematiksel Modelleme Araştırmalarının İçerik Analizi: Bir Meta-Sentez Çalışması. Eğitim ve Bilim, 179(40), 139-161. http://dx.doi.org/10.15390/EB.2015.4125
  • Berry, J. (2002). Developing mathematical modelling skills: the role of CAS. Zentralblatt für Didaktik der Nathematik-ZDM, 34(5), 212-220.
  • Berry, J. S., & Houston, S. K. (1995). Mathematical modelling. London: Edward Arnold.
  • Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. Zentralblatt für Didaktik der Mathematik-ZDM, 38(2), 163-177.
  • Blum, W. (1993). Mathematical modelling in mathematics education and instruction. In T. Breiteig, I. Huntley & G. Kaiser-Messmer (Eds.), Teaching and learning mathematics in context (pp. 3-14). New York: Ellis Horwood.
  • 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 students and 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). Chichester: Horwood Publishing.
  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM, 38(2), 86-95.
  • Borromeo Ferri, R. (2018). Learning How to Teach Mathematical Modeling in School and Teacher Education. Cham: Springer.
  • Cetinkaya, B., Kertil, M., Erbas, A. K., Korkmaz, H., Alacaci, C., & Cakiroglu, E. (2016). Pre-service teachers’ developing conceptions about the nature and pedagogy of mathematical modeling in the context of a mathematical modeling course. Mathematical Thinking and Learning, 18(4), 287-314. https://doi.org/10.1080/10986065.2016.1219932
  • Chamberlin, 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.
  • Chang, Y. P., Krawitz, J., Schukajlow, S., & Yang, K. L. (2019). Comparing German and Taiwanese secondary school students’ knowledge in solving mathematical modelling tasks requiring their assumptions. ZDM Mathematics Education, 52, 59-72. https://doi.org/10.1007/s11858-019-01090-4
  • Cohen, L., Manion, L., & Morrison, K., (2007). Research Methods in Education, Research methods in education (Sixth Edition). London: Routledge.
  • Common Core State Standards Initiative (CCSSI) (2010). Common Core State Standards for Mathematics.Washington, DC: National Governors Association Center for Best Practices and the Council of ChiefState School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf
  • Çiltaş, A., & 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.
  • Deniz, D., & Akgün, L. (2016). Ortaöğretim Matematik Öğretmenlerinin Model Oluşturma Etkinliği Tasarım Prensiplerine Uygun Etkinlik Tasarlayabilme Yeterlikleri. Karaelmas Journal of Educational Sciences, 4, 1-14.
  • Deniz, D., & Akgün, L. (2017). Ortaöğretim matematik öğretmenlerinin matematiksel modelleme yöntemi ve uygulamalarına yönelik görüşleri. Muş Alparslan Üniversitesi Sosyal Bilimler Dergisi, 5(1), 95-117. http://doi.org/10.18506/anemon.272677
  • Doerr, H., & English, L. (2006). Middle Grade Teachers’ Learning through Students’ Engagement with Modeling Tasks. Journal of Mathematics Teacher Education, 9(1), 5–32. http://doi.org/10.1007/s10857-006-9004-x
  • Durandt, R., & Jacobs, G. J. (2017). Mathematical modelling strategies and attitudes of third year pre-service teachers. In G. A. Stillman, W. Blum & G. Kaiser (Eds.), Mathematical modelling and applications: Crossing and researchng boundaries in mathematics education (pp. 243–254). New York: Springer.
  • English, L. D., Fox, J. L., & Watters, J. J. (2005). Problem posing and solving with mathematical modeling. Teaching Children Mathematics, 12(3), 156–163. https://doi.org/10.5951/TCM.12.3.0156
  • Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Matematik Eğitiminde Matematiksel Modelleme: Temel Kavramlar ve Farklı Yaklaşımlar. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1607-1627. https://doi.org/10.12738/estp.2014.4.2039
  • Ferrance, E. (2000). Action research. Providence, RI: Northeast and Islands Regional Education Laboratory.
  • Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155–177.
  • Gravemeijer, K. (2002). Preamble: From models to modeling. In K. Gravemeijer, R. Lehrer, B. Oers, ve L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 7-22). Dordrecht: Kluwer Academic Publish.
  • Johnson, A. P. (2012). A short guide to action research (4th ed.). New Jersey: Pearson Education.
  • Julie, C. (2002). Making relevance in mathematics teacher education. In I. Vakalis, D. Hughes Hallett, D. Quinney ve C. Kourouniotis (Compilers). Proceedings of 2nd International Conference on the Teaching of Mathematics. New York: Wiley.
  • Julie, C. (2020). Modelling competencies of school learners in the beginning and final year of secondary school mathematics. International Journal of Mathematical Education in Science and Technology, 51(8), 1181-1195. https://doi.org/10.1080/0020739X.2020.1725165
  • Jung, H., Stehr, E. M., & He, J. (2019). Mathematical modeling opportunities reported by secondary mathematics preservice teachers and instructors. School Sience and Mathematics, 119(6), 353-365. https://doi.org/10.1111/ssm.12359
  • Kaiser, G., & Maaß, K. (2007). Modelling in Lower Secondary Mathematics Classroom — Problems and Opportunities. In: Blum, W., Galbraith, P.L., Henn, HW. & Niss M. (Eds), Modelling and Applications in Mathematics Education New ICMI Study Series, vol 10 (pp. 99-108). Boston MA: Springer. https://doi.org/10.1007/978-0-387-29822-1
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310.
  • Karalı, D., & Durmuş, S. (2015). Primary school pre-service mathematics teachers’ views on mathematical modeling. Eurasia Journal of Mathematics, Science & Technology Education, 11(4), 803– 815. https://doi.org/10.12973/eurasia.2015.1440a
  • Kemmis, S., & McTaggart, R. (2005). Communicative action and public sphere. In N. K. Denzin & Y. S. Lincoln (Eds.), The Sage handbook of qualitative research (pp. 559–603). Thousand Oaks, CA: Sage.
  • Korkmaz, H. (2014). An ınvestıgatıon of prospectıve secondary mathematıcs teachers’ thınkıng about mathematıcal modelıng and pedagogy of modelıng throughout a modelıng course. Yayımlanmamış Doktora Tezi: Ortadoğu Teknik Üniversitesi.
  • Köklü, N. (2001). Eğitim eylem araştırması-öğretmen araştırması. Anakara Üniversitesi Eğitim Bilimleri Fakültesi Dergisi, 34(1), 35-43. https://doi.org/10.1501/Egifak_0000000040
  • Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modelling perspective on mathematics teaching, learning and problem solving. In R. Lesh & 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.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. Lesh & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591-645). Hillsdale, NJ: Lawrence Erlbaum.
  • Lingefjärd, T. (2007). Mathematical modelling in teacher education – necessity or unnecessarily. In W. Blum, P. Galbraith, H. Henn, and M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 333-340). New York: Springer.
  • Maaß, K. (2006). What are modelling competencies? The International Journal on Mathematics Education, 38(2), 113-142.
  • Maaß, K. (2010). Classification scheme for modelling tasks. J Math Didakt, 31, 285-311.
  • McKernan, J. (2008). Curriculum and imagination: Process theory, pedagogy and action research. London: Routledge.
  • McTaggart, R. (1997). Participatory action research: International contexts and consequences. Albany: State University of New York Press.
  • MEB, (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: MEB Talim Terbiye Kurulu Başkanlığı.
  • Merrill, S. J. (2003). Solving problems: Perchance to dream. In S. J. Lamon, W.A. Parker, & S. K. Houston (Eds.), Mathematical modelling: A way of life (pp. 97—105). Chichester: Horwood.
  • Mertler, C. A. (2016). Action Research Improving Schools and Empowering Educators (Fifth Edition). Thousand Oaks, California: SAGE Publications.
  • NCTM (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical competencies (pp. 43-59). New York: Springer.
  • Niss, M., Blum, W., & Galbraith, P. (2007). How to replace the word problems. In W. Blum, P. Galbraith, H-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). New York: Springer.
  • Oliveira, A. M. P., & Barbosa, J. C. (2009). The teachers’ tensions in mathematical modelling practice. In Blomhøj, M. & Carreira, S. (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics : 461. Proceedings from Topic Study Group 21 at the 11th International Congress on Mathematics Education (pp. 61–71).
  • Oliveira, A. M. P., & Barbosa, J.C. (2013). Mathematical modelling, mathematical content and tensions in discourses. In Stillman, G. A., Kaiser, G., Blum, W. & Brown J. P. (Eds.), Teaching Mathematical Modelling: Connecting to Research and Practice, International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 67 – 76). Dordrecht: Springer.
  • Özdemir, E. (2014). Matematik eğitiminde modelleme üzerine öğrenme-öğretme uygulamaları. Yayımlanmamış Doktora Tezi: Balıkesir Üniversitesi Fen Bilimleri Enstitüsü.
  • Özturan Sağırlı, M. (2010). Türev konusunda matematiksel modelleme yönteminin ortaöğretim öğrencilerinin akademik başarıları ve öz-düzenleme becerilerine etkisi. Yayımlanmamış Doktora Tezi. Atatürk Üniversitesi Eğitim Bilimleri Enstitüsü. Patton, M. Q. (2002). Qualitative research & evaluation methods (3rd ed.). Thousand Oaks, CA: Sage.
  • Sevinc, S., & Lesh, R. (2017). Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses. ZDM, 50, 301–314. https://doi.org/10.1007/s11858-017-0898-9
  • Simon, L. H., & Cox, D. C. (2019). The role of prototyping in mathematical design thinking. The Journal of Mathematical Behavior, 56, 100724. https://doi.org/10.1016/j.jmathb.2019.100724
  • Sriraman, B. (2006). Conceptualizing the model-eliciting perspective of mathematical problem solving. In M. Bosch (Ed.), Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (CERME 4) (pp. 1686-1695). Sant Feliu de Guíxols, Spain: FUNDEMI IQS, Universitat Ramon Llull.
  • Steen, L. A. (1999). Twenty question about mathematical reasoning. In L. V. Stiff, F. R. Curcio. (Ed.), Developing mathematical reasoning in grades K-12. 1999 yearbook (pp. 270-285). Reston, VA: National Council of Teachers of Mathematics.
  • Stillman, G.A. (2015). Applications and modelling research in secondary classrooms: What have we learnt?. In Cho, S. (Eds), Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 791-805). Cham: Springer. https://doi.org/10.1007/978-3-319-17187-6_44
  • Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in ımplementing mathematical modelling in the secondary classroom. In J. Watson & K. Beswick, (Eds.). Mathematics: Essential research, essential practice (pp. 691-700). Australia: Merga.
  • Superfine, A. C., & Wagreich, P. (2010). Developing mathematics knowledge for teaching in a content course: A “Design Experiment” involving mathematics educators and mathematicians. In D. Mewborn (Eds.), Scholarly practices and inquiry in the preparation of mathematics teachers (pp. 15–27). San Diego, CA: Association of Mathematics Teacher Educators.
  • Şahin, N., & Eraslan, A. (2016). İlkokul öğrencilerinin modelleme süreçleri: Suç problemi. Eğitim ve Bilim, 41(183), 47-67. http://dx.doi.org/10.15390/EB.2016.6011
  • Taşpınar Şener, Z. (2017). Ortaokul matematik öğretmen adaylarının tasarladıkları model oluşturma etkinliklerinin incelenmesi ve bu etkinliklerin öğretim sürecinde kullanımlarına ilişkin görüşleri. Yayımlanmamış Doktora Tezi: Gazi Üniversitesi Eğitim Bilimleri Enstitüsü.
  • TDK (2018). Türk Dil Kurumu. Erişim adresi: https://sozluk.gov.tr/
  • 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.
  • Wagner, T. (2008). Rigor redefined. Educational Leadership, 66(2), 20-24.
  • Weber, R. P. (1990). Basic content analysis. Beverly Hills, CA: Sage.
  • Zawojewski, J. (2010). Problem solving versus modeling. In R. Lesh, P. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 237-244). New

Ayrıntılar

Birincil Dil Türkçe
Konular Eğitim, Eğitim Araştırmaları
Bölüm Makaleler
Yazarlar

Muhammet ŞAHAL (Sorumlu Yazar)
Yildiz Technical University
0000-0003-3625-2456
Türkiye


Ahmet ÖZDEMİR
MARMARA ÜNİVERSİTESİ
0000-0002-0597-3093
Türkiye

Yayımlanma Tarihi 25 Haziran 2021
Yayınlandığı Sayı Yıl 2021, Cilt 6, Sayı 1

Kaynak Göster

APA Şahal, M. & Özdemir, A. (2021). Matematiksel Modelleme Eğitiminin İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Modellemenin Doğasına İlişkin Bilgilerine Katkısı: Bir Eylem Araştırması . Türkiye Eğitim Dergisi , 6 (1) , 124-145 . Retrieved from https://dergipark.org.tr/tr/pub/turkegitimdergisi/issue/62994/884742