The Compatibility of Model Eliciting Activities of Secondary School Teacher Candidates with Design Principles

Year 2020, , 305 - 322, 25.03.2020

Aysun Nüket Elçi

https://doi.org/10.18009/jcer.695253

Cited By: 1

Abstract

The purpose of this study is the investigation of the compatibility of model eliciting activities of secondary school teacher candidates with design principles. This study was conducted in the scope of Mathematical Modelling course with the students who were the secondary school mathematics teacher candidates. The participants of this case study were thirty-nine mathematics teacher candidates who worked in eight groups. The data of this study consisted of eight model eliciting activities which were created within the eight groups and their analysis. The activities created by the groups were analyzed by document analysis method in terms of design principles that were defined for model eliciting activities. It was concluded that the created model eliciting activities satisfied the construct share ability and reusability principle at minimum while they satisfied the reality principle at maximum. The effective prototype principle could not be determined. It can be ensured that the secondary school mathematics teacher candidates gain more experience by making more implementations related to model eliciting activities. The implementation of model eliciting activities in class can be effective in reducing the modelling deficiencies of secondary school mathematics teacher candidates.

Keywords

Mathematical modeling, model eliciting activities, the principles of model eliciting activities, secondary school mathematics teacher candidates

References

• Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education-Discussion document. Zentralblatt für Didaktik der Mathematik. 34(5), 229-239.
• Borromeo Ferri, R. (2007). Personal experiences and extra-mathematical knowledge as an influence factor on modelling routes of pupils. D. Pitta-Pantazi & G. Philippou (Eds), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 2080-2089). Larnaca: Zypern.
• Bukova-Güzel, E. (2011). An examination of pre-service mathematics teachers’ approaches to construct and solve mathematical modelling problems. Teaching Mathematics and Its Applications, 30, 19–36.
• Bukova-Güzel, E. (Ed.). (2016). Matematik eğitiminde matematiksel modelleme araştırmacılar, eğitimciler ve öğrenciler için [Mathematical modelling in mathematics education: for researchers, educators and students]. Ankara: Pegem Akademi Yayınları. [Pegem Akademi Publishing.]
• Bukova-Güzel, E., & Uğurel, I. (2010). Matematik öğretmen adaylarının analiz dersi akademik başarıları ile matematiksel modelleme yaklaşımları arasındaki ilişki [The relatinship between pre-service mathematics teachers’ academic achievements in calculus and their mathematical modelling approaches]. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 29(1), 69-90.
• Carlson, M., Larsen, S., & Lesh, R. (2003). Integrating models and modelling perspective with existing research and practice. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 465-478). Mahwah, NJ: Lawrence Erlbaum.
• Chamberlin, S. A., & Moon, S. (2005). Model-eliciting activities: an ıntroduction to gifted education. Journal of Secondary Gifted Education, 17, 37-47.
• Cheng, K. A. (2001). Teaching mathematical modelling in singapore schools. The Mathematics Educator, 6(1), 62-74.
• Creswell, J. W. (2013). Nitel araştırma yöntemleri, beş yaklaşıma göre nitel araştırma ve araştırma deseni [Qualitative Inquiry & Research Design Choosing Among Five Approaches]. Çev. Ed. Bütün M. & Demir, S. B. Ankara: Siyasal Kitabevi.
• Çepni, S. (2007). Araştırma ve proje çalışmalarına giriş [Introduction to research and project studies]. Trabzon: Celepler Matbaacılık [Celepler Printing].
• Deniz, D., & Akgün, L. (2016). Ortaöğretim matematik öğretmenlerinin model oluşturma etkinliği tasarım prensiplerine uygun etkinlik tasarlayabilme yeterlikleri [The sufficiency of high school mathematics teachers’ to design activities appropriate to model eliciting activities design principles]. Karaelmas Eğitim Bilimleri Dergisi, 4(1), 1-14.
• Deniz, D., & Akgün, L. (2018). İlköğretim matematik öğretmeni adaylarının matematiksel modelleme becerilerinin incelenmesi [Investigation of prospective secondary mathematics teachers’ mathematical modellling skills]. Akdeniz Eğitim Araştırmaları Dergisi, 12(24), 294-312.
• English, L. D. (2006). Mathematical modelling in the primary school: Children's construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303-323.
• Eraslan, A. (2012). İlköğretim matematik öğretmen adaylarının model oluşturma etkinlikleri üzerinde düşünme süreçleri [Prospective elementary mathematics teachers’ thought processes on a model eliciting activity]. Kuram ve Uygulamada Eğitim Bilimleri, 12(4), 2953-2968.
• Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: temel kavramlar ve farklı yaklaşımlar Mathematical modeling in mathematics education: basic concepts and different approaches]. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1-21.
• Eric, C. C. M. (2008). Using model-eliciting activities for primary mathematics classroom, The Mathematics Educator, 11(1/2), 47-66.
• Hıdıroğlu, Ç. N., & Bukova-Güzel , E. (2013). Matematiksel modelleme sürecini açıklayan farklı yaklaşımlar [Different approaches clarifying mathematical modeling process]. Bartın Üniversitesi Eğitim Fakültesi Dergisi, 2(1), 127-145.
• Hıdıroğlu, Ç. N., & Bukova-Güzel, E. (2015). Teknoloji destekli ortamda matematiksel modellemede ortaya çıkan üst bilişsel yapılar [Metacognitive structures occuring in mathematical modelling within a technology enhanced environment]. Turkish Journal of Computer and Mathematics Education, 6(2), 179-208.
• Kaiser, G., & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM - Zentralblatt für Didaktik der Mathematik, 38(2), 196-208.
• Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi [Investigating problem solving ability of pre-service mathematics teachers in modeling process]. Unpublished Master Thesis, Marmara Üniversitesi Eğitim Bilimleri Enstitüsü.
• 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, NJ: Lawrence Erlbaum.
• Lesh, R., & Harel, G. (2003). Problem solving, modelling, and local conceptual development. Mathematical Thinking and Learning, 5(2 & 3), 157–189.
• Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591-646). Mahwah, NJ: Lawrence Erlbaum.
• Lesh R., & Yoon C. (2004). Evolving communities of mind: in which development involves several interacting simultaneously developing strands. Mathematical Thinking and Learning, 6(2), 205-226.
• Maaß, K., & Mischo, C. (2011). Implementing modelling into day-to-day teaching practice-the project STRATUM and its framework. Journal Für Mathematik-Didaktik, 32(1), 103- 131.
• Lingefjärd, T., & Holmquist, M. (2005). To assess students’ attitudes, skills and competencies in mathematical modelling. Teaching Mathematics and its Applications, 24(2-3), 123-133.
• Miles, M, B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded Sourcebook. (2nd ed). Thousand Oaks, CA: Sage.
• Ministry of National Education (MONE). (2005). İlköğretim matematik dersi 1-5.sınıflar öğretim programı [Primary school mathematics lesson (grades 1-5) curriculum]. Ankara: Devlet Kitapları Basımevi.
• Ministry of National Education (MONE). (2018). Matematik dersi öğretim programı,1-8.sınıflar [Mathematics curriculum (Primary and Secondary School grades 1-8)]. Ankara: Devlet Kitapları Basımevi.
• Moore, T., & Diefes-Dux, H. (2004). Developing model-eliciting activities for undergraduate students based on advanced engineering content. Paper presented at the 34th ASEE/IEEE Frontiers in Education, Savannah, GA.
• Mousoulides, N. G., Christou, C., & Sriraman, B. (2008). A modeling perspective on the teaching and learning of mathematical problem solving. Mathematical Thinking and Learning, 10(3), 293-304.
• Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H-W. Henn & M. Niss. (Eds.) (2007), Modelling and Applications in Mathematics Education. The 14th ICMI Study (pp 3–32). New York, NY: Springer Science + Business Media, LLC.
• Özaltun-Çelik, A., & Bukova-Güzel, E. (2018). Doğrusal fonksiyonun öğrenilmesine yönelik tasarlanan matematiksel modelleme etkinliği üzerine çalışan öğrencilerin nicel muhakemeleri [Students' quantitative reasoning while engaging in a mathematical modeling task designed for learning linear function]. Adıyaman Üniversitesi Eğitim Bilimleri Dergisi, 8(2), 53-85.
• Peter-Koop, A. (2004). Fermi problems in primary mathematics classrooms: Pupils’ interactive modelling processes. In I. Putt, R. Farragher, and M. McLean (Eds), Mathematics Education for the Third Millenium: Towards 2010, Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 454461). Townsville, Queensland: MERGA.
• Pollak, H. (2012). What is mathematical modelling? In Mathematical Modelling Handbook, edited by Heather Gould, Diane R. Murray, and Andrew Sanfratello, pp. viii–xi. Bedford, Mass.: Consortium for Mathematics and Its Applications (COMAP).
• Şahin, N., & Eraslan, A. (2019). Ortaokul matematik öğretmeni adaylarının matematik uygulamaları dersinde modelleme etkinliklerinin kullanılmasına yönelik görüşler [Middle-school prospective mathematics teachers' opinions on the use of modeling activities at the course of mathematics applications]. Turkish Journal of Computer and Mathematics Education, 10 (2), 373-393.
• Tekin, A., Hıdıroğlu, Ç., & Bukova-Güzel , E. (2011). Examining of model eliciting activities developed by prospective mathematics teachers. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education. 10-15 Temmuz 2011, ODTU, Ankara.
• Tekin, A. (2012). Matematik öğretmenlerinin model oluşturma etkinliği tasarım süreçleri ve etkinliklere yönelik görüşleri [Mathematics teachers’ views concerning model eliciting activities, developmental process and the activities themselves] (Master’s thesis, Dokuz Eylül Üniversitesi, Institute of Educational Sciences, İzmir). Re-trieved from https://tez.yok.gov.tr/UlusalTezMerkezi/.
• Tekin-Dede, A. (2015). Matematik derslerinde öğrencilerin modelleme yeterliklerinin geliştirilmesi: bir eylem araştırması [Developing students' modelling competencies in mathematics lessons: An action research study] Doktora Tezi. Dokuz Eylül Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir. [Doctoral dissertation, Dokuz Eylül University, Institute of Educational Sciences, İzmir. Retrieved from https://tez.yok.gov.tr/UlusalTezMerkezi/
• Tekin-Dede , A., & Bukova-Güzel, E. (2013). Matematik öğretmenlerinin model oluşturma etkinliği tasarım süreçlerinin incelenmesi: obezite problemi [Examining the mathematics teachers’ design process of the model eliciting activity: obesity problem]. İlköğretim Online, 12(4), 1100-1119.
• Tekin-Dede , A., & Bukova-Güzel, E. (2014). Model oluşturma etkinlikleri: kuramsal yapısı ve bir örneği [Model eliciting activities: the theoretical structure and its example]. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 33(1), 95-112.
• Tekin-Dede, A. T., Hıdıroğlu, Ç. N., & Bukova-Güzel, E. (2017). Examining of model eliciting activities developed by mathematics student teachers. Journal on Mathematics Education. 8(2), 223-242.
• Tural-Sönmez, M. (2017). Matematiksel modelleme problemlerinin yapılandırılması üzerine tasarım tabanlı inceleme: finansal içerik örneği [Design based investigation on construction of mathematical modelling problems: example of financial content]. Journal of Computer and Education Research, 5(10), 218-240. DOI:10.18009/jcer.307314
• Tural-Sönmez, M. (2019). Ortaya çıkan modelleme yaklaşımıyla parantez kullanımının anlamlandırılma süreci. Journal of Computer and Education Research, 7(13), 62-89. DOI:10.18009/jcer.499845
• Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences]. Ankara: Seçkin Yayıncılık [Seçkin Publishing].
• Yin, R. (1984). Case study research: design and methods. (3. Ed.). California: Sage Publications.
• Yoon, C., Dreyfus, T., & Thomas, O. J. (2010). How high is the tramping track? mathematising and applying in a calculus model-eliciting activity. Mathematics Education Research Journal, 22(1), 141-157.
• Yu, Shih-Yi, & Chang, Ching-Kuch. (2011). What did Taiwan mathematics teachers think of model-eliciting activities and modelling teaching? In G. Kaiser, W.Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (Vol. 1, pp. 147–156). New York, NY: Springer.