Mathematics Teachers’ Evaluations Regarding the Task of Eco-Friendly Transportation Designed for Constructing Relationship Between Diameter and Circumference of a Circle

Year 2020, , 691 - 716, 30.06.2020

Aytuğ Özaltun Çelik , Esra Bukova Guzel

https://doi.org/10.17522/balikesirnef.692718

Cited By: 1

Abstract

The purpose of this study was to examine mathematics teachers’ evaluations of the real-life contextual task designed for constructing the relationship between the circle's diameter and circumference. The participants of the study which was conducted based on case study design were twenty-four middle school mathematics teachers. The data were collected during a workshop on mathematical modeling and integration of mathematical modeling on teaching. The participants worked on the task in groups and then individually evaluated the task. The collected data were analyzed by content analysis and the categories were formed in the direction of evaluation questions. It was revealed that the teachers evaluated the task by focusing on the concept and the teacher instead of focusing on students and their understandings. In this direction, it is suggested that teachers should be supported for designing teaching which they focused on students’ cognitive processes by considering perspectives of teaching and learning.

Keywords

circle, covariation, mathematical modeling, quantitative reasoning, realistic mathematics education, ratio.

Çemberin Çapı ile Çevresi Arasındaki İlişkinin Oluşturulması Amacıyla Tasarlanan Çevre Dostu Ulaşım Aracı Etkinliğine Yönelik Matematik Öğretmenlerinin Değerlendirmeleri

Abstract

Çalışmanın amacı matematik öğretmenlerinin çemberin çapı ile çevresi arasındaki ilişkiyi oluşturmak için tasarlanan gerçek yaşam bağlamlı etkinliğe yönelik değerlendirmelerini incelemektir. Durum çalışması desenine dayalı yürütülen çalışmanın katılımcıları 24 ortaokul matematik öğretmenidir. Çalışmanın verileri matematiksel modelleme ve öğretime entegrasyonu konulu bir çalıştay kapsamında toplanmıştır. Öğretmenler kendilerine sunulan etkinlik üzerinde gruplar halinde çalışmışlar ve ardından bireysel olarak etkinliğe yönelik değerlendirme formunu tamamlamışlardır. Elde edilen veriler içerik analizi ile analiz edilmiş ve değerlendirme soruları doğrultusunda kategoriler oluşturulmuştur. Öğretmenlerin etkinliği öğrencilerden ve öğrencilerin anlamalarından bağımsız olarak kavram ve öğretmen odaklı değerlendirdikleri sonucuna ulaşılmıştır. Bu doğrultuda öğretmenlerin öğretim perspektiflerinin güçlendirilerek matematiği öğrencilerin zihinsel süreçleriyle ilişkili bir şekilde ele aldıkları öğretim süreçleri tasarlayabilmelerine yönelik desteklenmeleri önerilmektedir.

Keywords

çember, eş zamanlı değişim, gerçekçi matematik eğitimi, matematiksel modelleme, nicel muhakeme, oran

References

• Alacacı, C. (2016). Gerçekçi matematik eğitimi. E. Bingölbali, S. Arslan, & İ. Ö. Zembat, (Ed.), Matematik Eğitiminde Teoriler (pp. 341-354). Ankara: Pegem Akademi.
• Baki, A. (2018). Matematiği öğretme bilgisi (1. Baskı) Ankara: Pegem Akademi.
• Belue, P. T., Overman Cavey, L. & Kinzel, M. T. (2017). An exploration of a quantitative reasoning instructional approach to linear equations in two variables with community college students. School Science and Mathematics, 117(5), 183-193.
• Cobb, P., Zhao, Q., & Visnovska, J. (2008). Learning from and adapting the theory of realistic mathematics education. Éducation et Didactique, 2(1), 105–124.
• Confrey, J. & Smith, E. (1995). Splitting, covariation and their role in the development of exponential function. Journal for Research in Mathematics Education, 26, 66–86.
• Constantinou, C. (2018). Implications of mathematics standards on geometry education in New York State. Yayınlanmamış doktora tezi, Columbia Üniversitesi.
• Deichert, D. (2014). The conceptual field of proportional reasoning researched through the lived experiences of nurses. Yayınlanmamış doktora tezi, Central Florida Üniversitesi.
• Ellis, A. B. (2007). The influence of reasoning with emergent quantities on students' generalizations. Cognition and Instruction, 25(4), 439-478.
• Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: Temel kavramlar ve farklı yaklaşımlar. Educational Sciences: Theory and Practice, 14(4), 1607–1627.
• García, F. J. G., Maass, K., & Wake, G. (2010). Theory meets practice—Working pragmatically within different cultures and traditions. In R. Lesh, P. Galbraith, C. Haines & A. Hurford (Eds.), Modelling students’ modelling competencies (pp. 445–457). New York: Springer.
• Gravemeijer, K. (2004). Local instruction theories as a means of support for teachers in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105-128.
• Haciomeroglu, G. (2017). Reciprocal relationships between mathematics anxiety and attitude towards mathematics in elementary students. Acta Didactica Napocensia, 10(3), 59-68.
• Lai, M. Y. (2013). Constructing meanings of mathematical registers using metaphorical reasoning and models. Mathematics Teacher Education and Development, 15(1), 29-47.
• Lesh, R. A., & Doerr, H. (2003). Foundations of model and modelling perspectives on mathematic teaching and learning. In R. A. Lesh & H. Doerr (Eds.), Beyond constructivism: A models and modelling perspectives on mathematics teaching, learning and problem solving (pp. 3-33). Mahwah, NJ: Lawrance Erlbauum.
• Maguire, T. J. (2012). Investigation of the misconceptions related to the concepts of equivalence and literal symbols held by underprepared community college students. Yayınlanmamış doktora tezi, San Francisco Üniversitesi.
• Milli Eğitim Bakanlığı [MEB] (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara: MEB Yayınları. Moore, K. C., Carlson, M. P., & Oehrtman, M. (2009). The role of quantitative reasoning in solving applied precalculus problems. Proceedings of the Twelfth Annual Conference on Research in Undergraduate Mathematics Education. Raleigh, NC: North Carolina State University.
• National Council of Teachers of Mathematics [NCTM]. (2000). Practice-based professional development for teachers of mathematics. Reston, VA: National Council of Teachers of Mathematics.
• Rowland, T., Turner, F., & Thwaites, A. (2014). Research into teacher knowledge: a stimulus for development in mathematics teacher education practice. ZDM, 46(2), 317-328.
• Royce, C. A. (2010). A revolutionary model of professional development. Science Scope, 34(3), 6.
• Simon, M. A. (2013). Promoting fundamental change in mathematics teaching: a theoretical, methodological, and empirical approach to the problem. ZDM: The International Journal on Mathematics Education, 45(5), 573-582.
• Simon, M. A., Kara, M., Placa, N., & Avitzur, A. (2018). Towards an integrated theory of mathematics conceptual learning and instructional design: The Learning Through Activity theoretical framework. Journal of Mathematical Behavior. 52, 95-112.
• Simon, M. A. (2000). Constructivism, mathematics teacher education, and research in mathematics teacher development. L.P.. Steffe & P.W. Thompson ( Ed.). Radical Constructivism in Action: Building on the Pioneering Work of Ernst von Glasersfeld (s. 213-230). London: Routledge-Falmer.
• Simon, M. A. (2017). Challenges in mathematics teacher education from a (mostly) constructivist perspectıve. S. E. Kastberg, A. M.Tyminski, A. E. Lischka & W. B Sanchez,. (Eds.) Building support for scholarly practices in mathematics methods (s. 39-48). IAP.
• Thompson, P. W. (1995). Notation, convention, and quantity in elementary mathematics. J. Sowder & B. Schapelle (Ed.), Providing a foundation for teaching middle school mathematics (pp. 199-221). Albany, NY: SUNY Press.
• Thompson, P. W. (1990). A theoretical model of quantity-based reasoning in arithmetic and algebraic. Progress report to the National Science Foundation. San Diego State University, Center for Research in Mathematics and Science Education.
• Thompson, P. W. (2002). Didactic objects and didactic models in radical constructivism. K. Gravemeijer, R. Lehrer, B. van Oers & L. Verschaffel (Ed.), Symbolizing and modeling ın mathematics education. Dordrecth, The Netherlands: Kluwer.
• Thompson, P. W. (2008). Conceptual analysis of mathematical ideas: Some padework at the foundation of mathematics education. Plenary Paper Delivered at the 32nd Annual Meeting of the International Group for the Psychology of Mathematics Education. O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. SÈpulveda (Ed.), Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education, (Cilt 1, s. 45-64). MorÈlia, Mexico: PME.
• van den Heuvel-Panhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour (Freudenthal Institute CD ROM for ICME9) (Utrecht, Utrecht University).
• van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic mathematics education. S. Lerman (Ed.), Encyclopedia of mathematics education (s. 521-525). Springer Netherlands.
• Yin, R.K. (2003). Case study research design and methods. 3rd Edition, Thousand Oaks: Sage.
• Zaslavsky, O., & Leikin, R. (2004). Professional development of mathematics teacher educators: Growth through practice. Journal of mathematics teacher education, 7(1), 5-32.Abowitz, D.A. & Knox, D. (2003). Life goals among Greek college students. College Student Journal, 37, 96-100.