Mathematics Student Teachers’ Modelling Approaches While Solving the Designed Eşme Rug Problem

Çağlar Naci Hıdıroğlu; Ayşe Tekin Dede; Semiha Kula Ünver; Esra Bukova Güzel

doi:10.12973/eurasia.2017.00648a

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Çağlar Naci Hıdıroğlu ¹, Ayşe Tekin Dede ², Semiha Kula Ünver ², Esra Bukova Güzel ² ^*

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¹ Pamukkale University, TURKEY² Dokuz Eylül University, TURKEY^* Corresponding Author

Abstract

The purpose of the study is to analyze the mathematics student teachers’ solutions on the Eşme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems’ main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were collected from the participants’ written solutions related to the problem. To analyze the students’ answers through mathematical modelling process, the researchers compiled 7-stage mathematical modelling process from the literature. It was observed that the problem created an appropriate process for mathematical modelling. While examining the solutions of the participants who were informed about this 7-stage mathematical modelling process, it was generally observed that their solution approaches toward the problem decreased while progressing in modelling stages.

Keywords

mathematical modelling
mathematical modelling process
modelling problem
mathematics student teachers

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2017, Volume 13, Issue 3, 873-892

https://doi.org/10.12973/eurasia.2017.00648a

Publication date: 18 Feb 2017

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References

Ärlebäck, J. B. (2009). On the use of realistic Fermi problems for introducing mathematical modelling in school. The Montana Mathematics Enthusiast, 6(3), 331- 364.
Ärlebäck, J. B. & Bergsten, C. (2010). On the use of realistic fermi problems in introducing mathematical modelling in upper secondary mathematics. In R. Lesh, P. L. Galbraith, W. Blum & A. Hurford (Eds.), Modelling students' mathematical modelling competencies, ICTMA 13, 597-609, Springer.
Beerli, G. (2003). Realitaetsbezug im unterricht mit fermifragen. In H. Henn (Ed.), Beiträge zum Mathematikunterricht, (pp. 89-92). Hildesheim: Franzbecker.
Berry, J. & Houston K. (1995). Mathematical modelling. Bristol: J. W. Arrowsmith Ltd.
Blomhoj, M. & Kjeldsen, T.H. (2006). Teaching mathematical modelling through project work - Experiences from an in-service course for upper secondary teachers, Zentralblatt für Didaktik der Mathematik–ZDM, 38 (2), 163-177.
Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education-Discussion document. Educational Studies in Mathematics, 51(1), 149-171.
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. (2007). Personal experiences and extra-mathematical knowledge as an influence factor on modelling routes of pupils. In Pitta-Pantazi D. and Philippou, G. (Eds): Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, 2080-2089.
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(1), 19- 36.
Dirks, M. K., & Edge, D. R., M. (1983). Problem solving: Enrico Fermi and the bull moose. School Science and Mathematics, 83(7), 25-28.
Doerr, H.M. (1997). Experiment, simulation and analysis: An Integrated instructional approach to the concept of force. International Journal of Science Education, 19(3), 265-282.
Doğan Temur, Ö. (2012). Analysis of prospective classroom teachers’ teaching of mathematical modelling and problem solving. Eurasia Journal of Mathematics, Science & Technology Education, 8(2), 83-93.
English, L. D. & Watters, J. J. (2004). Mathematical modelling in the early school years. Mathematics Education Research Journal, 16(3), 59-80.
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.
Hıdıroğlu, Ç. N., Tekin, A., & Bukova Güzel, E. (2010). Öğrencilerin modellemede bireysel ve birlikte çalışarak ortaya koydukları yaklaşımlar ve düşünme süreçleri. 9. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, 21-26.
Kapur, J. N. (1982). The art of teaching the art of mathematical modelling. International Journal of Mathematical Education in Science and Technology, 13(2), 185-192.
Lee, C., Chen, M., & Chang, W. (2014). Effects of the multiple solutions and question prompts on generalization and justification for non-routine mathematical problem solving in a computer game context. Eurasia Journal of Mathematics, Science & Technology Education, 10(2), 89-99.
Lesh, R., & Doerr, H. M. (2003). A modelling perspective on teacher development. In Lesh R. A. & Doerr H. (Eds.): Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum, 3-33.
Lingefjärd, T. (2006). Faces of mathematical modelling. Zentralblatt für Didaktik der Mathematik-ZDM, 38(2), 96-112.
Miles, H. B. & Huberman, A. M. (1994). Qualitative data analysis. Second Edition. Thousand Oaks, CA:Sage.
Milli Eğitim Bakanlığı. (2006). Ortaöğretim matematik dersi öğretim programı. Ankara: Yazar.
National Council of Teachers of Mathematics (2000). Principles and standarts for school mathematics: An Overview. National Council of Teachers of Mathematics. Reston: Author.
Niss, M. (1989). Aims and scope of applications and modelling in mathematics curricula. In Blum, W. Berry, J. S. Biehler, R. Huntley, I. Kaiser-Messmer G. & Profke L. (Eds): Applications and modelling in learning and teaching mathematics. Chichester: Ellis Horwood, 22-31.
Peter-Koop, A. (2003). Modellbildungsprozesse beim bearbeiten von Fermi-Problemen in kleingruppen. In Ruwisch S. & Peter-Koop A. (Eds): Gute Aufgaben im Mathematikunterricht der Grundschule. Offenburg: Mildenberger, 111-130.
Peter-Koop, A. (2004). Fermi problems in primary mathematics classrooms: Pupils’ interactive modelling processes. In Putt, I. Farragher, R. & McLean M. (Eds): Mathematics education for the third millenium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics Education. Townsville, Queensland: MERGA, 454-461.
Peter-Koop, A. (2009). Teaching and understanding mathematical modelling through Fermi problem. In Clarke, B. Grevholm B. & Millman R. (Eds): Tasks in Primary Mathematics Teacher Education. Springer, 131-146).
Skolverket. (2006). Förslag till kursplan [Curriculum proposal]. Stockholm: Liber distribution, 2637-2638.
Sriraman, B., & Lesh, R. (2006). Modelling conceptions revisited. Zentralblatt für Didaktik der Mathematik - ZDM, 38(3), 247- 254.
Sriraman, B., & Knott, L. (2009). The Mathematics of estimation: possibilities for interdisciplinary pedagogy and social consciousness. Interchange: A Quarterly Review of Education, 40(2), 205-223.
Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A Framework for success in implementing mathematical modelling in the secondary classroom. Mathematics: Essential Research, Essential Practice, 2, 688- 697.
Taplin, M. (2007). Teaching values through a problem solving approach to mathematics. Available from: http://www.mathgoodies.com/articles/teaching_values.html
Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction, 7(4), 339-359.
Yanagimoto, T. (2005). Teaching modelling as an alternative approach to school mathematics. Teaching Mathematics and Its Applications, 24(1), 1-13.
Yıldırım, A., & Şimşek, H. (2005). Sosyal bilimlerde nitel araştırma yöntemleri. Seçkin Yayıncılık, Ankara.

How to cite this article

APA

Hıdıroğlu, Ç. N., Dede, A. T., Ünver, S. K., & Güzel, E. B. (2017). Mathematics Student Teachers’ Modelling Approaches While Solving the Designed Eşme Rug Problem. Eurasia Journal of Mathematics, Science and Technology Education, 13(3), 873-892. https://doi.org/10.12973/eurasia.2017.00648a

Vancouver

Hıdıroğlu ÇN, Dede AT, Ünver SK, Güzel EB. Mathematics Student Teachers’ Modelling Approaches While Solving the Designed Eşme Rug Problem. EURASIA J Math Sci Tech Ed. 2017;13(3):873-92. https://doi.org/10.12973/eurasia.2017.00648a

AMA

Hıdıroğlu ÇN, Dede AT, Ünver SK, Güzel EB. Mathematics Student Teachers’ Modelling Approaches While Solving the Designed Eşme Rug Problem. EURASIA J Math Sci Tech Ed. 2017;13(3), 873-892. https://doi.org/10.12973/eurasia.2017.00648a

Chicago

Hıdıroğlu, Çağlar Naci, Ayşe Tekin Dede, Semiha Kula Ünver, and Esra Bukova Güzel. "Mathematics Student Teachers’ Modelling Approaches While Solving the Designed Eşme Rug Problem". Eurasia Journal of Mathematics, Science and Technology Education 2017 13 no. 3 (2017): 873-892. https://doi.org/10.12973/eurasia.2017.00648a

Harvard

Hıdıroğlu, Ç. N., Dede, A. T., Ünver, S. K., and Güzel, E. B. (2017). Mathematics Student Teachers’ Modelling Approaches While Solving the Designed Eşme Rug Problem. Eurasia Journal of Mathematics, Science and Technology Education, 13(3), pp. 873-892. https://doi.org/10.12973/eurasia.2017.00648a

MLA

Hıdıroğlu, Çağlar Naci et al. "Mathematics Student Teachers’ Modelling Approaches While Solving the Designed Eşme Rug Problem". Eurasia Journal of Mathematics, Science and Technology Education, vol. 13, no. 3, 2017, pp. 873-892. https://doi.org/10.12973/eurasia.2017.00648a