## Main Article Content

## Abstract

This study aims to examine the perceptions of pre-service mathematics teachers about mathematical modelling activities. Participants of the study comprised 23 pre-service mathematics teachers who undertook a course on mathematical modelling. A 12-hour mathematical modelling course revealed the perceptions of participants. After it, the participants found/developed a modelling problem and explained why they evaluated it as a model eliciting activity (MEA). MEA found/developed by participants were examined by taking the principles of developing MEA into consideration. Results showed that many participants considered having more than one solution, the principle based on real-life context, and suitability for group work for MEA. The participants did not focus on the model documentation principle. Based on this result, faculty members can help pre-service teachers by using activities that can be considered appropriate for this principle in modelling education.

## Keywords

## Article Details

This work is licensed under a Creative Commons Attribution 4.0 International License.

*How to Cite*

*MIER Journal of Educational Studies Trends and Practices*,

*11*(2), 180–199. https://doi.org/10.52634/mier/2021/v11/i2/1988

* * References

- Blum, W. (2011). Can Modelling Be Taught and Learnt? Some Answers from Empirical Research. In K. G, B. W. and B F R, & S. G (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (p. 15-30). Springer.
- Çakmak-Gürel, Z., & Isik, A. (2018). Investigation of the competencies of pre-service secondary school mathematics teachers related to the mathematical modelling. International Journal of Educational Research, 9(3), 85-103.
- Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. Prufrock Journal, 17(1), 37-47.
- Cheng, A. K. (2001). Teaching mathematical modelling in Singapore schools. The Mathematics Educator, 6(1), 63-75.
- Common Core State Standards Initiative. (2021). Standards for mathematical practice. Retrieved from http://www.corestandards.org/Math/Practice/#CCSS.Math.Practice.MP2
- Dede, A. T., Hidiroglu, C. N., & Guzel, E. B. (2017). Examining of model eliciting activities developed by mathematics student teachers. Journal on Mathematics Education, 8(2), 223-242.
- Doerr, H., & Lesh, R. (2011). Models and Modelling Perspectives on Teaching and Learning Mathematics in the Twenty-First Century. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (p. 247-268). Springer.
- Galbraith, P. (2012). Models of modelling: genres, purposes or perspectives. Journal of Mathematical Modelling Application, 1(5), 3-16.
- Haines, C., & Crouch, R. (2007). Mathematical Modelling and Applications: Ability and Competence Frameworks. In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), (Vol. 10, p. 336-342). Springer.
- Hernández, M. L., Levy, R., Felton-Koestler, M. D., & Zbiek, R. M. (2017). Mathematical modelling in the high school curriculum. Mathemat?cs Teacher, 110(5), 336-342.
- Holmquist, M., & Lingefjärd, T. (2003). Mathematical Modelling in Teacher Education. In Q. Ye, W. Blum, S. K. Houston, & Q. Jiang (Eds.), Mathematical Modelling in Education and Culture ICTMA 10: Applications in Science and Technology (p. 197-208). Horwood Publishing.
- Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (p. 503-510). Springer.
- Kaiser, G., Sriraman, B., Blomhøj, M., & Garcia, F. J. (2007). Report from the working group modelling and applications-differentiating perspectives and delineating commonalities. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the fifth congress of the European society for research in mathematics education (p. 2035-2041). University of Cyprus.
- Kuntze, S. (2011). In-Service and Prospective Teachers’ Views About Modelling Tasks in the Mathematics Classroom – Results of a Quantitative Empirical Study. In K. G, B. W, B. F. R, & S. G (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (p. 279-288). Springer.
- Lesh, R., & Caylor, B. (2007). Introduction to special issue: modelling as application versus modelling as a way to create mathematics. International Journal of Computers for Mathematical Learning, 12(3), 173-194.
- Lesh, R., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In A. E. Kelly & R. A. Lesh (Eds.), Beyond Constructivism: A models & modelling perspective on mathematics problem solving, learning & teaching (p. 35-58). https://doi.org/10.4324/9781410602725
- Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. Handbook of Research Design in Mathematics and Science Education, 591- 645.
- Manouchehri, A., Yao, X., & Saglam, Y. (2018). Nurturing Knowledge of Mathematical Modelling for Teaching. In M. E. Strutchens, R. Huang, D. Potari, & L. Losano (Eds.), ICME-13 Monographs (p. 205-223). Springer International Publishing.https://doi.org/10.1007/9783-319-91059-812
- MEB. (2018). Secondary mathematics education program. Retrieved from https://www.yok.gov.tr/Documents/Kurumsal/egitim_ogretim_dairesi/Yeni-Ogretmen-Yetistirme-Lisans-Programlari/Matematik_Ogretmenligi_Lisans_Programi.pdf
- Mousoulides, N., Sriraman, B., & Christou, C. (2007). From problem solving to modelling - the emergence of models and modelling perspectives. Nordic Studies in Mathematics Education, 12(1), 23-47.
- Ozer, A. O., & Guzel, E. B. (2016). Mathematical Modelling Problems From the Viewpoint of Students, Prospective Teachers and Teachers. Manisa Celal Bayar University Journal of the Faculty of Education, 4(1), 57-73. Retrieved from https://dergipark.org.tr/en/pub/mcbuefd/issue/54502/742770
- Peter-Koop, A. (2004). Fermi problems in primary mathematics classrooms: Pupils’ interactive modelling processes. In R. Faragher & M. McLean (Eds.), Mathematics education for the third millennium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia, Townsville) (p. 454-461). MERGA.
- Urhan, S., & Dost, S. (2018). Analysis of Ninth Grade Mathematics Course Book Activities Based on Model-Eliciting Principles. International Journal of Science and Mathematics Education, 16(5), 985-1002. https://doi.org/10.1007/s10763-017-9808-4
- Winston, W. L. (2003). Operations research: Applications and algorithms. Brooks/Cole.
- Yan?k, H. B., Ba?dat, O., & Koparan, M. (2017). Investigating prospective middle-school teachers’ perspectives of mathematical modelling problems. Journal of Qualitative Research in Education, 5(1), 80-101.

#### References

Blum, W. (2011). Can Modelling Be Taught and Learnt? Some Answers from Empirical Research. In K. G, B. W. and B F R, & S. G (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (p. 15-30). Springer.

Çakmak-Gürel, Z., & Isik, A. (2018). Investigation of the competencies of pre-service secondary school mathematics teachers related to the mathematical modelling. International Journal of Educational Research, 9(3), 85-103.

Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. Prufrock Journal, 17(1), 37-47.

Cheng, A. K. (2001). Teaching mathematical modelling in Singapore schools. The Mathematics Educator, 6(1), 63-75.

Common Core State Standards Initiative. (2021). Standards for mathematical practice. Retrieved from http://www.corestandards.org/Math/Practice/#CCSS.Math.Practice.MP2

Dede, A. T., Hidiroglu, C. N., & Guzel, E. B. (2017). Examining of model eliciting activities developed by mathematics student teachers. Journal on Mathematics Education, 8(2), 223-242.

Doerr, H., & Lesh, R. (2011). Models and Modelling Perspectives on Teaching and Learning Mathematics in the Twenty-First Century. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (p. 247-268). Springer.

Galbraith, P. (2012). Models of modelling: genres, purposes or perspectives. Journal of Mathematical Modelling Application, 1(5), 3-16.

Haines, C., & Crouch, R. (2007). Mathematical Modelling and Applications: Ability and Competence Frameworks. In W. Blum, P. L. Galbraith, H. Henn, & M. Niss (Eds.), (Vol. 10, p. 336-342). Springer.

Hernández, M. L., Levy, R., Felton-Koestler, M. D., & Zbiek, R. M. (2017). Mathematical modelling in the high school curriculum. Mathemat?cs Teacher, 110(5), 336-342.

Holmquist, M., & Lingefjärd, T. (2003). Mathematical Modelling in Teacher Education. In Q. Ye, W. Blum, S. K. Houston, & Q. Jiang (Eds.), Mathematical Modelling in Education and Culture ICTMA 10: Applications in Science and Technology (p. 197-208). Horwood Publishing.

Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (p. 503-510). Springer.

Kaiser, G., Sriraman, B., Blomhøj, M., & Garcia, F. J. (2007). Report from the working group modelling and applications-differentiating perspectives and delineating commonalities. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the fifth congress of the European society for research in mathematics education (p. 2035-2041). University of Cyprus.

Kuntze, S. (2011). In-Service and Prospective Teachers’ Views About Modelling Tasks in the Mathematics Classroom – Results of a Quantitative Empirical Study. In K. G, B. W, B. F. R, & S. G (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (p. 279-288). Springer.

Lesh, R., & Caylor, B. (2007). Introduction to special issue: modelling as application versus modelling as a way to create mathematics. International Journal of Computers for Mathematical Learning, 12(3), 173-194.

Lesh, R., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In A. E. Kelly & R. A. Lesh (Eds.), Beyond Constructivism: A models & modelling perspective on mathematics problem solving, learning & teaching (p. 35-58). https://doi.org/10.4324/9781410602725

Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. Handbook of Research Design in Mathematics and Science Education, 591- 645.

Manouchehri, A., Yao, X., & Saglam, Y. (2018). Nurturing Knowledge of Mathematical Modelling for Teaching. In M. E. Strutchens, R. Huang, D. Potari, & L. Losano (Eds.), ICME-13 Monographs (p. 205-223). Springer International Publishing.https://doi.org/10.1007/9783-319-91059-812

MEB. (2018). Secondary mathematics education program. Retrieved from https://www.yok.gov.tr/Documents/Kurumsal/egitim_ogretim_dairesi/Yeni-Ogretmen-Yetistirme-Lisans-Programlari/Matematik_Ogretmenligi_Lisans_Programi.pdf

Mousoulides, N., Sriraman, B., & Christou, C. (2007). From problem solving to modelling - the emergence of models and modelling perspectives. Nordic Studies in Mathematics Education, 12(1), 23-47.

Ozer, A. O., & Guzel, E. B. (2016). Mathematical Modelling Problems From the Viewpoint of Students, Prospective Teachers and Teachers. Manisa Celal Bayar University Journal of the Faculty of Education, 4(1), 57-73. Retrieved from https://dergipark.org.tr/en/pub/mcbuefd/issue/54502/742770

Peter-Koop, A. (2004). Fermi problems in primary mathematics classrooms: Pupils’ interactive modelling processes. In R. Faragher & M. McLean (Eds.), Mathematics education for the third millennium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia, Townsville) (p. 454-461). MERGA.

Urhan, S., & Dost, S. (2018). Analysis of Ninth Grade Mathematics Course Book Activities Based on Model-Eliciting Principles. International Journal of Science and Mathematics Education, 16(5), 985-1002. https://doi.org/10.1007/s10763-017-9808-4

Winston, W. L. (2003). Operations research: Applications and algorithms. Brooks/Cole.

Yan?k, H. B., Ba?dat, O., & Koparan, M. (2017). Investigating prospective middle-school teachers’ perspectives of mathematical modelling problems. Journal of Qualitative Research in Education, 5(1), 80-101.