# Developing understanding of mathematical modeling in secondary teacher preparation

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## Abstract

This study examines the evolution of 11 prospective teachers’ understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include modeling as part of the school curriculum under current state standards. The module consisted of readings, analysis of the Common Core State Standards, carefully designed modeling activities, individual and group work, discussion, presentations, and reflections. The results show that while most prospective teachers had misconceived definitions of mathematical modeling prior to the module, they developed the correct understanding of modeling as an iterative process involving making assumptions and validating conclusions connected to everyday situations. The study reveals how the prospective teachers translated the modeling cycle into practice in the context of a carefully designed open-ended problem and the strong connections between modeling activities and promoting mathematical practices.

## Keywords

Mathematical modeling Secondary mathematics Secondary mathematics pre-service teacher education## References

- Anhalt, C., & Cortez, R. (2015). Mathematical modeling: A structured process.
*Mathematics Teacher,**108*(6), 446–452.CrossRefGoogle Scholar - Balicer, R. D. (2007). Modeling infectious diseases dissemination through online role-playing games.
*Epidemiology, 18*(2), 260–261.Google Scholar - Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.),
*Handbook of research on teaching*(4th ed., pp. 433–456). Washington, DC: American Educational Research Association.Google Scholar - Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., et al. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress.
*American Educational Research Journal,**47*(1), 133–180.CrossRefGoogle Scholar - Blomhøj, M. (2009). Different perspectives in research on the teaching and learning mathematical modeling—Categorising the TSG21 Papers. In
*Mathematical applications and modelling in the teaching and**learning of mathematics*. Proceedings from Topic Study Group 21 at the 11th international congress on mathematical education in Monterrey, Mexico (pp. 1–17).Google Scholar - Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?
*Journal of Mathematical Modeling and Applications,**1*(1), 45–58.Google Scholar - Blum, W., & Leiss, D. (2005). “Filling Up”-the problem of independence-preserving teacher interventions in lessons with demanding modelling tasks. In
*CERME 4-Proceedings of the fourth congress of the European society for research in mathematics education*(pp. 1623–1633).Google Scholar - Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modeling, applications, and links to other subjects—State, trends and issues in mathematics instruction.
*Educational Studies in Mathematics,**22*(1), 37–68.CrossRefGoogle Scholar - Bokova-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. doi: 10.1093/teamat/hrq015.CrossRefGoogle Scholar - Cai, J., Cirillo, M., Pelesko, J. A., Borromeo Ferri, R., Borba, M., Geiger, V., et al. (2014). Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional, and teacher education perspectives. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.),
*Proceedings of the 38th conference of the international group for the psychology of mathematics education and the 36th conference of the North American chapter of the psychology of mathematics education*(p. 1). Vancouver: PME.Google Scholar - Common Core State Standards Initiative (CCSSI). (2010).
*National Governors Association Center for Best Practices and Council of Chief State School Officers*. http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf. - Conference Board of the Mathematical Sciences. (2012).
*The mathematical education of teachers II*. Providence, RI and Washington, DC: American Mathematical Society and Mathematical Association of America.CrossRefGoogle Scholar - Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In
*Modelling and applications in mathematics education*,*New ICMI Study Series*(Vol. 10, pp. 69–78).Google Scholar - Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data.
*Journal for Research in Mathematics Education,**34*(2), 110–137.CrossRefGoogle Scholar - English, L. D. (2007) Cognitive psychology and mathematics education: Reflections on the past and the future. In B. Sriraman (Ed.),
*Zoltan Paul Dienes and the dynamics of mathematical learning, Monograph 2. The Montana Mathematics Enthusiast series*(pp. 119–126). Charlotte, NC: Information Age Publishing. Google Scholar - English, L. D., Fox, J. L., & Watters, J. J. (2005). Problem posing and solving with mathematical modeling.
*Teaching Children Mathematics,**12*(3), 156–163.Google Scholar - Eraslan, A. (2011). Prospective elementary mathematics teachers’ perceptions on model eliciting activities and their effects on mathematics learning.
*Elementary Education Online,**10*(1), 364–377.Google Scholar - Gailbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process.
*ZDM: The International Journal on Mathematics Education,**38*(2), 143–162.CrossRefGoogle Scholar - Kaiser, G., & Schwartz, B. (2006). Mathematical modelling as bridge between school and university.
*ZDM: The International Journal on Mathematics,**38*(2), 196–208.CrossRefGoogle Scholar - Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education.
*ZDM: An International Journal on Mathematics Education,**38*(3), 302–310.CrossRefGoogle Scholar - Kaiser, G., & Stender, P. (2013). Complex modelling problems in co-operative, self-directed learning environments. In G. A. Stillmann, et al. (Eds.),
*Teaching mathematical modelling: Connecting to research and practice, international perspectives on the teaching and learning of mathematical modelling*(pp. 277–293). Dordrecht: Springer.CrossRefGoogle Scholar - Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development.
*Mathematical Thinking and Learning,**5*(2–3), 157–189.CrossRefGoogle Scholar - Meier, S. (2009). Mathematical modelling in a European Context—a European Network-Project. In M. Blomhøj & S. Carreira (Eds.),
*Mathematical applications and modelling in the teaching and learning of mathematics. Proceedings from Topic Study Group 21 at the 11th international congress on mathematical education*(pp. 207-216). Monterrey, Mexico.Google Scholar - Mooney, D., & Swift, R. (1999).
*A course in mathematical modeling*. Washington, DC: Mathematical Association of America.Google Scholar - Moschkovich, J. (2012). Mathematics, the Common Core, and language: Recommendations for mathematics instruction for ELLs aligned with the Common Core. In
*Paper presented at the Understanding Language Conference*, Stanford University. http://ell.stanford.edu/publication/mathematics-common-core-and-language. - Munz, P., Hudea, I., Imad, J. & Smith, R. J. (2009). When zombies attack! Mathematical modelling of an outbreak of zombie infection. In J. M. Tchuenche & C. Chiyaka (Eds.),
*Infectious disease modelling research progress*(pp. 133–150). Hauppauge, NY: Nova Science Publishers, Inc.Google Scholar - National Council of Teachers of Mathematics. (2000).
*Principles and standards for school mathematics*. NCTM: Reston, VA.Google Scholar - National Council of Teachers of Mathematics. (2005). Mathematics assessment: A practical handbook for grades 9–12. In W. Bush & A. Greer (Eds.), Reston, VA: NCTM.Google Scholar
- Saeki, A., & Matsuzaki, A. (2011). Dual modelling cycle framework for responding to the diversities of modellers. In G. A. Stillmann, G. Kaiser, & W. Blum (Eds.),
*Proceedings of ICTMA15, teaching mathematical modelling: Connecting to research and practice*(pp. 89–99). Dordrecht, NLD: Springer.Google Scholar - Schichl, H. (2004). Models and the history of modeling.
*Applied Optimization,**88*, 25–36.CrossRefGoogle Scholar - Smith, R. (2014).
*Mathematical modelling of zombies*. Ottawa, Canada: University of Ottawa Press.Google Scholar - Sole, M. (2013). A primer for mathematical modeling.
*Journal of Mathematics Education at Teachers College,**4*, 44–49.Google Scholar - Strauss, A., & Corbin, J. (1990).
*Basics of qualitative research: Grounded theory procedures and techniques*. Newbury Park, CA: Sage.Google Scholar - Tam, K. C. (2011). Modeling in the common core state standards.
*Journal of Mathematics Education at Teachers College,**2*(1), 28–33.Google Scholar - Tekin, A., Kula, S., Hidiroğlu, C. N., Bukova-Güzel, E., & Uğurel, I. (2011). Determining the views of mathematics student teachers related to mathematical modelling. In
*Paper presented at the 35th conference of the international group for the psychology of mathematics education, Middle East Technical University*, Ankara, Turkey.Google Scholar - Türker, B., Saglam, Y., & Umay, A. (2010). Preservice teachers’ performances at mathematical modeling process and views on mathematical modeling.
*Procedia Social and Behavioral Sciences,**2*, 4622–4628.CrossRefGoogle Scholar - Widjaja, W. (2013). Building awareness of mathematical modeling in teacher education: A case study in Indonesia. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.),
*Teaching mathematical modeling: Connecting to research and practice*. Dordrecht: Springer.Google Scholar - Yoon, C., Dreyfus, T., & Thomas, M. O. J. (2010). How high is the tramping track? Mathematising and applying in a calculus model-eliciting activity.
*Mathematics Education Research Journal,**22*(2), 141–157.CrossRefGoogle Scholar - Zawojewski, J. S. (2010). Problem solving versus modeling. International perspectives on the teaching and learning of mathematical modelling. In
*Modeling students’ mathematical modeling competencies*(pp. 237–243).Google Scholar - Zazkis, R., & Mamolo, A. (2011). Reconceptualizing knowledge at the mathematical horizon.
*For the Learning of Mathematics,**31*(2), 8–13.Google Scholar