Abstract
The context of sense-making is used to frame the activities of a study group of secondary school teachers, post-secondary faculty, mathematicians, and mathematics educators working to characterise engagement with mathematical modelling within the classroom. The perspectives of the participants and points of discussion illuminate aspects of the mathematical modelling process that are difficult to reconcile, such as dealing with ambiguity and uncertainty and distinctions between interpretation and computation. The group organised their experiences and knowledge into a framework for faculty practice that describes characteristics of mathematical modelling tasks and student work at three different levels within four stages of a mathematical modelling process.
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References
Abel, T., & Salinas, T. M. (2017). Challenges to agreeing how to teach mathematical modeling. MAA Focus, 37(3), 16–19.
Abel, T., Baird, A., Hirst, H., & Salinas, T. M. (2016). Introducing students to the mathematical modeling process. The Centroid, 41(2), 13–17.
Bliss, K. M., Fowler, K. R., & Galluzzo, B. J. (2014). Math modeling: Getting started and getting solutions. Philadelphia: Society for Industrial and Applied Mathematics (SIAM).
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). New York: Springer.
Cirillo, M., Pelesko, J., Felton-Koestler, M., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In C. Hirsch & A. McDuffie (Eds.), Annual perspectives in mathematics education: Mathematical modeling and modeling mathematics (pp. 3–16). Reston: National Council of Teachers of Mathematics.
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report. Alexandria: American Statistical Association.
Freudenthal, H. (1968). Why to teach mathematics as to be useful. Educational Studies in Mathematics, 1(1), 3–8.
Giordano, F., Fox, W., Horton, S., & Weir, M. (2008). A first course in mathematical modeling (4th ed.). Boston: Brooks Cole.
Goos, M. (2014). Researcher-teacher relationships and models for teaching development in mathematics education. ZDM Mathematics Education, 46(2), 180–201. https://doi.org/10.1007/s11858-013-0556-9.
Gould, H., Murray, D., & Sanfratello, Y. (Eds.). (2012). Mathematical modeling handbook. Bedford: The Consortium for Mathematics and it Applications.
Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155–177.
Hull, T. H., Miles, R. H., & Balka, D. S. (2012). The common core mathematics standards: Transforming practice through team leadership. Thousand Oaks: Corwin Press.
Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 503–510). New York: Springer.
Manouchehri, A., Yao, X., & SaÄŸlam, Y. (2017). Mathematical modeling for teaching: An exploratory study. In E. Galindo & J. Newton (Eds.), Proceedings of PMENA 29. Indianapolis: Hoosier Association of Mathematics Teacher Educators.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author.
Pirolli, P., & Russell, D. M. (2011). Introduction to this special issue on sense-making. Human-Computer Interaction, 26, 1–8.
Rogers, E. M. (2003). Diffusion of innovation (4th ed.). New York: The Free Press.
Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. In J. Watson & K. Beswick (Eds.), Proceedings of MERGA30 (Vol. 2, pp. 688–707). Adelaide: MERGA.
Weick, K. E. (1995). Sense-making in organizations. Thousand Oaks: Sage.
Weick, K. E. (2015). Ambiguity as grasp: The reworking of sense. Journal of Contingencies and Crisis Management, 23(2), 117–123.
Weick, K. E., Sutcliffe, K. M., & Obstfield, D. (2005). Organizing and the process of sense-making. Organization Science, 16(4), 409–421.
Zbiek, R., & Conner, A. (2006). Beyond motivation: Exploring mathematical modeling as a context for deepening students’ understandings of curricular mathematics. Education Studies in Mathematics, 63, 89–112.
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Abel, T., Searcy, M.E., Salinas, T.M.L. (2020). Sense-making with the Mathematical Modelling Process: Developing a Framework for Faculty Practice. In: Stillman, G.A., Kaiser, G., Lampen, C.E. (eds) Mathematical Modelling Education and Sense-making. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-030-37673-4_11
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