Abstract
In this theoretical chapter, we draw on a models and modelling perspective on teaching and learning to elaborate on the components of model development sequences using the lens of variation theory. We give empirical examples of how model exploration activities and model application activities can be described and understood from a variation theory perspective. The chapter concludes by presenting tentative principles for the design of such activities within a model development sequence.
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References
Ärlebäck, J. B., Doerr, H. M., & O’Neil, A. H. (2013). A modelling perspective on interpreting rates of change in context. Mathematical Thinking and Learning, 15(4), 314–336.
Barquero, B., Bosch, M., & Gascón, J. (2007). Using research and study courses for teaching mathematical modelling at university level. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the fifth congress of the European Society for Research in Mathematics Education (pp. 2050–2059). Larnaca: University of Cyprus.
Barquero, B., Serrano, L., & Serrano, V. (2013). Creating necessary conditions for mathematical modelling at university level. In B. Ubuz, C. Haser & M. A. Mariotti (Eds.), Proceedings of the eighth congress of the European Society for Research in Mathematics Education (pp. 950–959). Antalya: Middle East Technical University.
Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects: State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.
Chevallard, Y. (2004, May). Vers une didactique de la co disciplinarité. Notes sur une nouvelle épistémologie scolaire. Paper presented at Journées De Didactique Comparée, Lyon. Retrieved from yves.chevallard.free.fr/spip/spip/article.ph3?id_article = 45
Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the IVth congress of the European Society for Research in Mathematics Education (pp. 22–30). Barcelona: Universitat Ramon Llull Editions.
Diefes-Dux, H. A., Hjalmarson, M. A., Zawojewski, J. S., & Bowman, K. J. (2006). Quantifying aluminum crystal size part 1: The model-eliciting activity. Journal of STEM Education: Innovations and Research, 7(1&2), 51–63.
Dominguez, A., Zavala, G., & Alanis, J. A. (2013). Integrated physics and math course for engineering students: A first experience. Proceedings of the American Society for Engineering Education Annual Conference and Exposition, Atlanta.
Dominguez, A., de la Garza, J., & Zavala, G. (2015). Models and modelling in an integrated physics and mathematics course. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 513–522). Cham: Springer.
Galbraith, P. L., & Clatworthy, N. J. (1990). Beyond standard models – Meeting the challenge of modelling. Educational Studies in Mathematics, 21(2), 137–163.
Iversen, S. M., & Larson, C. J. (2006). Simple thinking using complex math vs. complex thinking using simple math – A study using model eliciting activities to compare students’ abilities in standardized tests to their modelling abilities. ZDM, 38(3), 281–292.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310.
Kaput, J., & Roschelle, J. (1996). SimCalc: MathWorlds [Computer software].
Ko, P. Y., & Marton, F. (2004). Variation and the secret of the virtuoso. In F. Marton & A. B. M. Tsui (Eds.), Classroom discourse and the space of learning (pp. 43–62). Mahwah: Erlbaum.
Lesh, R. A., & Doerr, H. M. (2003a). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Mahwah: Erlbaum.
Lesh, R. A., & Doerr, H. M. (Eds.). (2003b). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah: Erlbaum.
Lesh, R. A., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763–804). Greenwich: Information Age Publishing.
Lesh, R. A., Hoover, M., Hole, B., Kelly, A. E., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591–645). Mahwah: Erlbaum.
Lesh, R. A., Cramer, K., Doerr, H. M., Post, T., & Zawojewski, J. S. (2003). Model development sequences. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 35–58). Mahwah: Erlbaum.
Lo, M. L. (2012). Variation theory and the improvement of teaching and learning (Gothenburg studies in educational sciences 323). Göteborgs: Acta Universitatis.
Marton, F. (1994). Phenomenography. In T. Husén & T. N. Postlethwaite (Eds.), The international encyclopedia of education (2nd ed., pp. 4424–4429). Oxford: Pergamon.
Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah: Erlbaum.
Marton, F., & Tsui, A. (2004). Classroom discourse and the space of learning. Mahwah: Erlbaum.
Marton, F., Runesson, U., & Tsui, A. B. M. (2004). The space of learning. In F. Marton & A. B. M. Tsui (Eds.), Classroom discourse and the space of learning (pp. 3–40). Mahwah: Erlbaum.
Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI study (pp. 3–32). New York: Springer.
Runesson, U. (2005). Beyond discourse and interaction. Variation: A critical aspect for teaching and learning mathematics. Cambridge Journal of Education, 35(1), 69–87. doi:10.1080/0305764042000332506.
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.
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Ärlebäck, J.B., Doerr, H.M. (2015). Moving Beyond a Single Modelling Activity. In: Stillman, G., Blum, W., Salett Biembengut, M. (eds) Mathematical Modelling in Education Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-18272-8_24
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DOI: https://doi.org/10.1007/978-3-319-18272-8_24
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