Abstract
A model is generally assumed to be built by translating a real world problem into a mathematical representation. We attempt to re-construct this interpretation and point to at least two distinct meanings: (Role 1) models as hypothetical working spaces, and (Role 2) models as physical/mental entities for comparing and contrasting. This leads us to draw attention to four different perspectives of modelling: (a) where modelling is interpreted as interactive translations among plural worlds not between two fixed worlds; (b) where models have the potential to incorporate scenarios beyond the initial problem situation; (c) where the mathematical world is used as a source of mental entities for comparing and contrasting; (d) where modelling competency means knowing how to balance between these different roles. Perspectives (a) and (d) are concerned with Role 1 and (b), (c) and (d) are concerned with Role 2.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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.
Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (Eds.). (2007). Modelling and applications in mathematics education, the 14th ICMI-study. New York: Springer.
Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht: D. Reidel Publishing Company.
Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht: Kluwer.
Gravemeijer, K. (2007). Emergent modelling as a precursor to mathematical modelling. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 137–144). New York: Springer.
Hesse, M. B. (1966). Models and analogies in science. Notre Dame: University of Notre Dame Press.
Ikeda, T. (2013). Pedagogical reflections on the role of modelling in mathematics instruction. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 255–275). Dordrecht: Springer.
Ikeda, T., & Stephens, M. (1998). Some characteristics of students’ approaches to mathematical modelling in the curriculum based on pure mathematics. Journal of Science Education in Japan, 22(3), 142–154.
Ikeda, T., & Stephens, M. (2011). Making connections between modelling and constructing mathematics knowledge: An historical perspective. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 669–678). New York: Springer.
Ikeda, T., Stephens, M., & Wada, Y. (2012). A teaching experiment in modelling through scale reduction methods: A bridge to later trigonometric methods. Journal of Mathematics and System Science, 2(6–7), 359–367.
Kaiser, G. (1991). Application-orientated mathematics teaching: A survey of the theoretical debate. In M. Niss, W. Blum, & I. Huntley (Eds.), Teaching of mathematical modelling and applications (pp. 83–92). Chichester: Ellis Horwood.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310.
Kerr, D., & Maki, D. (1979). Mathematical models to provide applications in the classroom. In S. Sharron & R. E. Reys (Eds.), Applications in school mathematics, 1979 yearbook (pp. 1–7). Reston: The National Council of Teachers of Mathematics.
Lesh, R., & Yoon, C. (2007). What is distinctive in (our views about) models & modelling perspectives on mathematics problem solving, learning, and teaching? In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 161–170). New York: Springer.
Moscardini, A. (1989). The identification and teaching of mathematical modelling skills. In W. Blum, M. Niss, & I. Huntley (Eds.), Modelling, applications and applied problem solving (pp. 36–42). Chichester: Ellis Horwood.
Niss, M. (2008). Perspectives on the balance between applications and modelling and ‘pure’ mathematics in the teaching and learning of mathematics. In M. Menghini, F. Furinghetti, L. Giacardi, & F. Arzarello (Eds.), The first century of the international commission on mathematical instruction (1908–2008) reflecting and shaping the world of mathematics education (pp. 69–84). Rome: Encyclopedia Italiana.
Pinker, A. (1981). The concept ‘model’ and its potential role in mathematics education. International Journal of Mathematical Education in Science and Technology, 12(6), 693–707.
Skovsmose, O. (2005). Travelling through education-uncertainty, mathematics, responsibility. Rotterdam: Sense.
Skovsmose, O., & Nielsen, L. (1996). Critical mathematics education. In A. J. Bishop, M. A. Clements, C. Kietel, J. Kilpatrick, & C. Laborde (Eds.), First international handbook of mathematics education (pp. 1257–1288). Dordrecht: Kluwer.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Ikeda, T., Stephens, M. (2015). Reconsidering the Roles and Characteristics of Models in Mathematics Education. 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_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-18272-8_29
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18271-1
Online ISBN: 978-3-319-18272-8
eBook Packages: Humanities, Social Sciences and LawEducation (R0)