Mathematical modelling

Mathematical modelling can be understood as solving realistic, open problems by means of mathematics. Teaching mathematical modelling at school is supposed to enable pupils to apply mathematics in their daily lives, thus giving them a better understanding of the world they live in and a better understanding of the utility of mathematics (Niss et al. 2007). When modelling a so-called modelling process (Niss et al., 2007) has to be carried out. Based on Blum and Leiss (2005, p. 19), we conceptualize the following steps of the modelling process: (1) understanding the instruction and the real situation (situation model); (2) making assumptions and simplifying the situation model (real model); (3) mathematizing the real model (construction of a mathematical model); (4) working within the mathematical model (mathematical solution); (5) interpreting the solution; (6) validating the interpreted solution. The modelling process may be illustrated by the following scheme (Blum & Leiss, 2005). (see also Mischo & Maaß 2013).

For a more in-depth discussion of modelling, please refer to Mischo & Maass (2013), Artigue & Blomhoej (2013) and Niss et al. (2007).

 

References

Blum, W., & Leiss, D. (2005). Modellieren im Unterricht mit der „Tanken“-Aufgabe [Modelling in class with the “Refueling” task]. Mathematik lehren, 128, 18-21.

Mischo, C. & Maaß, K. (2013). Which personal factors affect mathematical modelling? The effect of abilities, domain specific and cross domain-competences and beliefs on performance in mathematical modelling. Journal of Mathematical Modelling and Application, 1(7), 3-19.

Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 3-32). New York: Springer.

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