Dual Modelling Cycle Framework for Responding to the Diversities of Modellers

Abstract

The modelling cycle (e.g., Blum and Leiß How do students and teachers deal with modelling problems? In: Haines C, Galbraith P, Blum W, Khan S (eds) Mathematical modelling (ICTMA12): education, engineering and economics. Horwood, Chichester, pp 222–231, 2007) contains the repeated processes that modellers are asked for in deepening their thinking. When we investigate the modelling cycle of modellers, we have to consider the diversities of various modellers in their modelling progress (Blum and Borromeo Ferri J Math Model Appl 1(1):45–58, 2009). In addition, problems or tasks can be changed from the initial real situation and problem with the aim of meeting the need of modellers. In this chapter, we make two modelling cycles parallel and focus on interactions between cycles, and call it the dual modelling cycle. We show three types of modelling cycles based on the dual modelling cycle framework through the example of one modelling cycle based on an Oil Tank Task, and another modelling cycle based on a Toilet Paper Tube Task.