Evidence of a Dual Modelling Cycle: Through a Teaching Practice Example for Pre-service Teachers

Abstract

A proposed dual modelling cycle is illustrated with a typical dual modelling cycle example. The purpose is to verify some stages of a dual modelling cycle. In a typical case, the dual modelling cycle indicates switching between two modelling cycles, for example between those for an Oil Tank Task and a Toilet Paper Tube Task. Some modellers might imagine a toilet paper tube from an Oil Tank Task because the tank shape and the spiral banister are similar to an intact toilet paper tube and when it is slit, respectively. Verification methods are (1) to conduct experimental classes for pre-service teachers, and (2) to analyse their worksheets for evidence of the dual modelling cycle. We confirm that the intended transition to answer the initial Oil Tank Task was enabled by consideration of the other model/situation.