Modelling as Interactive Translations Among Plural Worlds: Experimental Teaching Using the Night-Time Problem

Abstract

This case study examines the advantages in interpreting students’ modelling from the perspective of interactive translations among plural worlds. This perspective has greater pedagogical potential than a simplified perspective which treats mathematical modelling as involving transitions only between two fixed worlds – a real world and a mathematical world. Experimental lessons with the Night-Time Problem for Japanese 10th grade students were held over a period of 100 min, using a structured investigation. As a result, the following two advantages are exemplified. The first enables a teacher to direct attention to intermediate models which can help students build further abstract models, and the second focusses attention on meaningful contradictions to help students to verify/critique/modify their original models.