Task Mathematical Modelling Design in a Dynamic Geometry Environment: Archimedean Spiral’s Algorithm

Over the last twenty years, several research studies have recognized that integrating, not simply adding, technology (Computer Algebra System - CAS, Dynamic Geometry Software - DGS, spreadsheets, programming environments, etc.) in the teaching of mathematics helps students develop essential understandings about the nature, use, and limits of the tool and promotes deeper understanding of the mathematical concepts involved. Moreover, the use of technology in the Mathematics curricula can be important in providing the essential support to make mathematical modelling a more accessible mathematical activity for students. This paper presents an example of how technology can play a pivotal role in providing support to explore, represent and resolve tasks of mathematical modelling in the classroom. Specifically, a mathematical modelling task design on the tracing of Archimedean spiral with use of a Dynamic Geometry Environment is shown. The aim is to emphasize the meaning and the semantic value of this rich field of study that combines tangible objects and practical mechanisms with abstract mathematics.