Considerations on the use of mathematics in modeling activities.

This paper aims to investigate the following question: How do students use mathematics in modeling activities? With this purpose, the paper reports on mathematization and use of mathematics, and deals with empirical data with focus on modeling activities performed by students in the first year and in the fourth year of a degree in mathematics. After the description of a theoretical framework of modelling, what can be seen by means of a qualitative analysis is that the perception of messy world situations leads to idealization, and the idealized situation acts as the basis for mathematization in each activity. The mathematization in turn leads to different mathematics concepts, tools and procedures. The use of mathematics that students perform is anchored in their previous experiences, be it in their experiences with the concepts and tools of mathematics, or in their experiences with mathematical modeling practices. Besides that, after this process students have advanced and have expanded their knowledge and made significant progress by means of a balance between teacher guidance and students’ independence. Moreover, beyond mathematical knowledge, the research indicated that success in performing modeling activities also requires knowledge-based mathematical modeling anticipation. [ABSTRACT FROM AUTHOR]