About the role of real-world knowledge and experiencesin mathematical modelling

In this paper we will discuss some teaching experiments that consist of a series of classroom activities in upper elementary school based on the use of suitable artifacts, interactive teaching methods and new socio mathematics norms in order to create a substantially modified teaching/learning environment. Through these studies we can show how an extensive use of suitable artifacts, with their incorporated mathematics, can play a fundamental role in bringing students’ out-of-school reasoning and experiences into play, by creating a new tension between school mathematics and real world with its incorporated mathematics. The focus is on fostering a mindful approach toward realistic mathematical modelling, problem solving and also a problem posing attitude. We feel that it is not only possible but also desirable even at the primary school level to introduce early on fundamental ideas about modelling. We also argue for modelling as a means of recognizing the potential of mathematics as a critical tool to interpret and understand reality, the communities children live in, and society in general. An important aim for compulsory education should be to teach students to interpret critically the reality they live in and understand its codes and messages so as not to be excluded or misled.