How it is possible to make real-world mathematics more visible: some results from two Italian Projects.

In this contribution we will present some results of two ongoing Italian projects, the first aimed at primary schools, the second at high schools. The first project is articulated in some teaching experiments using suitable cultural artifacts, interactive teaching methods and new socio-mathematical norms in order to create a substantially modified teaching/learning environment. The focus is on fostering a mindful approach toward realistic mathematical modelling and applications of mathematics, as well as a problem posing attitude, even at the primary school level. The second project is part of a national project launched in 2005 sponsored by the Italian Ministry of Education, in cooperation with the Faculties of Science of the Italian Universities and the Confederation of Italian Industries. Its main purpose is to encourage high-school graduates entering Universities to apply for degrees in the \u201chard\u201d sciences, including Mathematics, Physics, and Chemistry