Abstract:

The recommendation (2006/962/EC) of the European Parliament on key competences for lifelong learning define Mathematical competence as "the ability to develop and apply mathematical thinking in order to solve a range of problems in everyday situations, with the emphasis being placed on process, activity and knowledge".

This aim implies a radical renewal of the teaching practice and promotes an education based on mathematical modeling. In Italy the problem is strongly felt by the School.

A dynamic interaction between the real world and mathematics is the proposal of Mathematics & Real life (M&R), Department of Mathematics and Informatics of the University of Perugia (http://www.matematicaerealta.eu), a project of which we are creators and animators. M&R is operative since 1994 and involves every year about 3500 students and more than 150 teachers. M&R's key word is: education to mathematical modelling.

With the aim of spreading its proposal, M&R organizes many activities devoted to Schools of all levels, from Primary School to University.
We only mention here proposals to the teachers: training courses, laboratories of educational research, dissemination of innovative educational materials; activities for students: laboratories of math training, games, national competitions.
- the Mathematical Models Games now in its sixth year, is an individual competition which has involved more than 13.500 young people. It takes place in two phases (local selection and national final) and is inserted by the Ministry of Education in the activities for the promotion of excellence;
- the Creative Mathematical Relay in its second year, is a group competition, where the participants become also authors and judges, not just beneficiaries of the event. The materials produced during the competition reveal significant educational meaning;
- the Competition in Mathematics Communication which reached the nineteenth year, takes place during the year-end national meeting.

Groups of students, in 15 minutes, present to a large audience of young people and teachers their original contribution to mathematical popularization (developed under the guidance of the teachers). Every year more than 40 communications from any school level contain the prizes.

Our contribution to the meeting is to share this experience with Colleagues of different countries presenting in more details M&R's activities and their great teaching potential.

Keywords:

Mathematical skills, elementary mathematical models, mathematical games and didactical innovation.