# “Real World” Problems

## by Lucia Doretti

### Department of Mathematics and Computer Science, University of Siena, Italy

### INTRODUCTION

We consider it important that pre-service teachers master both mathematical problem solving and the choice and analysis of problems, together with the way of posing them in the classroom, so that pupils’ thinking processes may be better stimulated. The teacher must make several decisions about the organisation of their own teaching: these relate to the choice and systematisation of ‘good’ problems, the management of pupils’ personal solutions in the sharing phases (discussion), the possible ways for making these personal solutions evolve towards expert solutions, which are the main goal. In this context, a priori analysis becomes one of the professional tools helping teachers to formulate their choices and decisions (Charnay, 2003). The “Real world” problems proposal sits within a set of activities that stimulate work with problems starting from a suitable a priori analysis, in order to identify the mathematical concepts at stake and to determine whether, how and with what aims they can be used in teaching. The proposal provides an opportunity to select at least one of the suggested set of three problems “What a family!”, “Bizarre colouring” and “The pursuit”, taken from the RMT – Rallye Mathématique Transalpin (Transalpine Mathematical Rally).

**Main Piloting **
- by Lucia Doretti

**Second piloting **
- by Marie Hofmannová and Jarmila Novotná

*Faculty of Education, Charles University in Prague, Czech Republic*

**Third piloting (at the Catholic University in Ružomberok, SK) and conclusion**
- by Lucia Doretti