Towards Applied Problem Solving

We present the guidelines and the first results of a research, carried oui with 11-12 year olds, aimed at improving their ability to mathematicize problem situations and to improve their attitude and performance when faced with "the problem". The research is based on a certain number of key problems which depict realistic situations and in which the pupils are required to understand which are the questions to be asked, which are the relevant data and the difficulty or cost involved in obtaining them. Furthermore, the problems are presented in such a way as to induce the pupils to "optimise" their solution methods. The first results show that the pupils acquire a broader understanding of the concept of "the problem" and acquire the ability to approach it hypothetically, thereby enhancing their metaknowledge and improving their ability to solve problems.