نبذة مختصرة : Mathematics occupies a privileged place in the educational system. It is one of the main disciplines in a learner's school life that allows him to develop problem-solving strategies and different learning abilities. Indeed, it is very important to make the learner to become active in the learning process of Mathematics. As a result, problem solving has become a crucial aspect. It helps the learner in the development of strategies for problem solving. Also, the learner must be adaptive to new situations from other disciplines or everyday life. In this study, we used the Georges Polya's "How solve it" guide and we applied it to solving some problems by insisting on the importance of applications in the teaching of Mathematics. We talked about the definition of the open problem and its educational objectives according to the IREM of Lyon. Then we discussed the activities by describing some difficulties encountered by the trainee teachers. These activities include: (1) A problem solved by three different methods: analytical geometry, GeoGebra software, and the Maple software to make a comparison of methods by practice; (2) Solving some open problems. We concluded this study by implementing problem-solving strategies and reasoning methods as tools for trainee teachers for "solving some open problems".
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