On these Dante aspects (1989), it affirms that a problem is any situation that demands thinking of the citizen to solve it and that problem-mathematician is any situation that demands the mathematical way of to think about mathematical knowledge to solve it. With regard to the didactic conception one knows that … essential in the mathematical learning is to construct the direction of the knowledge and that the resolution of problems is an indispensable activity … in the reflection on what was made: the employed procedures and the involved knowledge must be become into reflection object. … This reflexiva activity will enrich, reciprocal, the future resolutions of all the pupils. (PANIZZA, 2006, p.113) Many times, exercise with problem is confused, is necessary to know to differentiate one of the other to get proper resolutions for each one of them, in the majority of the cases they is applied as if they were one only.
The exercise is an used activity to train what already it was learned, using some type of mathematical knowledge acquired by the pupil. Already the problem is necessary a more complex reasoning involving an invention or even though the creation of answers significant for each situation. Despite good part of the Mathematics if destines the application of algorithms to decide problems, we live today in an age circulated for electronic inventions that the resolution of these problems facilitates, but in what it says respect to the learning, with the manuscript of these electronic artifices what would be responsible to teach, makes with that the use of these algorithms is mere mechanized, leaving of side the uses of adequate strategies. It is in this manner that adopting … a point of view based on strategies, we will have of having in them with some critical questions: 1) What techniques we will use in the resolution of problems? 2) That strategies of resolution of problems we will use in the pertaining to school mathematics? 3) How we will be able to stimulate the resolution of problems in the classroom?