This offers a way to solve the contradiction. As a theoretical position, we think that we must follow the Charity principle as defined by Quine and Davidson7, considering that thefact that a pupil is illogical is less probable than a misunderstanding. On an other hand, we can see here that the teacher insists on the fact that a sentence with a counter-example is false (In mathematic, it’s like this !) ; however, M. who tries to “save” the truth of the sentence by reducing the domain considered is not so far from mathematical practice ; indeed, it is quite relevant to look the truth value of the sentence in a structure which domain is N minus all the 11’s multiples. According with this point of view, it is possible to change this kind of situation, proposing open sentences, and asking for the largest domain on which the sentence is true; in this case, pupils can’t give a definitive answer, because they can’t characterize examples and counterexamples ; but in other cases, such a question may lead to elaborate one, or two, or more theorems