C. Jordán, A. Cordero, J.R. Torregrosa

Universitat Politècnica de València (SPAIN)
It is a fact that society has changed a lot in the last years and our pupils, as part of it, too. The change is appreciated year after year, but is very noticeable if we look a few years back. This society with its new technologies causes that the situation in the classroom is very different from not long ago.

Overall, it has changed the attitude of the student in front of what is taught to him, for them previous direct motivation is totally needed to study, work capacity has gone down, also the depth that different issues are discussed with. Online search leads to do an analysis very quickly, jumping from one thing to another, without stopping enough time in any of them. The ability of a correct reasoning and a good understanding have been become secondary aspects, the goal is to obtain solutions quickly by using some established method, by applying something that surely the students have found in the Web. Then, we often find that, faced to a math problem for which a guideline has not been given, students stand around not knowing how to do. They have not strategies to implement because nobody has taught them such kind of approach.

That is the reason why our math classes should serve, more than ever, to lay the foundation of reasoning, to show them to be critical, to tackle problems, whatever type they are. We must repeatedly explain the mechanisms that, subconsciously, we use when we begin to solve a problem although it may seem trivial to us, only common sense. We should not give them guidance, which is what they expect, but emphasize the understanding of the statement, to translate it into their own words, to relation with concepts that they know, to take into account the different possibilities of approaching the problem, ...

When we have been working with the statement for a while, before starting to solve the problem, we remind them that actually the only we have done is to think in it in order to clarify and structure it. Asking them if they would have done the same, we will find that the most of them will tell us surprised "No".

[1] de Guzmán, M., Cómo hablar, demostrar y resolver en Matemáticas, Ed Anaya, 2004.
[2] Polya, G., Cómo plantear y resolver problemas, Ed. Trillas, 1989
[3] Scheinerman, E.R., Matemáticas discretas, Ed. Thomson Learning,2001