In fact those to whom we think we are not problems but exercises.
The problems in fact, to be solved, require productive thinking,
while the exercises require a type of reproductive thinking.

The debate on the problems in the school is not new, already in the 40's Ernesto Codignola he wrote:
"It should be avoided at all costs the problem-normal type, school, unreal, of which only the teacher holds the only solution, and that is, for the pupils, a training of the most make stupid"

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This what it says Dario Antiseri:

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The problem ... is also the primum teaching.
The problem is the foundation of motivation to research.
Is the problem that transforms the local school of boredom and pain where you give answers to questions not posed in "research center"

... But where are the "problems" in a textbook? ... Are at the bottom of the text ... They, in fact, are not problems but exercises ... the young man should not find out anything, because everything has been discovered; should not use fantasy, you should not go wrong. He must not be a discoverer, but only a performer.

Conversely, if you stumble into a problem, runs into a question in which he has no answer yet, his mind must try. All this triggers the imagination, forces her to make assumptions to find solutions.

While a problem encourages research, operating the locks

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D.ANTISERI, Teoria e pratica della ricerca nella scuola di base, La Scuola, Brescia, 1985

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But then, we, at school, we have always given exercises and never problems?
I say that at school we treated them and treat them with the problems but you can do better ...
for example, all those exercises that are in the books, and we call problems, but problems are not, can be transformed easily in activities that foster and cultivate ability to productive rather than reproductive thinking.