Problèmes, exercices, apprentissage, science et technologie

J'avais oublié ces mots assez justes :

A great discovery solves a great problem, but there is a grain of discovery in the solution of any probel. Your problem my be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. Such experiences at a susceptible age may create a taste for mental work and leave their imprint on mind and character for a lifetime.
THus, a teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations, he kills their interests, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowlege, and helps them to solve their problems with stimulating questions, he may give them a taste for, ans some means of, independent thinking.
Also a student whose college curriculum includes some mathematics has a singular opportunity. This opportunity is lost, of course, if he regards mathematics as a subject in which he as to earn so and so much credit, and which he should forget after the final examination as quickly as possible.

How to solve it, G. Polya, Princeton University Press, Princeton, New Jersay, 1945.

Je discute toutefois la confusion entre mathématiques et calculs.