A great discovery solves a great problem, but you can find a grain of discovery in the solution of every problem. You can have a modest problem in front of you; but if it will arouse your curiosity and put into play your faculties of inventiveness, and if you solve that problem by your own without any external help, then you can feel the tension before discovery and you can enjoy the triumph of its creation. Such experiences, at an age where you have maximum receptivity, can create the taste for the intellectual work putting its imprint on the mind and the character for life.
In these conditions the Math teacher has great possibilities. If he fills his time by reprimanding his students with routine operations, he kills their interest, he hampers their intellectual development and he uses really bad his great possibilities. But if he arouse their curiosity, proposing problems which are proportional with their knowledge and if he helps them to solve the problems by stimulating questions, he can inculcate them a taste for independent thinking and suitably develop their aptitudes.
The student whose program also includes a math course, has big possibilities. Of course, these possibilities loose themselves, if he considers Math just an object in which he just needs to give a certain number of exams and and that he will forget as soon as possible after the graduation exam. These possibilities also can be lost in the case when the student has
certain natural skills for mathematics, because, just as any other one, he must discover his talents and his tastes; he doesn't know if he likes the pudding with raspberries in case he never tasted before. But he can get to find that a math problem can be just as captivating as solving a crossword puzzle or that a strained intellectual work can represent an exercise so appropriate as a tennis match. After he has tasted the pleasure of mathematics, he will never forget it easily and exists then big chances that mathematics may come to mean something to him: an amateur concern, an instrument in his profession, maybe even his profession or a big ambition.
When I was a student I was eager to understand a little bit of Math and Physics. I was listening to lectures, reading books, I was searching to assimilate solutions and facts that were presented to me, but there was a question which always troubled me: " Yes, the solution seems to work, makes the impression that is correct; but how can be invented such a solution? Yes, this experiment seems to achieve his goal, it shows like a fact; but how can people discover such facts? And how can I invent or discover myself this kind of things? ". I imagine or hope that some of the students with more thirst for knowledge put themselves similar questions and, for this reason, I am trying to satisfy their curiosity. Searching to understand the solution of such and such problems, also the motivation for the solution found and the processes by which it was obtained, I can explain to others also my findings. The interest to discover or invent seems more widely spread than at first glance. The space that the newspapers and the magazines for the general public give to crossword puzzles and other games seems to show that people spend some time to solve problems without practical value. At the base of this wish to solve different problems which do not give material advantages can stay a more profound curiosity, a desire to understand the ways and meanings, themotivations and solution procedures. Thank you
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