1. Be interested in your subject. |
Abbi interesse per la tua materia. |
2. Know your subject. |
Conosci la tua materia. |
3. Try to read the faces of your students; try to see their expectations and difficulties; put yourself in their place. |
Cerca di leggere sul viso degli studenti; cerca di capire le loro aspettative e le loro difficolta'; mettiti al loro posto. |
4. Realize that the best way to learn anything is to discover it by yourself. |
Tieni conto che il miglior modo per imparare qualsiasi cosa e' di scoprirla da soli. |
5. Give your students not only information, but know-how, mental attitudes, the habit of methodical work. |
Dai ai tuoi studenti non soltanto informazioni, ma anche sapere-come, attitudini mentali, abitudine al lavoro metodico. |
6. Let them learn guessing. |
Fai loro imparare a congetturare. |
7. Let them learn proving. |
Fai loro imparare a dimostrare. |
8. Look out for such features of the problem at hand as may be useful in solving the problems to come – try to disclose the general pattern that lies behind the present concrete situation. |
Cerca quegli aspetti del problema in questione che possono essere utili per problemi futuri - cerca di mettere in evidenza lo schema generale che sta dietro la situazione concreta presente. |
9. Do not give away your whole secret at once - let the students guess before you tell it - let them find out by themselves as much as is feasible. |
Non rivelare immediatamente tutto quello che sai e devi spiegare agli studenti - fallo congetturare dagli studenti prima di dirlo - fai loro scoprire, da soli, quanto piu' e' possibile. |
10. Suggest it; do not force it down they throats. |
Suggeriscilo; non forzarlo. |
La traduzione italiana del 1971 e' di Pietro Canetta. Su questa traduzione sono state fatte delle libere modifiche da L. Tomasi.
A quote from Polya regarding teaching in general :
Teaching is not a science; it is an art. If teaching were a science there would be a best way of teaching and everyone would have to teach like that. Since teaching is not a science, there is great latitude and much possibility for personal differences. ... let me tell you what my idea of teaching is. Perhaps the first point, which is widely accepted, is that teaching must be active, or rather active learning. ... the main point in mathematics teaching is to develop the tactics of problem solving.