I started reading Polya's "How to Solve It" this morning and found some tasty gems immediately:
- "Thus, a teach of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking."
- "... overhearing Polya's comments to his non-existent teacher can bring that desirable person into being, as an imaginary but very helpful figure leaning over one's shoulder."
- "Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics."
- "... to teach mathematics well, one must also know how to misunderstand it at least to the extent one's students do!"
- "Experienced mathematicians know that often the hardest part of researching a problem is under standing precisely what that problem says. [...] 'If you can't solve a problem, then there is an easier problem you can't solve: find it.'"
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