A teacher 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 independent means of, independent thinking.
O'Brien, Thomas C.; Wallach, Chris; and Mash-Duncan, Carla
"Problem-Based Learning in Mathematics,"
The Mathematics Enthusiast: Vol. 8
, Article 7.
Available at: http://scholarworks.umt.edu/tme/vol8/iss1/7