It seems to me that many (perhaps most) teachers look favorably on methods that do not require of them any creative output. One of the favorite methods in an average teacher's repertoire is the principle of systematic work.

Systematic work is based on the old adage of practice makes perfect. This is what you say to little kids who want to be in the Olympics: you work hard and you can get there. And there is no reason to doubt that. The fact is that to be successful in sports requires an enormous amount of systematic work. However, there is one caveat that they don't mention - it only works if there is a limited amount of people doing this. If we all started working systematically, no matter how good we'd be, the Olympics wouldn't have space for 7 billion of us anyway. But I digress.

But if you look at it from a structural point of view, systematic work means brute force. So basically you work at it for as long as it takes, until it cracks. And sometimes this works. But it assumes that your understanding of the problem has some sort of linear behavior, so the more you work on it the more you understand. And that is by no means a law of nature.

It's much worse when the behavior is asymptotic. You can work on it forever and you still won't get it. To illustrate this, imagine there is a tree in your yard that is blocking your otherwise excellent view. You want that tree out of there. So you grab a rope and tie it to the tree. You take the other end and tie it to your bike. Now if the tree is a certain size, you can try all you want to pull it out of the ground, and the tree won't budge. Apparently, this simple fact is lost on some teachers. (For more on this read The Truth About Homework.)

Brute force often works, but it's the last resort and it's not the smartest way of solving a problem. To be able to work systematically in any sort of productive way you need to know more than just to work systematically, which is basically a synonym to the word repeat. If you find yourself in the middle of a lake, in a rowing boat, systematic work is no doubt your best strategy. But even then you have to set a course first. This is a question some teachers don't have an answer to. If they explain something and you don't understand it, then there must be something wrong with you and you need to "work harder". Since everything can be solved through systematic work, well there you go. You just need to help yourself.

What is worse is that sometimes you need to deliver creative solutions, either because the problem cannot be solved otherwise, or because that is the only way you can score a high grade. Now, creativity is the opposite of systematic work. I can easily imagine that systematic work originates from an earlier time when schools thought "teaching discipline" was an integral part of their business, and therefore if you're very disciplined you're going to be working systematically, it fits like a glove.

Now try combining that with creativity. Here I am working at something systematically and all of a sudden I have an idea "what if I tried to... no! I will not allow myself to be distracted, I have self discipline!" But it is interesting that teachers expect creativity when they themselves have no obligation to muster any. It's precisely those cases where something is hard to explain that you so desperately need the ability to think creatively and come up with a different description of the same thing. The best teacher I've ever had (high school, English) was also the most creative one I've seen.