Exams mean nothing. That goes for math as well as they are merely a test. Not research to find a new theory or anything. And it is certainly needed on exams to get inside heads of the more important people of history.
But those exams are what count for your grades. At least the history-related high school and undergraduate exams I took were all about regurgitating facts out of the textbook by writing essays, and after which you could proceed to forget everything.
Of course, a history course of that type would be quite cool (e.g. thinking about what might have happened in history if certain events had been different), but I have never really heard of such a thing as widespread.
The curricula too is not as you say it is. The courses of study of history need more creativity then you think. Theories have to be made up just as in math. The only difference is that with math you cn check them and with History you can't. You need more creativity to create such a theory. And yes you can use data from your history books to prove those theories but that is exactly the same as math.
That is what I am saying; since no theory can be easily proved or even tested, any theory becomes correct to some extent and the number of acceptable theories on exams grows much larger. In math you can't do such things because there are precise rules on what is correct and what is not.
With math you learn and learn. Same as history. You learn cold hard facts. However, with history you cannot use one fact to create another, no. You need to create whole NEW facts if you wish to make discoveries.
Exactly; that first part is what I am saying. Many subjects are like this in the current academic structure even if the research is all good (some fields are genuine BS, but not the ones we are talking about). But how exactly do you "create" a fact in history?
Or do you mean propose a new theory?
If its so precise you don't need the creativitry to create whole new facts. You can use the facts you have for new theories based on previous facts.
It is the usage of those facts in the appropriate way that requires the creativity since there are infinities of them, but at the same time you cannot put out anything other a strict truth. There is no general method for discovering/proving a formula but there are ways to check the validity of the formula or its proof, which is what causes the difficulty.
Basically, we can argue over this endlessly as we are dealing with 2 different kinds of creativity here. And each kind is as valueble as the other and needed in equal quantaties but in different ways that cannot be compared. 
I think the two are the really same thing, but anyway I can never pass up a chance to hit out against the education systems, which I think are the single worst aspect of the world today.
And at any rate, arguing rules.
