I think math is somewhat special in that it isn’t about solving specific problems, but about learning to recognize patterns, and that the tests don’t check whether they know the patterns, but whether they can apply those patterns to problems that they need not even have ever seen.
In many other disciplines applying what students learned to things they’ve never seen before isn’t really possible.
For example, you can teach students what factors were needed to start the Industrial Revolution and why, but then, to answer “why didn’t the Industrial Revolution start in the 1750s in South America?” students would have to know about South America in the 1750s. If they don’t, all they can answer is “it must be because not all of the prerequisites foo, bar, baz, … were available, but I wouldn’t know which one(s)”.
Because of that, that question isn’t better than the dull “why did the Industrial Revolution start where and when it started?”, the answer to which can be learned by rote learning.
I would say that studying history is almost defined by rote memorization. Once a pattern emerges, you're not studying pure history but rather historical economics or sociology or something else. Things don't usually fit neatly into pure categories but I can imagine well written tests for pretty much any subject that require extrapolation or speculation of some kind, except "pure history".
You make a good point. I believe that there are ways to get students outside of maths to apply what they've learned to things they haven't seen before, though it won't be as novel or challenging as a maths exam. In history for example, you could have students analyze primary sources they've never encountered, which would require them to apply their knowledge of the context to something novel. Definitely more challenging than in STEM though.
In many other disciplines applying what students learned to things they’ve never seen before isn’t really possible.
For example, you can teach students what factors were needed to start the Industrial Revolution and why, but then, to answer “why didn’t the Industrial Revolution start in the 1750s in South America?” students would have to know about South America in the 1750s. If they don’t, all they can answer is “it must be because not all of the prerequisites foo, bar, baz, … were available, but I wouldn’t know which one(s)”.
Because of that, that question isn’t better than the dull “why did the Industrial Revolution start where and when it started?”, the answer to which can be learned by rote learning.