Albert Einstein had an interesting account of his school experiences in his longest autobiographical writing, the introductory section of a book I grew up having in my home library (because my dad bought the book when he was a student of the philosophy of science).
http://learninfreedom.org/Nobel_hates_school.html
The examination system that Einstein encountered as a student in Switzerland actually allowed him to spend minimal time getting ready for examinations and most of his time independently pursuing his interest in physics. As Einstein wrote, "There were altogether only two examinations; aside from these, one could just about do as one pleased." If his school grades had been based more on daily homework assignments (as in the United States), then he probably would have seen his "holy curiosity of inquiry" entirely strangled by the school system, to use his words.
If passing the exams requires spending most of your school time preparing for them, it's a very different situation.
I did have a few project-based science courses, based more on having to propose something and justify your proposal, rather than giving a pre-determined answer. But I wasn't able to find more than a handful of those, and they tended to only be senior-level elective seminars, with a small number of students. I would guess the trend towards large, lecture-based courses (whether in-person, or MOOCs) will make them even more rare.
When your just starting out its harder, you can't say "explain the impact of European colonization on the Americas" you have to say "When did Columbus discover America?" and yes, poor educators sometimes try to give multiple choice exams because it is easier for them, but that doesn't say anything about the need to measure the effectiveness of the child at learning the material.