Comment by openfuture

For me this is how I learned mathematics up until university. By just going unprepared to exams or doing extracurricular competitions and then "inventing the math" in the exam. In the case of competitions it was a bit more fun than exams which would still just be testing one or two ideas with a few examples but still it is in my opinion the more fun way to go about it. All these kids who were memorizing things, or studying the thing to death, a lot of them had trouble understanding what it was that they were doing.