When we say that someone has “learned” a subject, we typically mean that they have shown evidence of mastery not only of basic cognitive processes like factual recall and working mechanical exercises but also higher-level tasks like applying concepts to new problems and judging between two equivalent concepts. A student learning calculus, for instance, needs to demonstrate that s/he can do things like take derivatives of polynomials and use the Chain Rule. But if this is all they can demonstrate, then it’s stretching it to say that the student has “learned calculus”, because calculus is a lot more than just executing mechanical processes correctly and quickly.
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