Daniel Grubb <email@example.com> wrote: > >>>a significant role. They often stumble because (among other problems) >>>they don't realize they need to _memorize_ definitions _precisely_. > >>Memorize? I can't remember ever memorizing anything. Better just to >>practice until you understand. Discuss, ask questions, apply. That way >>you memorize, of course, but that's just a side-effect. > > No, for proof classes, which linear algebra is in many places, > it is crucial to *memorize* the definitions. This holds for > all the proof classes at higher levels also. There is simply no > way of giving rigorous proofs if you don't know the actual > definitions. All too often, students have some very vague ideas > of what is going on and then can't even get started on a proof > because they don't know the *exact* definiton used in the course.
No disagreement here. Perhaps Thomas only meant to warn against blind memorization without understanding. This way a student would end up with the ability to repeat the memorized definition but nothing else. This danger is even greater, when those definitions are memorized as isolated entities, without checking them against examplex, counterexamples and proofs.