OK. So, with that definition, what do you call the skill that controls the ability to memorize? And can that skill be improved upon?
The ability to create a memory functions on a physiological level which include hormones, neurotransmitters, and proteins, as well as nutrients for the support and growth of the cells in the brain. Because it functions at this level there is very little that can be done to improve upon the brain's physiology. Stress (sleep deprivation, environmental, and illness) reduces the normal functioning of the brain thereby limiting the ability to form new memories. As a result, the best way to improve upon your memory is simply to limit stress. You're not really improving it, you're simply reducing the factors that limit the ability to create memories. Also, a healthy diet does wonders for both the body and brain.
The teacher actually hands out charts to the students for them to keep track of how many times they do a [beginner level] specific skill (ex. play an open A) - literally with 10,000 boxes to check off... I thought it was a little silly. Not so much the idea of repeating because - like you said - your memory will store things for years to recall later, but to actually tally and tediously keep track of every skill needed for the violin?? Though I understand that the neurons connect with repetition and that it needs to happen many times, why isolate it like that? Why not play Twinkle, then Lightly Row, then several other pieces that require you to play an open A? Why make a child aware of all the repetition? When I teach, I am always coming up with creative ways to get repetition out of my students without them realizing that that's what I'm doing.
There are psychological experiments that have tested exactly what you've described, isolated practice and liberal practice, to figure out which works best. The results:
Isolated practice improves individual skills quickly but combining skills takes much longer.
Liberal practice takes less time to combine skills, but individual skills do not improve as much.
In the long term, even though isolated practice takes much longer, the effects of learning last significantly longer while skills developed through liberal practice tend to fade quicker.
If you are limited in time, say a student who has only some interest but not a lot, then a liberal approach would work best because the student will learn a lot in a short amount of time, perhaps enough to increase his interest. However, for a student who is already interested, then isolated practice is the more effective approach.
To answer your question about keeping track of each skill: it's actually quite important at the cognitive level to be aware of all the minute details. Imagine asking a young child to draw a picture of a woman. It will most likely be quite bad. Now if you compare this drawing to the
Mona Lisa, da Vinci's painting is quite beautiful. It is full of details even down to the individual hairs of the brows. (The painting appears to have no eyebrows because the paint has faded over the centuries.) If you were a museum curator, which picture would you hang on the wall? For this reason, the details matter incredibly. It allows the student to focus on individual aspects which can latter be recalled for use with ease.
But I also believe that people remember in different ways. For example, the son I mentioned thinks visually, like me. His younger brother remembers audially. So, for him, repeating lines over and over does not take very long at all before he remembers it. Another example is how my husband will say a phone number over and over until he starts dialling. I do much better by looking at it for a few seconds and then I can imagine it written on the paper to recall the numbers.
Unfortunately, the idea that we are visual, auditory, or kinesthetic learners (memorizers) is a myth. This myth pervades current education practices and is very difficult to put out because it appears to make sense. If the neurological physiology were understood, it becomes very obvious why this is the case. Even in the psychological literature, there is very little evidence that supports multi-modality learning (memorizing.) The majority of experiments indicate that it doesn't matter how information is presented, just as long as it is remembered.
This is absolutely critical in understanding anything about learning and memory: LEARNING IS MEMORIZATION. Specifically, learning is the process in which you memorize. So if you've learned something, you've simply memorized it.
Memorization requires the act of attention. When teachers tell students to pay attention, they are speaking a truth far beyond anything they themselves understand. Without paying attention, it won't become a memory. The examples you've described about being auditory or visual memorizers are different ways to remember but this does not validate multi-modal learning. A persons visual cortex is far larger than the auditory cortex. (Look at the brain's anatomy and this will be clear just how much larger it is.) If so much of the brain is devoted to processing sight and so little to sound, wouldn't everyone be a visual learner? The answer is: yes. Mnemonic techniques uses almost exclusively visual cues to make information more memorable.
I'm tired. I'll have to finish this later.