I think it is a common mistake by people starting to learn for example an instrument. You play the new piece, often a bit too fast, and make a mistake. Then just repeat in the same way, making exactly the same mistake over and over again. The hope is that if you play it enough times and put in enough effort you will cease making the mistake. That is of course wrong. Instead you learn the mistake really really well.
What you should do is to play it slow enough so you are sure not to make any mistakes. Sometimes that is ridiculously slow.
Split the thing you are learning into chunks... making each chunk as small/simple/easy as you can.
Learn the chunks in reverse order. Starting with chunk N, then N-1, all the way to chunk 1. This way, you always start with the hardest part and then move onto the easier (more practiced) parts.
This keeps the focus on the part you are trying to learn, and reduces learning stress.
With memorizing numbers as well, splitting them into chunks is also a good tactic, for example 392619582767 -> 392 619 582 767. It makes the whole thing a lot more tractable.
agreed, practicing slow enough to get it right is the most important thing for sure. once thats in the bag, then the problem becomes getting it up to speed, and techniques you were using at the slow pace can be non-viable past certain tempos. for me, getting it up to speed involves constantly interspersing the slow flawless practice with attempts that are right on the threshold of what i can do, tempo wise.
That seems surprising. It's not like there's a discrete threshold between "able" and "too fast". I'm not a violin player, but just about anything I can play slowly on a bass or piano, I can also play quickly, given enough practice, even if it means I can only initially play it at quarter or third speed with a metronome. Aside from some virtuouso performances, I think any beginner/intermediate player with a decent ear and headphones/sheet can play any piece at quarter speed. It seems like muscle memory is one of those things you really can achieve through mindless repitition with good technique, while theory requires a lot more focused practice.
edit: Okay, disregard that, the above comment is completely different and I guess I agree now.
An example of the parent comment's point: learning a piece slowly but with poor fingering or posture can lead to one's fingers getting tangled or becoming exhausted and stiff when trying to speed up.
I read somewhere that good practice for music specifically involves playing the piece through fast, ignoring your own errors, playing it through slowly enough that you don't make an error (and repeating this until you don't make an error), and then playing it at the intended tempo. So to someone this is a well-known idea. Is it not part of standard music instruction?
I think the point of it is just to push you out of ruts so that you can gain the motivation to get back on track in learning. A good coding analogy might be in biting the bullet and start coding when stuck in a paralysis analysis loop is often a necessity to move on.
Not a proficient musician by any stretch of metrics/imagination. But adding onto learning new pieces, what worked for me personally is hearing the parts in the original recording, and singing the melody with my voice if it's melody or vocalizing and tapping the rhythm with my whole body (foot and spine engaged) if it's a rhythm pattern.
That way, when I am playing my instrument when that problematic measure comes, I'll simultaneously sing out the melody or tap out the rhythm; and even if my technique is poor and can't play the fast series 16th notes, I'll hear the correct melody/rhythm/gestalt in my head and what I am off by and try again.
This happens in learning new languages as well , often speaking quickly the wrong way is counter productive. Speak very slowly at first and focus on being correct
What you should do is to play it slow enough so you are sure not to make any mistakes. Sometimes that is ridiculously slow.