Ability equals knowledge plus 10,000 times. - Suzuki
Susan Baer presented "The Value of Repetition" at Parents as Partners. After discussing the value, and relating repetition as a way which we also learn the spoken language, she shares some ideas to make those repetitions in music practice easier, more fun, but still effective, rather than just tedious, mindless repeating.
You may find that in one piece there are several problems which need to be addressed - incorrect rhythms, out of tune notes, trouble with a bowing technique, a shift, etc. Playing through the whole piece, trying to correct everything, is not a very effective way to practice or an efficient use of time. It's much more effective and efficient to practice small units, addressing only one problem at a time.
Even in small units there may be more than one issue. Break it down to just one thing at a time. Maybe the notes are out of tune and the rhythm is incorrect, and the bowing technique is difficult. First you may eliminate the bowing and rhythm just to work on intonation. Play the notes in a slow, smooth, even way. Once the notes are consistently in tune, increase the speed. When it is corrected and becomes easy, work on the rhythm. But just use one note, such as an open string. Then try to use that rhythm in a song you already know - Twinkle, anyone? :-) And again, use an open string to work on the bowing technique, etc. Once each individual element is corrected, then you can put them together again.
First you will work towards accuracy. This may happen in a day or two. Then you want it to be solid. It may take a week or more. Then it will become easy. In a few months it should be performance ready!
Repetitions are most effective when spread over time. I know in my experience I can do this kind of small practice, and find much improvement after several repetitions at one practice session. But if I leave it at that, when I next come back to it, it likely will have slipped back a few steps, and more repetition is needed the next day, and the next, etc. 10,000 times doesn't happen overnight.
Robotic or musical?
In order to keep the repetition from being mindless, and in order to keep the repetitions from only reinforcing the problems, there must be careful attention and brief and frequent feedback! Getting the child involved in the evaluation will help you to know if the they understand the concepts, lead to more confidence, and be an invaluable tool for later independent practice.
For each repetition, ask a yes-no question. Is that F# high enough? If the answer is no more than yes, perhaps a smaller unit of practice is needed.
Get creative! You will want a game appropriate to your child's age and attention span. How do you determine the number of repetitions? The child's age? Or maybe take two dice and roll them. Or more than two! Or a deck of cards. The low numbers might have special rules: A= 20 repetitions, 2 = add the next two cards drawn together, 3 = triple the next card drawn, etc..
Or maybe the repetitions will be guided by how successful the repetition. Use two cups and some marbles. The goal is to get all the marbles moved from one cup to the other. Use the yes - no questions. Each time the answer is "yes", move a marble to the 2nd cup. If it is no, no marble is moved. Or, if it is no, a marble moves back to the first cup. Again, find something which suits your child's level.
Amateurs practice until they get it right. Professionals practice until they can't get it wrong!
We are what we repeatedly do. Excellence then, is not an act, but a habit. - Aristotle