Practicing piano as your child would during the lessons might become dull and monotonous, which I find ironic because piano is the opposite of monotone! Jokes aside, I will continue to beat the “3 minutes per year of age” drum, so your ten-year-old should practice his lessons for thirty minutes at least four times a week.
If he has a repertoire of lengthy pieces, he can play them during the last twenty minutes of practice (because warm ups take up the first ten minutes), focusing on volume dynamics, tempo, slurred phrases, and all the trills and frills that come with pretty music. The next time that he sits at the piano to practice, the may then concentrate on his new piece.
Focusing on details is important because he will develop muscle memory, playing the pieces on “auto-pilot,” very similarly how you would type your usernames and passwords. Repeating phrases is how this happens, and that’s just what practice is, playing the same thing over and over. Being that it also involves listening skills, the fingers will be guided by which sounds should come next.
You will notice that once he commits a piece to memory, he will practice it more smoothly and gracefully. This is how he prepares for lesson day. Come time for his lesson, he and his teacher will spend less time on reviewing and more time on new pieces. His teacher will be impressed by these developments, and you’ll feel that you got more bang for your buck in terms of piano lessons.
Even one day of solely focusing on repertoire with enhance his skills. Just as you would become tired of hearing the same thing over and over, your child will, too, which is a good thing! He will learn to change the music subtly but keeping within the written notation, hence, furthering what is called “interpretation.”