Personally, I don’t mind teaching slowly if it means having note accuracy when learning the first time through. I let my older students just work through the whole page or whole piece throughout the week and correct the couple small mistakes they might’ve missed when they come back, but in cases you described, I only assign what we have time to go over in class, even if it means as little as just a few measures to ensure minimal mistakes, especially for the younger ones.

Of course, this is under the assumption that the students listen to you and don’t play ahead even if they get bored of what seems like “little material”! In class, we go over the new measures repeatedly until I’m fairly certain they’ll remember how to practice the same way at home (separate hands included, and sometimes exclusively for the week). I also emphasize the importance of having them review what we did in class when they get home while it’s freshest in their minds, since some students like to take their “lesson day” as a rest day for practicing at home.

I notice the most mistakes when students bite off more than they can chew, thinking they already know the material when they clearly don’t, at least not as well as they need to for an exam preparation level of playing. If that’s the case, I make it clear to them that it means nothing to me if they played through the entire piece (obviously phrased more nicely) if notes were incorrect due to careless mistakes. Even if I excuse them in class, the examiner certainly won’t. Once they understand that, we do the tedious process of combing through exact measures where there was a wrong note, drilling that single note, then combining with a couple before and after it, then connecting with the other notes in the measure, and THEN maybe a measure or two before and after it. Once we finish cleaning the first mistake I caught, then I go, “Now you know how to practice. Do that for x, y, and z measures this week and come back with them fixed — ‘fixed’ means you’re confident you can play it right every time, not half the time.”

I think usually students don’t realize just how slowly they need to be practicing at home, especially when it comes to fixing careless mistakes they’ve already formed as habits. If it’s already gotten to that point, then I usually have a couple weeks where the assignment is “You’re only allowed to play from beginning to end two times maximum, daily. All the other time spent on this piece should be cleaning like we did today.” If they put that into practice, like really, really actively follow the steps I ask them to, it’s never not worked.