Is there hope?

[dinulip]

When and how can one tell if a child has the potential to become a good musician?  I have a couple of students -- between 6 and 10 years old -- who progress significantly slower than average, but are otherwise quite intelligent, practise everyday, and love to come to their lessons.  Is there a chance that, with persistence and hard work, they eventually become above average pianists - even though things don't look promising at first?    

[Bob]

Yes.

[hfmadopter]

Some people, not just kids are slow on the uptake, you have to explain in multi ways to plant the seed, get that info in there. Once they digest that then yes, they can excel. Not to say your students will but you have to think the potential exists ! Sometimes you have to take a little different approach.

[timothy42b]

but are otherwise quite intelligent, practise everyday, and love to come to their lessons.  

You've met 3 of the 4 criteria.  If the 4th is present, I think yes they will succeed. 

[coke]

I believe everyone have potential - so if you say they practise everyday, but still can't improve much, there should be something wrong.

Maybe they THINK they practise everyday but indeed they didn't spend so much time?
Maybe they used wrong method? (Some of my student never separate left and right hand to practise.)
Maybe they just THINK they love piano? (One of my student said she love piano but she never practise... She love 7 more hobbies as well...)
Maybe they spend sooooo much time to practise but not practising the new songs?

There're so many reason for a student who always practise but still process slowly. Not because they don't have potential. We, the piano teachers, should be the one to find out the most effective method and bring students level up.

[mstar]

To be honest, I must admit that for the first four or five years of my most formal musiccal education, I did not enjoy classical music at all! Resulting was that practice was scarce and tedious. It was evident that I did not want to play, though it was mentioned that I had "musical talent." Nevertheless, it was not until a few years ago that I began to listen to and very much enjoy classical music, and I practice for hours a day, generally whenever I can. Unaccustomed to break (Thanksgiving break in this case), I have practiced more hours than I've slept! 

The answer thus being all children and people have potential, which we only need to bring out in them. They may then decide for themselves.

[mo24rt]

Yes.

I have several students like this and absolutely there is always hope but.....I have to say that the sheer fact that you inspire them to practice and love their lessons is a testament to you as a teacher and ultimately secures their future progression. There lies the hope!.