Children do not like to be told that what they do is wrong but you can guide them to improvement with positive reinforcement. When I teach children I take out of my vocabulary any negative words, like wrong, no, not etc. Instead always talk about what is better not that what they are doing is not good. It is difficult to tune into the child to know how to transmit this because some are very sensitive to any changes to how they are currently doing something. A parent who knows their child better than a teacher knows how their child deals with change to their methodology/routine etc in life, it is perhaps very important as a parent to tell the teacher what your child is like, if they need help in certain areas more than others.
I have parents come to me telling me please be very strict with my child because they have a strict upbringing at home. However you get a lot of children who are very sensitive and any changes you try to make in them must constantly take care that it is not depressing or making them feel stupid. I try to strike up a friendship with my younger students, we always talk about their interests before lessons etc. They get little prize rewards related to their interests when they complete musical tasks I set them. Children like to play games, they don't like serious work, most of them at least are like this. Childhood is about having fun and playing games, when teaching most children you need to make them look at piano just like that, the difficult thing is to make them practice on their own, it is actually quite a lot to ask of a young child to be consistent with their practice routine and more often than not requires someone older to always watch over them while they practice.
Playing games with young students can last as long as it is required. Often they grow out of it but by that time they have already acquired a head start in their musical learning. Some young children learn piano for a very brief time and then never return to it because their experience with the teacher was not fun or encouraging. Where if you took in a young student, make the experience fun, they might stick with the music for longer and as they get older have such a head start over waiting until they where mature enough to study the piano seriously.
We often accept the notion that children do not know what is good for them and need to be told what to do. This is true more often than not however in learning something creative you must not suffocate the individuality in your young student. Let them do things which are not completely correct but make changes to their approach which points them in the correct direction. We do not have to force them into models of what is to be expected of a diligent student, let them grow up first then when they are ready to take that step you can make that change. The musical journey is forever various and changing, if you get comfortable with your routine and approach then you have stopped living and learning music. At the young age you must plant the seeds of discipline but don't expect it to sprout immediately, but certainly you need to set everything up and make it a positive experience.
You need to say things which challenges the child but at the same time does not put them down. You need to highlight that you think they can do better and have seen/heard them do better. They need to realize that they already have it in them to improve because you have noticed it before but at the moment they are not being careful enough to produce it (or doing it half heartedly). I use to play a game with one of my younger students, when they expressed the sad emotion I would pretend to cry, or if it was happy I would be happy. It makes them forget about you trying to improve their playing and when they don't do it right they don't get the reward of seeing their teacher being effected by the music so.
I would sometimes reward bad mistakes by joking around. Falling asleep and pretend to snore if they made the error over and over again or going ARRRRRGGGGG lol. Then when they finally do it somewhat right I might go Oh??? etc etc. You don't have to say in words its bad just make a sound is good enough but at the same time you don't want to make them feel like you are being serious about the sounds, it is for fun. I guess it depends on your personality as a teacher, I love teaching children and playing games with them, it makes the lesson much more productive and interesting for me and the student. You can sneak in knowledge through this medium, teach them without them even noticing it, making changes to their approach, technique, observation of the piano etc. The soft approach can work wonders and inspire a young student to continue with piano for the rest of their life, taking a hard approach with children can produce great results with the child that can deal with it but it has crushed and damaged too many more young minds than the good it has done.
Being soft doesn't mean you do not instill discipline in your student. I certainly mix a little bit of hard teaching with soft but I have to say I am predominantly soft. I only unleash some tough teaching when it is needed. If a student never practices I will make them practice in the lesson for me and I will get them to show me how they practice. Then I will tell them how to practice and force them through the drills, reconsidering and then repeating again. I have made at least all of my students sweat in a lesson or be totally exhausted once. As a teacher you need to know your students limitations of focus and push them to that limitation. For young children you need to be very careful when you do this and it needs to be in spurts during the lesson, grabing their attention for say 10 full minutes is already extremely difficult for most young minds. Then reward them with a break, maybe do something they can do easily, then finish off putting them through the disciplined routine again. A child needs to be guided and encouraged all the way during disciplined study of anything if they are to gain that habit when they grow older. The best place is to start when they are young but you must be wary of how you expose them to it. 99.999% of us are not disciplined naturally and we have to work on it, I would say however this is made a lot easier if you had an idea of what perseverance produces at a young age (and not only in the form of annoying mum and dad daily for toys or lollies or whatever else!). They are good in asking for what they want in life but when it comes to work they can easily ignore it. Call them up on that too I do all the time to my little students who I feel can remember every day to ask parents for money but can't remember to clean their own room every day or do household chores.
You have to learn to compliment the smallest of improvements in young students no matter how microscopic, forgive inefficiencies but don't let totally incorrect errors become habit. This is where as a teacher you have to know what you can let your student get away with, you do not want them to play within anyones preconception of mastery, it totally bores a young students mind, don't push for mastery, just let them carry on. Often it is a maturity, both in personality and musical ear training, the young mind has to realize that they don't always do things the best way and need to always improve, they also have to acquire a taste for sound, that is be interested in producing a good sound instead of just poking away at notes. I have found through teaching a lot of young children 4-7 that they need space to develop in this area and we should not hound them but constantly guide with positive reinforcement.