Neuroscience shows that children benefit from positive reinforcement while learning and practicing their skills, whether its in school, sports, or music! (Judy Willis, MD, MED) By knowing this, you can change the way your child views practicing their skills. Keeping track of their improvement, and rewarding their work, will train them to set personal goals and motivate them to practice more often. You can do this through games and activities for durable memorization; not only is it more fun to learn this way, but your child will develop a positive association with learning, and therefore, improve steadily!
What can be done to make sure your child is on the right pathway to play their instrument correctly? The simple answer would be to practice it correctly more than the amount of times they mess up. Repetition, after all, is a key factor in learning anything. However, if they are misguided and unfocused, they will repeat their mistakes if they are not concentrated on fixing them. So, give them something to focus on-playing their instrument correctly more times than they aren't, while minimizing the chances that they fumble with their performance. For example, while learning a piece, you might tell them to practice a measure five times, but instead of only using this repetition, give them the consequence of starting over if they mess up. Using this pattern of correct sequential repetition will not only enforce concentration, but allow them to think more about the way they are playing.