An excellent analogy of the role parents have in their child's progress is to imagine a motor boat. The teacher is at the front, steering the boat. The child is in the boat. The parent is at the rear of the boat moving it forward.
Yes, you are that important parents! Your involvement in home practise is crucial, especially for young students' progress.
Advice from Leona's Piano Studio
Philip A. Johnston in his book The Practice Revolution also stresses the parent's role. He states that the single most important thing you can do is to be 'over the top' genuinely interested in what they are doing. Children love to be the center of attention, and this is a way of letting them know that you are excited about what they are learning. Be sure to ask right after the lesson how things went, look in their notebook to see what the teacher has written, and have conversations about their music any time of the day - be interested in how they are progressing.
His second point is to encourage them. If you hear them playing something extra well, stop and encourage them! Also, if they are frustrated, try to help them persevere through the time that they feel that way.
Thirdly, he advises to help your child reflect on what happened at the lesson. By asking them questions, you are helping to cement what really did go on at the lesson and what their new goals are .
His next advice is to steer them in their practising. If they are repeating something they already know well, suggest they work on another area that is not as strong!
Next, he advises parents to be enthusiastic about what they are playing and about their progress!
His sixth point is to make practise charts. Check half way through the week to see how they are doing at achieving their goals! If they are having trouble, you can suggest they contact their teacher to get clarification on what was intended.
Another source, the Alfred's Premier Course "At Home Book" makes suggestions such as the following: