Playing straight through a piece is not practicing. If there is a measure with a problem, playing the piece over and over again is never going to fix it. Practicing is dissecting the piece and working through the tough spots to make them smooth. It is like putting dirt over weeds to make them go away. You need to get to the roots for the problem to disappear. Someone once told me (many times) "practice the passage until you can't get it wrong." HOW? What child likes to play a measure 100 times? give them DIXIE CUPS and M&Ms!
Let the child play the piece once. Find one spot that you feel needs work (there may be several but just pick one.) Ask them to play it 10-20 times. Each time they get it correct, put an M&M in the cup. Pretty soon your child will be asking to re-work several measures of the piece.