Let's be honest, all students whine sometimes. The causes differ from not wanting to practice, to getting frustrated with a piece of music, to being frustrated with an instrument. So what's a parent to do???
Here's some ideas.
First, try to get to the root of the whine. Is it that they don't want to stop playing outside or with friends and have to come inside and practice? They are frustrated with the piece of music? Frustrated with the concept? Frustrated with the instrument? Bored with the piece? Now address that root.
Not wanting to stop playing: Change the time of practice. If they want to play with their friends in the afternoon when they get home from school, change practice time to the morning after breakfast. Or even give them the "treat" of being able to stay up a little bit later so that they can practice in the evening after dinner.
Frustration with piece of music: I have been teaching out of the same curriculum for quite a while and now know that some songs are just plain hard. Students of varying degrees of natural talent will reach a certain song and no matter what, they will struggle. That taught me that its ok to skip songs or to supplement with another piece that teaches the same concept. That being said, as a parent talk to the teacher if the same song is being assigned for more than 2 weeks. Ask what specifically the student needs to work on and what the teacher's plan is if the student continues to struggle in grasping the concept. One piece of music is not worth frustration.
Frustration with a concept: There are some students that really struggle with certain concepts. I've had students who cannot seem to master the feeling of a 3/4 time signature or crescendo/decrescendo. If your young musician is getting frustrated with a concept like one of these, during practice take the concept away from the piece and let the musician concentrate on the successful parts of the song, like correct notes, hand position, steady beat, etc. Talk to the teacher at the next lesson and ask if there is another way to teach the same concept. This is where the teacher's creativity can shine! You as the parent see if you can apply the concept to the student in other non-musical ways. (Check out my other posts to see examples of these).
Boredom with the piece: 30 minutes goes by extremely fast. If your young musician is getting bored with the pieces because they are mastering them quickly, ask the teacher for either a longer lesson (like 45 minutes) or even better, two 30 minute lessons per week. Some musicians are so very talented, that they really could master a concept and a piece of music in just a day or so. Ask the teacher also for supplemental music outside of the lesson book. The Faber curriculum that I use has many books that run parallel to the lesson book levels so that students can find matching music to their level of performance.
Frustrated with the instrument: For some piano students, when they reach a level of performance but are still playing on a lower end keyboard, they can begin to get frustrated that their instrument is not making the sound that they think it should be making. If that's the case, then its time to invest in a better quality keyboard. Also read my other post on practicing w/o a piano. On the other end of the spectrum, I've had students whose parents own pianos that need to be repaired or tuned badly and that can cause frustration of the musician as well. As parents, the ball's in your court for this one.
All in all, there is usually alot going on inside the musician's head when they start whining about practicing. If you take the time to find out what's really going on, not only will you be able to beat the whining blues, but also your musician will be happy that you took the time to find out what they were thinking/feeling inside. Its a win/win situation!!