Did you know that you can probably find that troubling piece of music on YouTube? If you're learning a piece from a lesson book, just visit youtube.com and search for the title of your piece, the composer if there is one, and the name of the method book that you're working from. (Make sure you ask your parent/gaurdian if it's ok first!). For example, I might search for Toreador Song from the Opera Carmen by George Bizet, John Thompson Book 3. Here's what you'll find: http://youtu.be/AuUpyFOYUUE It may not be exactly the way your teacher wants it, but it gives you a good idea of what the piece sounds like and some stylistic ideas. If your piece is an excerpt from a larger work, like this one is, you can search for the original work to get more ideas.
If you feel like your piano playing at home is always better than when you have your lesson, record yourself playing and upload it to YouTube and send your teacher a link to your best work. Or record your trouble spots so he or she knows how to help you best during lesson time. You can make your own private YouTube channel accessible only by links that you give out.
For even more fun, you can research technique demonstartions such as the C major scale here: http://youtu.be/0QBlq75LWck
Maybe you'll even discover some new pieces you'd like to learn, such as Canon in D: http://youtu.be/tzsZDN_Ic5U
Or try this Youtube metronome: http://youtu.be/NHwt-IOQ1nE
Or just enjoy this: http://www.youtube.com/playlist?list=PL5D9951DA7E0E0DD4
What YouTube ideas do you have?