1) Know what end goals you want you and/or your child to achieve. Of course, the purpose of a music class is to learn music. That is a given, however, what ELSE do you want your kids to learn? Do you want them to learn how to do ensembles? Do you want them to make friends? Do you want them to learn one-on-one? At the end of your child's piano course, do you want them to play music because they can, or because they want to? Some teachers are very technical, and some are very passionate. Rarely, you will find both qualities in one teacher. Depending on what you want for your child, one or the other may be more appropriate.
2) Cost. How much can you afford to spend on an extracurricular music class? One-on-one private lessons usually run about $40.00 - $60.00 an hour, whereas group classes are a little less expensive. The typical problem with group classes is that many teachers don't know how to teach them properly, and wind up teaching four to five (depending on how many kids are in each class) 10-15 minute individual lessons. In that case, no, you're not getting what you've paid for. Finding a group teacher who is a quality teacher is not easy. Finding an individual teacher who meshes well with your child's personality isn't an easy feat, either. The key is RESEARCH!
3) What are your beliefs? What kind of influence do you want your child's teacher to have on your child? Many music teachers are independent contractors, and have the freedom to do as they please. That's okay, but only if it works with the belief system that you hold dear. For instance, if you're a devout Christian, it probably would make you a little nervous to employ a music teacher for your children who is not. While it should be common sense for teachers not to impose their values on their students, it isn't always. Make sure that your teacher either a) shares your beliefs, or b) is respectful of your beliefs.
4) Experience. Is your teacher qualified to teach? What individual talents does your teacher possess, and how will those talents accelerate your child's learning? Are those talents compatible with what you want your child to learn? What I mean by that is this: You can find a teacher who plays the guitar, and you want your child to eventually perform, but... Does your chosen teacher have performance experience? Have they done stage work? Likewise, you would like to have a teacher who handle students with psychiatric disorders, but what kind of experience does that teacher have to handle a crisis?
5) Referrals. ASK, ASK, ASK! There is no better way to get to know your child's teacher than to talk to those who have had experience with said teacher. Ask those referrals what they liked the most about the teacher, and what could use improvement. The list of "likes" should go on and on, and the list of improvements should be relatively small.
As I said, I would love for everyone to choose me, but everyone's needs are different. When choosing for your child, however, shop around, and choose wisely! Happy Sunday, and God bless you and your families!