For the initial question from betricia, the problem I see with correctly deducing whether or not a teacher is "good" is that I think ultimately, opinions like this are probably entirely subjective. A person may learn more about music from closely observing an anthill than from a formal piano teacher, but this does not necessarily mean that the teacher is "no good".
How does one measure exactly where or from whom one learns what? Sometimes things just click, who knows what kind of preparation came from where in order for the click to occur. Sometimes things just don't click, but who really knows
why or who it is that is at fault?
I think ultimately it depends on
what this person is doing for you. Not just an overall impression (although you may have personal feelings about an overall impression that make it so a teacher does not work
for you).
For an individual who is comitted to music/piano study for a lifetime, one will be looking for and needing different things at various points in one's overall career. It really depends on what the student is needing at that specific time as to whether or not a certain teacher could be considered "good" at the time. All of my comments are, however, somewhat ethereal and maybe not so practical.
For the sake of practicality, I will pick on myself for a moment. I am a "piano teacher". I do what I can for my students, and I do what I have learned. There are gaps within my own understanding, however. Yet, probably if one looked at the biographies of the people I have studied with, one who does not know any better would assume that I must know what I am doing. For people such as these, perhaps I am as much of a teacher as they need at this point in thier lives. I know for certain that I am not the teacher I can be though, and a student who is looking for what I am not, would most certainly be able to discern what is missing. For these people I am not so helpful at this point.
Now this:
...you can take lessons for a good price through a community college or university and know for a fact that you have a good teacher.
Just because a person is in a college or university,
does not automatically mean that they are some kind of a superb teacher. In some cases, they may be accomplished pianists who have trained all of their life for performance (perhaps not even by their own choosing) and simply ended up there, teaching. This is not a call to doom in and of itself unless they have very little enjoyment with the instrument and the profession in general. Then there can be problems, big problems. People in this situation do not have the desire to really think through the teaching process and what kind of effort it may take from them to help their students learn. This exact thing happens with private teacher as well.
There are some fabulous teachers in Universities and Colleges. I am simply stating that for sure, the mere fact that one is there is not by any means a guarantee that they are a "good" teacher (although no matter what, it is a probably a good indication that at some point in their life, they have worked hard and probably do have something truly worth sharing).
Also, a teacher may be absolutely excellent and not be affiliated with any kind of music institution at all

. But this is not new information, it's just my two cents.
m1469