Did I ever play horribly at a lesson? Usually...lol
As others have said, this is perfectly normal. In fact, I really try to go out of my way to make students feel comfortable. I expect lots of mistakes. I expect lots of UNEXPECTED mistakes. It is just what happens. As a teacher, I can tell whether something has been worked on enough. As a teacher, I am not expecting nor am I listening for some type of flawless performance. The very habitual language I use reinforces the idea that we are looking at a work in progress. And I go out of my way to show my pleasure with the good things I see happening that has little to do with what is bothering the student.
There can't be any misunderstanding: Perhaps a student can't play as fast because they are tense. Perhaps they don't remember a section they though they knew already. Perhaps a student is forgetting a new fingering. Maybe the student plays lots of wrong notes because they are nervous and do not have the accuracy they have when they are relaxed at home. Hesitation here, stop-and-go there. It is PROBABLY a combination of all of those things! And that is okay!
It takes a long time for a student to truly begin to appreciate just how much repetition it takes to memorize something. It is also surprising to most students how many times something has to be memorized OVER and OVER again before it even BEGINS to be learned. And outside of a perfectly controlled environment, it STILL isn't there!
When you are playing for your teacher, it matters. It is important to you. And because of that, it is basically a performance. But we don't PERFORM new music do we? (God, I HOPE I'm never in that situation!) We don't perform things we are working on, or JUST got down. It is simply unreasonable to expect good performance to come out in this situation.
Once a piece really IS, under your fingers, then can you begin practicing something completely different: performance practice. Your teacher should be able to guide you through this, showing you how to begin developing this skill. It is COMPLETELY different. In a nutshell, we have to spend a consistent amount of our time in the practice chair pretending to perform. We do this so that we can gradually begin learning how to deal with minor errors, nerves, and anything else. It takes a lot of time and specific amount of work to be able to perform for others. In our to succeed, we have to need far less than 100% of our abilities in order to pull it off because almost none of us will EVER play as well for someone else as we do when we are alone in the practice chair.
With the right guidance and work, you will arrive. Then you will finally have the luxury and privilege of reaching another important milestone in your playing. After having your teacher change all the fingerings, "but I could play it at the BEGINNING of my lesson!"
Dr. Todd Tipton, Noda Guitar Studio
Charlotte, NC, USA (available via Skype)