I'm glad you didn't punish her at home, I agree that TV time or whatever doesn't have anything to do with her behavior at school. Please don't ask to switch her to a different class. The only thing she learns from that is that when faced with a difficult teacher or boss in the future, Mom will fix it. She doesn't learn to accept any responsibility for her part in the teacher-student relationship. When she gets a note back, I would have her apologize to the teacher and work very hard to make a better choice the next time the same scenario arises.
My 8th grader has one teacher this year that she really struggles with. This teacher is "not fair" She sweetly allows other students to go back to their locker for materials or grants extentions whereas my DD gets told angrily "no" or gets an incomplete if she forgets her work. I can imagine your DD feels a lot like mine when everyone around gets called on but her. I do believe teachers do this intentionally to demonstrate that better behavior gets better treatment. A very true life lesson. Whether or not my DD realizes it, her non-verbals send out messages of disrespect even when she is quite her she hasn't done anything wrong. My DD had made up her mind she doesn't like this teacher her attitude spoke volumes. When we got an email about her disrespectful behavior, DH and I talked to her. Both teacher and parents agree she will not get what she wants out of life by being disrespectful. My DD has a hard time not overreacting and letting go of her anger when she is frustrated by a correction. We told her she needed to go in and apologize to her teacher the very next day. At first she refused. When we told her she was grounded from privileges until she complied, she relented but screamed she wasn't going to mean it. Again, her reacting in anger. Too bad, it's our job as parents to make sure she does what is right. The next morning, very calmly she asked me for a ride to school so she could apologize to her teacher. Later in the day I saw the teacher who was so pleased to let me know that she did apologize and seemed very sincere. DD also asked her teacher if they could start over with each other. Teacher agreed to that. So far now, so good.
The night we talked my DD was really mad at me for not going up to the school with a "how dare you treat my baby unfairly" attitude. She asked me why I couldn't take her side against this teacher like other parents have done. Not surprised because this teacher is very strict. Her standards are the highest in the school. I'm sure a lot of parents are quick to blame the teacher when she calls a student out on something when the other teachers have not. We had a big discussion about how DD needs to be able to show respect to people (especially adults in positions of authority) even when she does not like them. I told my DD that she holds all the cards to mend a bad student-teacher relationship. It is not something I can do for her.
If you are going into a conference, please have your DD in attendance, and let her tell her teacher herself why she is frustrated and what she can do to be called on more often and not get behavior notes sent home. The teacher will work with you, I'm sure, if she sees you and your DD are concerned, and you're doing your part, and you have the same goal to improve the current situation.