J.,
I believe that it is the rare occasion that you should discipline a child at home for what goes on in school. I believe home should be for advice and support. A safe place. You can certainly let your child know how you would rather her behave, but I think the school should impose the punishment. I feel like it is doubled when you punish at home. All that said, I would privately talk to the teacher about ideas of what she/he can do at school.... both disciplinary when applicable, and to give your daughter some help.
What you do now for your daughter (if this continues, of course.....could be first week stuff) could make a big difference in her self-esteem. I kind of feel like avoid discipline until absolutely necessary. Better to use a few quiet techniques and ask the teacher to avoid pointing your child out. You don't want her labeled as a problem with the other kids.
For example: The teacher could gently ask your daughter to move if she is chatting with her neighbor. She could ask her a question to engage her, or simply touch her shoulder and point her towards the board (or whatever else they are working on). If disciplinary action is needed, try to make it for before or after school when the other kids aren't watching a drama unfold. I know you don't have big control over the teacher, but talking to her, being friendly, volunteering.....all this will help your child get better treatment. I'M SORRY.....BUT OFTEN IT IS TRUE!
If discipline is needed, let the teacher do it. If you think it is being more harmful than good, speak up. Don't take everything away. This will cause your little girl to give up at the tender age of 8. She will say to herself, "Why should I even try? It's too big. I can't succeed. I am bad and I'm not lovable." I agree with the Mom that offered positive reinforcement/rewards for success at home. Empathy for failure.
Gosh, sorry I went on so long. Truly, this could be first week adjustment stuff. I'm no expert, but I do know a little about this subject, as we lived it. This is just what worked for our family.
All My Best,
P.