Yesterday I got an email from our daughter's new teacher saying that some of the children performed poorly on a geography quiz and it was "not reflective of their true potential." As punishment she made them write an apology note explaining the reason for the poor result and that they will study harder in the future while the rest of the class got to go do a fun activity.
This doesn't make much sense.
One reason why we use grades instead of, say, a five-minute feedback talk with every child is that it's more objective. There is no "I think you can do better"-element in a grade. "I think you can do better" is a highly subjective opinion. Teachers all have them about their students, and sometimes it pays to tell the student something like that, but the way to do it is to tell the student "I'd like to talk to you for a moment after class is over" and then tell her whatever you think she needs to hear in order to reach the potential you see in her. What you don't do as a teacher is punish someone for not reaching a subjective potential that exists mostly in your head. Requiring a student to apologize for not doing better is not part of a teacher's job. I require apologies for showing up too late for class, for interrupting or disturbing the lesson etc, or generally for impolite behavior, but these are all things that are directly observable. I can't possibly know how much effort a student put into a test and how much of her potential she didn't reach, and even if I could, it's not my job to force him/her to put in the effort. Instead, I try to create a climate in which my students want to make an effort (which has been shown to have positive effects on learning outcomes, see below).
I teach teenagers, but I think the following is even more important for younger children: Some of the effort kids put into school work is because they like the teacher and want him/her to like them back. This is why sometimes after a test, a student comes up to me and tells me that he's sorry for the really bad answers he gave in the test - " I just didn't study, it's not bad teaching on your part". You destroy this relationship when you make a student apologize, and I think it will hurt future performance because eventually, the student will lose his trust in you and no longer try to look good in your eyes.
What you describe sounds like the teacher in question hasn't thought much about such consequences. I don't think it implies that there's a bigger problem with the school your daughter goes to, or even with the teacher herself, and I wouldn't approach any of the administrative staff of the school about it.
Instead, I'd ask the teacher in question for a short meeting, just like you're planning to. Since this is the second time you had an issue with something this teacher did, you can bring that up - say that of course a single event by itself doesn't mean anything, but since it's the second time something came up, you thought it important to have a talk.
Maybe there's something to the story you don't know yet that a meeting can clear up. For example, a lot hinges on the word "apology note". If the teacher requires an apology, as I said, that doesn't make sense. But maybe the word "apology" never left the teacher's mouth. Maybe she just required the kids to write down reasons why they didn't do better. There's a huge difference between an apology and an explanation. Requiring the kids to find possible explanations for their performance would be very valuable strategy to teach (again, see below for a reference).
If the teacher really acted the way you describe with no further justification, I'd gently bring up that you don't think the teacher handled the situation very well, and that you hope that he/she will think of a better way to reach his/her goals than resorting to punishment and shaming for not living up to the teacher's opinion of the student.
(If the teacher needs the class to work harder, for example, he/she can be up front about it: "I'm disappointed with some of your performances. For the next test, I expect everyone to reach a 70% minimum. Those of you who don't will have to retake the test/look up the right answers while the others can work on [fun activity xyz]". Note that the consequence of not reaching the expected goal is not writing an apology, which will not help the student to improve; it's something that will get the kids more time to practice). So it's not punishment; it's simply a consequence of not doing well enough - you get to practice more in an environment the teacher controls.)
But be careful in making any suggestions about how to handle this in a better way - your suggestions might not be welcome.
To take all of this out of the realm of supposition and ground it in a bit of science, there is a large-scale meta-study (commonly refered to as the "Hattie study") of which factors are helping children to achieve good results and which factors are holding them back. Check out https://visible-learning.org/, the study makes for a very interesting read.