«Help, our children's teacher is using a smiley face system!»
I well remember the «Bätzli», the round stickers, in primary school. A sun was called «very good». A spider the opposite. You might ask yourself how such a system of rewards and punishments should be judged didactically. And why the useful spider stands for the bad. But that applies to everything in the classroom. Neither the spiders nor the suns have caused me any long-term damage. And if your daughter is disruptive in class, she has to face the consequences, doesn't she? Apparently the reward system works when she is upset. So don't talk to the teacher, talk to your daughter: if you don't disturb her again until the next holidays, you'll get a certificate too!
How would we as adults feel if our boss walked through the open-plan office and handed out good behaviour stickers to the team for all to see? Probably ridiculous, perhaps even degrading. However, such systems are often used with children to get them to conform. The teacher is certainly acting with the best of intentions to create a calm working atmosphere that is conducive to learning. The problem is that these systems may motivate children who are already able to control themselves well and who find school easy. For everyone else, however, they cause frustration and embarrassment - and therefore defeat their purpose.
You can do that. And explain to her what you think of this stupid bonus system for the little ones. She'll give you a big look and won't understand what you're saying. Because the smiley nonsense is apparently already so widespread in schools that you have to argue very fundamentally to counter it. Which, of course, won't help. Once sects have reached a critical mass, you become a sectarian yourself if you try to counter the nonsense.