is this kind of teaching method in tajwid and tahsin permissible ?. so one person recite something from the qur'an the best he can, then the teacher asked the others whether that guy have made a mistake or not, and if yes, tell where the mistake is. Because im afraid this may be form of shaming someone in front of others.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

There is nothing wrong with a student reciting in front of the Shaykh, and then the Shaykh asks the rest of the students about the mistakes that the student has made in his recitation, if this is done in order to teach him (and others) and not to degrade or defame him.

Allah knows best.