censure usually affects the feelings of the censured person, especially if the censure took place publicly; therefore, the prophet, peace be upon him, followed a gentle manner in dealing with the mistakes or wrong actions made by his companions. the prophet, peace be upon him, was demonstrating and denouncing the wrong actions publicly but without mentioning the name of the doer. the purpose of mentioning the wrong action publicly is not distorting the picture of the wrongdoer; contrary, it is to demonstrate the wrong action and warn the others to avoid it in the future. here are some examples:

anas bin malek, may allah be pleased with him, said: (a group of three men asked the wives of the prophet, peace be upon him, how the prophet worshipped (allah)? when they were informed about that, they considered their worship insufficient and said, "where we are from the prophet as his past and future sins have been forgiven." then one of them said, "i will offer the prayer throughout the night forever." the other said, "i will fast throughout the year and will not break my fast." the third said, "i will keep away from women and will never marry." when the prophet, peace be upon him, heard their story, he praised allah and said to the congregation:  ((why some people said so-and-so? by allah, i am more submissive to allah and more afraid of him than you; yet i fast and break my fast, i do sleep and i also marry women. so he, who does not follow my tradition in religion (sunnah), is not from me (not one of my followers)).

the prophet, peace be upon him, said “why some people …”. he did not mention their names although some of the companions know them well. he just demonstrated the wrong action to warn the companions to avoid it. al-nawawi commented on this hadith saying: this sublime way is usual in the speeches of the prophet, peace be upon him. he does not mention the name of the wrongdoer; contrary, he addresses the wrongdoer and all people in order not to harm the feelings of the wrongdoer.

here is another example. the prophet, peace be upon him, appointed a man from the tribe of asd, called ibn 'al-lutbiyya for collecting the zakat. when he returned back with zakat returns he said, "this share (of zakat returns) is for you and this (part of the returns) has been given to me as a present. the prophet, peace be upon him, stood on his pulpit, praised allah and then said, ((why is it that  some a person sent to collect zakat comes saying this share of zakat is for you and this  share was presented to me as a gift, why hadn't he stayed in his house to see whether he would be given presents or not?… etc” (i.e. it is because of his position as zakat collector he got such presents and gifts as bribe; otherwise, if he was not a collector, he would not receive such gifts)).

the prophet, peace be upon him, said “some a person”. he did not mention his name although many companions knows such person well because he meant to warn them all, not only the wrongdoer, so that they will know the consequences thereof and avoid it in the future.  ibn hajar said: this hadith demonstrates also that if you see someone making incorrect explanation or interpretation for certain issue in a way which can harm or cause negative consequences to any person adopting such explanation or interpretation, you can then demonstrate such wrong explanation or interpretation to the people so that they can avoid acting according to it.

the teachers should follow this way in dealing with the mistakes of their students. they should demonstrate the wrong action, explain its consequences and warn the students to avoid it without mentioning the name of the student who committed the mistake, especially if the mistake was unintended. by that, the teacher will save the student from those who may disregard him due to his mistake and he can avoid any hatred by the student toward him. the teacher has the discretion to evaluate whether or not to mention the name of the wrongdoer in front of the other students to deterhim, or  shall he  follow other ways to deal  with such mistake. in all cases, the teacher should be neutral and avoid any feeling of revenge. anyway, the task of demonstrating the wrong action without mentioning the name of the doer is not an easy issue. the teacher should be smart enough to deal with the wrong action without hurting the feelings of the student. he should demonstrate the wrong action implicitly, not explicitly. in this regard, it is better to be kind with the student and avoid any statements which may unveil him. 

summary: 

1) the purpose of demonstrating the mistake is not to defame the doer thereof; contrary, it is to warn the doer and the others to avoid it in the future.

2) it is recommended not to mention the name of the person who committed the wrong action even if such person is known to some people.

3) if the student committed a mistake deliberately, the teacher can use another method to deal with and discipline such student.

4) the teacher should be smart enough to deal with the mistake of the student without mentioning his name.