All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If a woman, even if she wears Hijab, or a man teaches in a mixed college, this will entail many prohibitions like seeing forbidden things morning and evening and mixing with sinners. In fact, a Muslim is ordered to avoid mixing with sinners and their places if he can not change the evil that they are doing. Allaah Says (which means): {And it has already come down to you in the Book [i.e. the Quran] that when you hear the verses of Allaah [recited] they are denied [by them] and ridiculed; so do not sit with them until they enter into another conversation. Indeed, you would then be like them. Indeed, Allaah will gather the hypocrites and disbelievers in Hell all together}[Quran 4:140]. Imaam Al-Qurtubi commenting on this verse, said: 'This is evidence that it is an obligation to avoid dissolute people when they are committing a sin, because if one does not avoid them, it means that he is pleased with their act. So whoever sits with them while they are sinning and does not forbid them from it, will get the same sin like them. If he cannot change the evil they are doing, at least he is obliged to leave the place where these people are sitting so that he will not be included among the people who are mentioned in the above verse.'
Undoubtedly, the mixing of men and women is forbidden whether at schools or elsewhere. The place of this forbidden mixing is also forbidden and one should leave it.
By teaching them and seeing this forbidden mixing, a woman looses her conscience of rejecting evil.
There are also other prohibitions; for instance she cannot be safe from being tempted in this environment that incites and arouses one's desires, and stimulates the desire to commit adultery or fornication. Indeed there were many practising and religious Muslim girls who were harmed by dissolute people in mixed universities and colleges.
Because of the above prohibitions and others, we do not consider that it is permissible for a Muslim woman to teach in these mixed universities except in case of dire necessity; like when she could not find another permissible job and she has no one to spend on her. It is in this case only, that she is permitted to teach. Allaah Says (which means): {…while He has explained in detail to you what He has forbidden you, excepting that to which you are compelled.}[Quran 6:119].
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Allaah Knows best.