What is the ruling on women being taught by a mosque imam without a screen separating between them?

Muslims, past and present, have maintained that the mere presence of men and women in the same place is not prohibited per se. Gender mixing is only prohibited when it involves anything that contravenes Islamic law, such as women exposing their 'awra [those parts of their bodies which must remain concealed], men and women meeting over some prohibited act or for the purpose of committing one or if they are in khulwa [meeting in seclusion such that no one can invade their privacy without their permission]. Scholars have further determined that gender mingling is forbidden when it involves touching and not by merely being in the same place. The legal premise for this opinion are the following evidences from the Sunnah:

-Sahl Ibn Sa'ad Al-Sa'di (may God be pleased with him) said: "Abu Asid Al-Sa'di invited the Prophet (peace and blessings be upon him) and his Companions to his wedding. Abu Asid's wife prepared the food and served it to them herself" [recorded in the Sahih of Bukhari and the Sahih of Muslim. Bukhari included the hadith in a chapter entitled "A woman Serving Food to Men at Weddings"]. Al-Qurtubi wrote in his Tafsir: "Our scholars have said that it is permissible for a bride to serve food to her husband and his guests at her wedding." Ibn al-Batal wrote in his commentary on the Sahih of Bukhari: "[The report] indicates the non-obligation of separating between men and women when they are in the same place or during direct interaction. This separation was restricted to the Prophet's wives as mentioned in the Quran: “When you ask his wives for something, do so from behind a screen” [33: 53].

The hadith scholar, Ibn Hajar wrote in Fat-h Al-Bari: "The hadith attests to the permissibility of a woman serving [food and drink to] her husband and his guests. There is no doubt that this is only permissible when there is no fear of temptation and when a woman conceals those parts of her body which must remain concealed. It also demonstrates the permissibility of a man asking his wife to do this."

-Abu Huraira (may God be pleased with him) narrated the story of Abu Talha Al-Ansari's generosity to his guest and said: "Because they did not have enough food in the house, Abu Talha and his wife pretended to eat before their guest and spent their night hungry." Ibn Abu Al-Dunya mentioned in “Hospitality to Guests” that Anas narrated that Abu Talha told his wife: "Take this loaf of bread and crumble it with butter and tell the servant to put out the lights." They then pretended to lick their lips so the guest would think they were eating. The obvious and straight-forward reading indicates that they were sitting in the same place with their guest. The Prophet (peace and blessings be upon him) told Abu Talha: "God is pleased with what you did tonight." The verse: “They give preference over themselves, even if they too are poor [59: 9] was revealed in reference to this incident.

-Abu Juhayfa (may God be pleased with him) said: "The Prophet established a bond of brotherhood between Salman and Abu Al-Darda`. Salman once paid a visit to Abu Al-Darda` but he was not at home. He found his wife looking unkempt, so he asked her why she was in that state. She replied, "Your brother, Abu Al-Darda` has no worldly desires… " [recorded in the Sahih of Bukhari]. Commenting on this hadith in Fat-h Al-Bari, Ibn Hajar said: "This hadith contains some beneficial information … the permissibility of talking to non-mahram women (those with whom marriage is impermissible) and asking about what concerns them."

Women receiving knowledge from men
It is permissible for men to teach women Islamic law and give them scholarly direction. This is attested to by the hadith narrated by Abu Sa'id Al-Khudry (may God be pleased with him) who narrated that on one occasion, some women approached the Prophet (peace and blessings be upon him) and said: "The men have more access to you than us, so appoint a day for us." The Prophet (peace and blessings be upon him) then promised to set a day to instruct them on matters of religion [recorded in the Sahih of Bukhari and the Sahih of Muslim]. In Abu Huraira's narration of the hadith, the Prophet (peace and blessings be upon him) told the women: "We will meet at the house of so-and-so" [recorded by Al-Nisa`i and Ibn Haban].

At the Prophet's time, women used to participate in the public life of the society while observing the teachings of Islam concerning their dress code and etiquettes. Some females from among the Companions were even in charge of the hisbah [regulation of economic, commercial and public affairs]. Abu Balj Yahya Ibn Abu Selim said: "I saw Samra` Bint Nahik, a woman who lived at the Prophet 's time, wearing heavy armor and a thick face veil and holding a whip in her hand … she was directing the people, commanding the right and forbidding the wrong" [ recorded by Al-Tabarani in Al-Mu'jam Al-Kabir from a trustworthy chain of transmitters].

Based on the above, no one can deny such events that are established in the Sunnah and Islamic history. Moreover, it is impermissible to let customs and traditions prevail over religion since Islamic law takes precedence over all else and not vice-versa. It is impermissible for a person who is overly cautious in matters of religion to obligate others to emulate him, be prejudiced against them, or restrict what God the Almighty has left open and capacious.

The ruling
It is permissible for women to attend lessons and receive instruction from mosque imams without a screen separating between them.
And God the Almighty knows best.