the appropriate way for a non-Muslim male to address a Muslim females, as you put it, by saying that the issue at hand is not about a “non-Muslim male” addressing “a Muslim female”. Rather, it is about two kinds of dealing: (1) a male addressing a female, from an Islamic point of view, and (2) an “American male dealing with a female from a “non-American” or “mixed-American” culture.
1- There is a specific code of interaction between men and women, according to the Islamic point of view, which applies regardless of one’s religion, and whether it is initiated from the male or the female side.
First, there is no prohibition of interaction between men and women itself. What is prohibited is an interaction that has any “physical” dimension, by way of touching, talking, or even staring, which are all unacceptable in the Islamic code of morals. The Quran, which Muslims believe is the word of God, states what means:
[Tell the believing men to lower their gaze and to be mindful of their chastity: this will be most conducive to their purity – [and,] verily, God is aware of all that they do. And tell the believing women to lower their gaze and to be mindful of their chastity, and not to display their charms [in public] beyond what may [decently] be apparent thereof.] (An-Nur 24:30-31)
And the wisdom behind these rules is “blocking the means” or “cutting the roots” of adultery, which is a threat to the family structure and the morals of the society, according to the Islamic point of view.
However, “normal” interaction within a pure and decent atmosphere of politeness is absolutely fine. The Quran itself is full of incidences where men and women “interact” within these boundaries. For example:
[Now when he [Moses] arrived at the wells of Madyan, he found there a large group of men who were watering [their herds and flocks]; and at some distance from them he came upon two women who were keeping back their flock. He asked [them]: “What is the matter with you?” They answered: “We cannot water [our animals] until the herdsmen drive [theirs] home – for [we are weak and] our father is a very old man.” 28:24 So he watered [their flock] for them: and when he withdrew into the shade and prayed: “O my Sustainer! Verily, in dire need am I of any good which You may bestow upon me!] (Al-Qasas 28:23-24)
[She [the Queen of Sheba] added: “O you nobles! Give me your opinion on the problem with which I am now faced; I would never make a [weighty] decision unless you are present with me.] (An-Naml 27:32)
In fact, decent interaction happened everywhere during the time of the Prophet (peace be upon him); in the mosque, in the street, in the market, and on the front lines in wars. The idea of “segregation of sexes” simply did not exist at that time. I will cite a few hadiths and Companions’ practices below (out of thousands of similar narrations that one finds in Hadith collections).
Qaylah Al-Anmariyyah, a female Companion, came to the Prophet and said: “O Messenger of Allah! I am a woman who buys and sells”. And then she asked him about bargaining. (Ibn Al-Atheer)
Anas, one of the Companions of the Prophet Muhammad, narrated about the day of the battle of Uhud: I saw Aishah, the daughter of Abu Bakr, and Umm Sulaim rolling up their dresses, and I saw their leg-bangles, while they were carrying water skins on their back and emptying them in the mouths of the (wounded) people. They would return to refill them and again empty them in the mouths of the (wounded) people.” (Al-Bukhari)
Umar ibn Al-Khattab, when he was the Caliph, appointed a woman, Shifa bint Abdullah, as the administrator of the Market of Madinah, which was the main market.” (Ibn Hajar 333)
Caliph Umar also appointed a woman, Samra bint Nuhayk, as a police officer. (Al-Tabarani)
Having said that, there are issues to consider when an American male deals with a female from non-American or mixed-American culture.
The examples you mentioned, such as talking to your students’ mothers casually in the hallway of the school, with or without their husbands’ presence, or admiring their clothes or scarves, and so on, are perhaps no issues if these mothers were American (I mean by culture, whether Muslim or non-Muslim).
I am aware, however, that culture is a very complex concept, and even if we narrow things down to some American culture, it would be even hard to define that exactly.
However, from what I know about the Arab and Asian Islamic cultures, which manifest themselves very strongly amongst Muslim communities in the West, I would advise you not to admire these ladies’ clothes or scarves, and not to talk with them without the close presence of other people who could hear the conversation.
Thanks to : http://www.readingislam.com