"A woman should learn in quietness and full submission. I do not permit a woman to teach or to have authority over a man: she must be silent. For Adam was formed first, then Eve." (NIV) Hence, Teaching & Authority are based upon the creative order - not ability, experience, gifts, culture, or common church practice. The creative order hasn’t changed.

 Teach - 1321 didasko did-as'-ko}

a prolonged (causative) form of a primary verb dao (to learn);
to teach; to hold discourse with others in order to instruct them; deliver didactic discourses; to be a teacher; to discharge the office of a teacher; conduct one's self
as a teacher; to teach one; to impart instruction; instill doctrine into one; the thing taught or enjoined; to explain or expound a thing; to teach one something.

This word is related to 1319 didaskalia did-as-kal-ee'-ah} AV - doctrine, precepts

 Note that the word ‘Teach’ used is in the context of an office, position, or formal setting, not just answering some short questions to someone.

Authority - 831 authenteo ow-then-teh'-o}
from a compound of 846 and an obsolete hentes (a worker); v
AV - usurp authority over 1; 1
1) one who with his own hands kills another or himself
2) one who acts on his own authority, autocratic
3) an absolute master
4) to govern, exercise dominion over one

Some have imagined an ‘escape clause’ here since a woman ‘could’ be under church authority rather than her own and teach men. However, she still couldn’t "teach" and would have to be ‘silent’, as is further restricted by Paul in both 1 Tim 2:12 and 1 Cor 14:34.

Note also that women in the OT did not have authority over men (except wicked queens).

Also, a good follow-on study is of the Prophetess Deborah, who did not exercise authority (Barak did), but rather declared God’s plans (expounded). See Judges chap 4,5.

Silent - 2271 hesuchia hay-soo-khee'-ah}
from 2272;; n f
AV - silent 3, quietness 1; 4
1) quietness
1a) description of the life of one who stays at home doing his own
work, and does not officiously meddle with the affairs of others
2) silence

Notice that this isn’t the same word that’s used in 1 Cor 14:34, but is a synonym with a different emphasis.

Galatians 3:28 (Col 3:11) "There is neither Jew nor Greek , there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus." See the context preceding. All Christians have equal standing in our salvation. ‘Function’ in the body of Christ is different.

1 Cor 14:34-38 and appropriate word studies

"women should remain silent in the churches. They are not allowed to speak, but must be in submission, as the Law says. 35 If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church. 36 Did the word of God originate with you? Or are you the only people it has reached? 37 If anybody thinks he is a prophet or spiritually gifted, let him acknowledge that what I am writing to you is the Lord's command. 38 If he ignores this, he himself will be ignored."

Note in v 34 that the Old Testament "Law" in reference to this issue is referred to as still operative, since the NT did not supersede the creative order. Note also, that Paul is referring to formal church settings here.

Silent - 4601 sigao see-gah'-o} from 4602;; v
AV - hold (one's) peace 4, keep silence 3, keep close 1, keep secret 1; 9
1) to keep silence, hold one's peace
2) to be kept in silence, be concealed

Disgraceful - 149 aischron ahee-skhron'} from 150;; n n
AV - shame 3; 3
1.  shame, base, dishonorable

Deaconess (RSV) - Servant (NIV), Same word as ‘Deacon’ 1249 diakonos dee-ak'-on-os}
probably from an obsolete diako (to run on errands, cf 1377); TDNT - 2:88,152; n m/f
AV - minister 20, servant 8, deacon 3; 31
1) one who executes the commands of another, esp. of a master, a servant, attendant, minister
References to NT women are to Deaconesses (servants in the church), and not to teaching.

Deacon - 1249 diakonos dee-ak'-on-os} probably from an obsolete diako (to run on errands, cf 1377); TDNT - 2:88,152; n m/f

AV - minister 20, servant 8, deacon 3; 31
1) one who executes the commands of another, esp. of a master, a servant, attendant, minister
1a) the servant of a king
1b) a deacon, one who, by virtue of the office assigned to him by the church, cares for the poor and has charge of and distributes the money collected for their use
1c) a waiter, one who serves food and drink

Aquila and Priscilla

Priscilla and Aquila are referred to as "expounding the way" to Apollos, but they are always mentioned together as husband and wife. Later it is mentioned that there was a church in their house, but there is no statement of scripture of Priscilla being the teacher. Three times her name is mentioned first, and three times his name is mentioned first. There is no precedent for a woman to teach men under authority of a church board. Rather, it shows that Priscilla and her husband ministered in the gospel together. Although it is a narrow distinction, and not necessary for the doctrine, ‘expounding’ and ‘teaching’ are different words. Aquila and Priscilla were clearly testifying (expounding) the Gospel to Apollos, whereas ‘teaching’ has two different emphases, one is "to disciple", and the other is "to hold discourse in order to instruct", and may include "expounding".

Comments:

1. Authority of Scripture in the Church - We accept the authority of scripture in the Church of Jesus Christ. Both in Apostolic times and throughout Church History, the Holy Scriptures have been accepted as the only infallible source of guidance and direction for ordering our personal lives, and the Church of Jesus Christ. See also 2 Tim 3:16,17 ("Doctrine" - teachings on various subjects in the scriptures)
2. Guidance by biblical authors such as Paul in all of their Biblical writings (see 2 Pe 3:15-18) is acknowledged and accepted by the believing church of all ages.
3. Interpretation - Through the ages, non-literal interpretive methods (such as "spiritualizing", "mystical", or "metaphorical") have arisen even from godly men such as St. Thomas or St. Augustine. BUT the normative biblical interpretive method accepted and used by Jesus, the Apostles, the early church, and the Reformation, is to take scripture in it normal, natural sense unless the context shows a symbolic, apocalyptic, or ‘spiritual’ interpretation. Some scripture is obscure and hard to understand in its original (OT) context, and its interpretation must be left for the (NT) biblical authors. Much of the prophecies about Jesus and the ‘end times’ fall into this category and are interpreted for us by the biblical authors. BUT issues of Christian practice generally do not fall into this category and their interpretation for personal and church direction can be discerned and obeyed.
4. This interpretive method above is described as the "inductive, historical, grammatical, literary interpretation of scripture" (ala Luther, Matthew Henry, Spurgeon, Howard Hendricks, etc.). Literary means understanding such communication devices as parables, figures of speech, metaphor, simile, etc., but the straightforward meaning of the text is clear. For instance, we don’t really believe that God has His feathered wings around us, but rather that He protects us personally.
5. The ‘women teaching men’ issue has been a randomly obeyed doctrine depending upon the maturity of the church. See clear examples in 1^st & 2^nd Corinthians, plus in Rev 2:20. However, in Orthodox churches through the centuries, this has not been questioned until the recent accommodation to western culture in ‘evangelical’ churches.
6. Culture does not supersede nor negate the teachings of Scripture.
7. Church practices as established by the Apostolic Church, recorded in scripture, and affirmed by the Biblical writers must be accepted as God’s standard for church practice. There is no alternative for a Bible-believing church.

1. Teaching & Authority are based upon the creative order. The man was created first and has the authority and has the position of teaching men. 1 Tim 2:11-14 "A woman should learn in quietness and full submission. I do not permit a woman to teach or to have authority over a man: she must be silent. For Adam was formed first, then Eve." (NIV)
2. A woman is to be silent in church and ask questions to her husband, at home. 1 Cor 14:34-38 "women should remain silent in the churches. They are not allowed to speak, but must be in submission, as the Law says. 35 If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church." (NIV)
3. Culture does not supersede nor negate the teachings of Scripture.

Once again, I caution the reader to discern whether this is a "Cardinal Doctrine" - essential to salvation and godly living, or a "Secondary Doctrine", or a "Conviction", or "Opinion".  The individual student must discern their own beliefs, and with what vehemence to 'argue' their case.     For me, this ranks as a personal "conviction", and not either a "Secondary" nor "Cardinal" doctrine.  

My final word?  -  The Ministry of the Word, to the people of God’s Church, is never impeded by obedience to the Word of God.