If a woman wore a head covering, would this permit her to teach men?

Many Christians believe that 1 Corinthians 11 and 1 Timothy 2 are speaking about essentially the same thing. They argue that since 1 Corinthians 11 only regulates women teaching men, it is a faulty interpretation to say that 1 Timothy 2 prohibits women from teaching men. Thus, whatever Paul prohibited when he wrote 1 Timothy is no longer applicable today. But 1 Corinthians 11 does not mention women teaching men; rather, it speaks of women praying or prophesying. And prophecy is not the same as teaching. Some folks assume that it is the same as preaching, however, and therefore argue that if preaching to men is allowed, so is teaching men. But prophecy is not identical to preaching, either; it involves both forthtelling and foretelling. The reason women may prophesy but not teach or preach to men is that the message that the prophet gets from God is not filtered through the interpretive process—that is, it is directly mediated by the Spirit. Hence, in effect, prophecies are ‘tamper-proof,’ whereas teaching is not (cf. 1 Tim 2:12-14).