In RT France’s Women in the Church’s Ministry, chp 3, France looks at the contested passages in Paul’s letters: 1 Cor 14:34-35 and 1 Tim 2:8-15. I’ve loaded the texts into this post to make life easier for us today. But, there are lots of disagreements and debates here so we’ll have to work at civility.
1 Cor 14:34-35:

34 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.

1 Timothy 2:8-15

8 Therefore I want the men everywhere to pray, lifting up holy hands without anger or disputing. 9 I also want the women to dress modestly, with decency and propriety, adorning themselves, not with elaborate hairstyles or gold or pearls or expensive clothes, 10 but with good deeds, appropriate for women who profess to worship God. 11 A woman should learn in quietness and full submission. 12 I do not permit a woman to teach or to assume authority over a man; she must be quiet. 13 For Adam was formed first, then Eve. 14 And Adam was not the one deceived; it was the woman who was deceived and became a sinner. 15 But women will be saved through childbearing—if they continue in faith, love and holiness with propriety.

In essence, here are France’s conclusions and, of course, your comments are welcome.
On 1 Cor 14:34-35:
1. There is a major text-critical issue here. FF Bruce, for instance, told me it was “textually suspect” and should not be used to construct our theories about women and ministry. Fee agrees. France takes it as Pauline.
2.France says, wives are being counseled to ask their husbands at home, they are not to interrupt prophets while they are speaking. There is not a blanket silencing of women, since women could prophesy in the church (11:5).
On 1 Timothy 2:8-15:
1. Very complex discussion. The background is sketched. Women were empowered in Ephesus; they were assuming teaching roles for which they were not qualified. The Christian women were assuming the liberation of the freedom-dominated worship of Artemis.
2. Paul encourages wives (not women in general) to learn before they teach; he encourages those who want to be ascetic to be married; he does not think this is “creation” ordinance but “couple” teaching — Adam and Eve stand for a husband and wife team when the wife got out of line.
3. He points to the connection of 2:11-15 and 5:11-15. Notice the similarities:

11 As for younger widows, do not put them on such a list. For when their sensual desires overcome their dedication to Christ, they want to marry. 12 Thus they bring judgment on themselves, because they have broken their first pledge. 13 Besides, they get into the habit of being idle and going about from house to house. And not only do they become idlers, but also busybodies who talk nonsense, saying things they ought not to. 14 So I counsel younger widows to marry, to have children, to manage their homes and to give the enemy no opportunity for slander. 15 Some have in fact already turned away to follow Satan.

This house to house meddling and chatter could be what Paul means by teaching in 2:11-15, and their need to be formed and taught before they become teachers. And notice also the exhortation to marry and have children, and that in 2:11-15 childbirthing leads to redemption.
4. He points to “authenteo” (“usurp authority/have authority”) being an odd term to choose had Paul meant only “no authority over.”
5. He asks, as so many have, if it is not the case that the wide-scale dispute about so much in this text leads us to a much more difficult situation of using this text to determine central issues in women and ministry discussions.