Women should Prophesy and Keep Silent — A contradiction?

How do we reconcile these two passages from 1 Corinthians?

1 Corinthians 11:5 (NET)

But any woman who prays or prophesies with her head uncovered disgraces her head, for it is one and the same thing as having a shaved head.
1 Corinthians 11:5 (NET)

1 Corinthians 14:33–36 (NET)

As in all the churches of the saints, the women should be silent in the churches, for they are not permitted to speak. Rather, let them be in submission, as in fact the law says. If they want to find out about something, they should ask their husbands at home, because it is disgraceful for a woman to speak in church. Did the word of God begin with you, or did it come to you alone?
1 Corinthians 14:33–36 (NET)

Now consider this earlier description of a church gathering:

1 Corinthians 14:26 (NET)

What should you do then, brothers and sisters? When you come together, each one has a song, has a lesson, has a revelation, has a tongue, has an interpretation. Let all these things be done for the strengthening of the church.
1 Corinthians 14:26 (NET)

And note that prophecy required discernment:

1 Corinthians 14:29 (NET)

Two or three prophets should speak and the others should evaluate what is said.
1 Corinthians 14:29 (NET)

One way to harmonize these seemingly contradictory instructions is this: women were permitted to pray and prophesy in the assembly (as affirmed in 1 Corinthians 11:5), but they were to remain silent during the evaluation of those prophecies (as in 1 Corinthians 14:29–35).

This interpretation is sometimes called the Judging Prophecy View. For more on it, check out Mike Winger’s video section on this view or watch the full teaching for an overview of other harmonization attempts.