Since the woman, in the creation order of things, is under the authority of man, she is to teach only other women and children. Needless to say, intelligence is not the issue here. One gender is no more intelligent than the other.
<font color="ff4500"><b>But I want you to know that the head of every man is Christ, and the head of every woman is man, and the head of Christ is God.</font></b>
(1 Cor. 11:3)
<font color="6c2dc7"><b>The older women lilkewise, that they be reverent in behavior, not slanderers, not given to much wine, teachers of good things -- that they admonish the young women to love their husbands, to love their children, to be discreet, chaste, homemakers, good, obedient to their own husbands, that the word of God may not be blasphemed.</font></b>
(Titus 2:3-5)
The younger women and widows are urged to get married and bear children.
<font color="e45e9d"><b>Therefore I desire that the younger widows marry, bear children, manage the house, give no opportunity to the adversary to speak reproachfully.</font></b>
(1 Tim. 5:14)
So, in my understanding of Scripture on the issue of authority, man is to be the teacher over women, not the other way around.