1. Are women's choices about career, family, etc. made freely, or is it discrimination that leads them to not even try to succeed in male-dominated professions or to work as many hours as men do? My own experience and observations indicate that the most important determinant of women's choices is that they are the ones who God has decided will bear children. One might point out that women didn't choose this state of affairs, but one must admit there is little that government can do to change it. But I think the question of discrimination affecting women's choices is a real issue. Even if women's choices are mostly a product of biology, some of them are not. Megan McArdle has a nice discussion of this issue.
2. After adjusting the gender wage gap for women's choices, the gap almost--but not quite--disappears. Most research is able to explain all but 2 to 5 percent of the gap, but fails to note that a gap of that size is perfectly consistent with there being a great deal of wage discrimination. For example, a 2 percent gap can occur if one-quarter of all working women are being paid 8 percent less than the otherwise identical man doing the exact same job; or if one in ten women are being paid 20 percent less. Wage discrimination on either of these scales should be worth looking into. The focus on the easily debunked gap of 23 cents on the dollar means that more-accurate measures of discrimination are ignored too easily. But maybe those who choose innumeracy do so because they want to force the idea that all women are discriminated against all the time.