I was just about to cite this same paper (and here's the more formal paper it summarizes:
Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit ) as providing evidence against your point, OldWiseGuy. As essentialsaltes observed:
Did you read what you posted? "The findings suggest that a major factor in women's decision to leave a STEM path after Calculus I isn't ability, but confidence in their ability".
Self-confidence is a big factor, and that's not a difference in mathematical ability, but rather in how one sees one's self. Consider the student who takes Calculus I and gets a B or a C. One student looks at that and says "Yeah, I guess I'm not good at math after all. I made As in high school, but I'm not smart enough for college math." Another student with the same grade says "Well, good, I passed that class; on to Calc II!" That's not a difference in their mathematical aptitudes.
It's something I'm especially aware of, because I'm a computer science professor, and I watch for those students who are in the process of deciding they're no good at math or computer science because they're making Bs.
The answer to the problem of confidence is to separate the classes by gender. It is the presence of a majority of men in the course that affects the women's confidence. The instructor for the women should also be a women. I suggested this months ago when this topic first came up, trusting that my idea would make it into academia and thus solve the problem (this is the scientific method).
There are multiple approaches people are trying, with different degrees of success, and they are indeed being published in academic journals and conferences.
Some women do thrive in single-sex educational environments. I think that's one reason why it's important for women's colleges like Smith and Bryn Mawr to continue to exist, even though I wouldn't have chosen a women's college for myself. The absence of masculine bluster helps some women to feel more confident about themselves, as you note.
It seems also to be possible to made coed environments that encourage women to thrive in mathematical fields; Harvey Mudd is a well-known example, but there are others. The approach seems to be a mix of factors, aimed toward countering women's perceptions that they aren't welcome. Again, it's not at all about dumbing down math; but rather about making mathematical communities a place where women feel like they could belong, emotionally and socially.
I'll agree with you, OldWiseGuy, that representation in the faculty matters. If students can see female faces amongst their professors, it communicates -- to both female and male students -- that mathematics is a place where women belong.