The ACLU says no and is involved in a case in Louisiana:
In August 2009, the parents of students of the Rene A. Rost Middle School in Kaplan, Louisiana, learned that the school would begin segregating all core curriculum classes in four grades according to sex, and that no coed alternative would be offered. One parent, the mother of two daughters at Rene A. Rost, contacted the ACLU. We in turn contacted the school board, informing it that mandatory sex-segregated classes are unlawful, and we'd be forced to file a lawsuit unless they, at a minimum, offered a coed option.
The school board acquiesced, and responded that they would offer a coed option, making the choice of sex-segregated classes voluntary. But they didn't follow through: On the first day of the school year, August 17, 2009, core curriculum classes were sex-segregated. The school board then appeared to follow through on their promise of a coed option, sending a letter to parents asking them to choose between sex-segregated and coed classes. Our client elected coed classes for both of her daughters, an 8th grader and a 6th grader. In fact, 33 percent of parents selected coed classes for their kids.
But in fact, there was no real choice. The administration was actually asking parents to choose between sex-segregated classes or pre-existing special education classes that had always been coed. (Curiously, the school principal's belief in the superiority of sex segregation didn't extend to students with special education requirements.)
Whatever the legal issue is here, sex-segregated education is a dumb idea based, in this case, on a pseudoscientific understanding of biology. This particular school district (and others like it) are basing their policies on the idea that boys and girls learn differently, and thus they learn better if they're taught in separate classes.
Without even looking at the research on sex-segregated classes, you should smell something fishy in this argument. Sure, on average, there are developmental differences in girls' and boys' brains - for example, development of language skills. But biology isn't about averages: what you have are two extensively overlapping distributions, and the variation in developmental traits among girls and boys swamps out any differences in the averages. A priori, it's extremely unlikely that there will be any benefit to designing sex-segregated classes tailored to the supposeed learning styles of boys and girls.
As a parent of a 5th-grade daughter who has some learning issues that are more typically viewed as boys' problems, I've got experience with this kind of variation first hand. (And I can't tell you how many times I hear "you're lucky you have all girls - they don't do X like boys." Well, my girls always do X, whatever it is.)
I suppose it's possible that various social factors that adversely affect learning could, in principle, lead to some benefit for sex segregated classes, but a US Dept. of Education literature review (PDF) found no such benefit. And as the ACLU points out, the main effect of segregating classes can be to just reinforce stereotypes. You're much better off using the more adaptable, modern curricula found at most decent schools to tailor teaching to the different needs of the students as they come up.
In biology, it's generally the variation that counts, and not the mean.
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