Some recently reported research (I apologize for lack of a reference) explains that already in the crib girls are paying attention to people and boys, to things.
Then what the OP is describing about differences in K through the early grades is essentially just that the girls are more interested in people, e.g., pleasing the teachers, and the boys are more interested in the material, at least if it has to do with things, which in those grades it mostly doesn't.
In particular, of course the girls are much better behaved in class: From the crib, the girls are much better socially than the boys, and that means girls do better in groups, e.g., the social behavior in a classroom.
Next, in those early grades, the girls have much better verbal aptitude so do better at reading and writing, learning languages, etc.
Next, by paying more attention to people, girls have much better understanding of people in the fictional reading that is common and, thus, do better in that reading. Also the girls have much better understanding of emotions and, thus, better understand the emotional content of fictional readings. Also, as in D. Tannen, the girls are much more active in talking with their friends, i.e., their girlfriends, with gossip, and, thus, get still better at understanding people and social situations, including what is in the fictional readings, the classroom social dynamics, etc.
The OP also claimed that the girls are better at "math", but here I start to question. Sure, for math in K-8 or so, the girls are much better because they have much better clerical accuracy and much better handwriting (better at getting the columns of digits lined up important for accuracy). And, again the girls are better at and more interested in pleasing the teachers.
And, with some teaching and grading styles, the girls might be able to seem better at math through grade 12 or so. It can continue to be a really big advantage to be really good at sensing how to please the teachers, and girls are better at that.
But my experience in math (and I was a math major in college and my Ph.D. is in applied math), really, for much of anything like real math, the girls are a big step down. Somehow they don't get it; here maybe the main problem is lack of interest due to cultural stereotypes that girls are not supposed to concentrate on STEM subjects.
Last I heard, on the math SATs, the boys still do much better than the girls and, yes, on the verbal SATs the girls do better than the boys.
Then for the girls/women along come marriage and babies, and then on average their ability to compete with boys/men in most of more important work fades.