I do believe there are differences, but as someone else mentioned, how can we ever place them on a level playing field to measure it?
Some of the differences deal with the fact that boys mature more slowly than girls, so girls may more quickly adapt to the requirements of classroom and homework. Girls care earlier than boys about how their grades are perceived by their peer groups.
At the same time, because girls care so much about what their peers think, I believe this puts undue pressure on them to succeed, which may not be beneficial for overall success.
Also, how do we also account for social, familial, cultural issues that may affect the student in and out of school? I cannot believe that students don't feel the impact of these things in the classroom, or when they should be doing homework. Success is some much easier when live outside of school is "healthy."
Whereas the "normal" differences seem to level out more (though not completely) in the senior high years, it seems most noticeable with middle school when everything is crazy with so many of these kids.
Gender-based learning is controversial because it could lead to discrimination or sexism. There has been some evidence that boys are more likely to be successful under certain conditions, such as when they are active or when building or using their hands. There is also evidence that girls need more instruction in science and math and that their classrooms are dominated by boys. It is always dangerous to consider generalizations, but it is important to keep considering these issues and use all of the tools we have. In other words, try it. If it works, keep using it!
One of the other reasons that gender-based learning might be controversial is the idea that by trying to appeal to or structure learning and teaching towards a certain gender means that you are making assumptions about each individual that may or may not be true.
As many have mentioned, there do seem to be general differences between boys and girls but I think it is often more important and valuable to just note and work with the differences between individuals.
Just like with breed specific legislation for dogs, trying to lump things together so that one can act in a uniform fashion generally isn't going to work out in such a uniformly nice way for everyone involved.
An important word in your question is "controversial." Controversy, by definition, involves strong disagreement, extended debate, and the expression of opinion, as well as fact, so the idea of gender-based learning is indeed controversial!
The science isn't established beyond doubt or interpretation, not that settled science always squelches controversy. Gender-based learning is controversial to some extent, maybe to a large extent, because it is a new idea that challenges previous beliefs and old ways of doing things, not just in the classroom but throughout society. To accept it would require doing things differently, never a popular option for many. The status quo is more comfortable and convenient than change. Also, many people become defensive when it is suggested they have been doing things wrong. Educators and school administrators are no exception!
I would add that in my classroom and counseling experience, females are generally much quicker to empathize and draw connections (to literature for example) than males. I tend to be able to hook females faster because they are more willing to stretch to find similarities between themselves and the stories or characters we are discussing. Again, this may be more of a social issue than a gender issue, but my experience, males are much harder to convince that something is relevant to their lives when an obvious and immediate connection is not made.
There are differences in the way that boys and girls think, so it stands to reason that there are differences in the way they learn. For instance, there are studies that show that girls learn math better in a single-gender environment where they are not in direct competition with boys. I think there are two reasons for that: one, that at the time of the study, girls didn't respond well to competition in the classroom (that may well be very different today if the study were to be repeated, but generally, girls are more cooperative and willing to work together than the "must be first" mentality of boys) and two, girls tend to act "dumb" around boys so the boys will be motivated to "help, protect, yada, yada, yada".
I can only go with my teaching and learning knowledge, but I can say in my experience there are certainly a variety of learning styles evident in any classroom. Some students are more kinesthetic learners, some concrete, etc. I cannot clearly say that the differences in learning style and preference are just isolated to gender difference, however. I find variation as much a result of social and environmental factors, medical issues and cultural diversity as I do gender. There are too many other variables in each student to isolate gender specific learning styles for me!
It may well be impossible to prove one way or the other conclusively as to whether or not girls or boys learn in distinctly different ways. I can tell you from my eighteen years of teaching in high school classrooms that it often seems that way. Keep in mind this is anecdotal from my perspective, but I find that female students tend to respond more positively to structure and detail, while guy students tend to be better at grasping larger concepts, the "big picture" ideas. My female students see, to be better at learning by reading, while my guy students seem to be able to learn more visually.
I do agree that there are differences, and much controversy remains concerning whether males and females learn better in segregated groups. Any discussion about the relative merits or otherwise of any gender is bound to be extremely problematic because limited scientific empirical evidence exists to categorically support such distinctions. And thank goodness that it doesn't, as if it did it would not help us in striving for gender equality.
I don't believe we can ever know because we can never have boys and girls who are separated from their cultural upbringing. It seems likely that there are some differences (girls seem to develop their verbal skills more quickly, from what I've seen in my daughters' classrooms). But it also seems likely that much of the difference is cultural.
So I don't think we can know the origins of the differences. But if the differences are there, does it matter if they are biological or cultural?
There are two primary components to this controversy. One aspect is the inquiry into whether girls and boys have physiological differences that make them learn differently, and the other is the idea that girls and boys learn differently because they are raised differently. Whether one, the other, or both are true, there are some important implications for all of us.
Certainly, there are many physiological differences between males and females. One area that is being looked at is brain size and within that area, the size of different parts of the brain in males and females. There is research that shows male brains being generally larger than female brains, and even some to show a difference in various regions of the brain. But this research is not conclusive, and does not necessarily tell us how such differences affect learning. Another avenue of research might be an inquiry into how "male" and "female" hormones affect learning. One serious limitation of research is that we really do not know to what degree our environments affect brain development. I am not aware what research, for example, has been done on newborn brain size, which might at least tell us how girls and boys start out. But even that is a problem, because girls and boys are in prenatal environments that affect them, too.
On the other side, there are those who argue that there are no learning differences between boys and girls except those that we create by how we treat boys and girls from birth. Historically, for example, girls were actively discouraged from becoming scientists or mathematicians and the skills needed to enter various professions were not nurtured.
In my opinion, it is likely that the "truth" is a combination of both physiological and environmental factors, which leaves us in a bit of a quandary. If there are physiological and environmental factors that affect learning, what should we be doing for boys and girls?
There are many implications in this controversy. One that has arisen in the past few years is the idea of single-sex education. If boys and girls learn differently, perhaps they should be taught separately. And bear in mind that education is an lifelong endeavor. If males and females learn differently, what are the implications for employees who must learn on the job? Should we have separate job training for males and females? Should we have separate classes for senior citizens who want to learn to use computers? This is a complicated area because we could be making policy decisions based on what is now a very primitive level of understanding of how people learn, and people often use shaky scientific research to pursue their own agendas. I have included two links for you, to recent programs that discuss the controversy and also provide some good examples of how this issue is playing out, right now, as we speak.