I think it would be great if we could change methodology; I am strong in the maths, sciences, logic etc, but I am also very strong in visual comprehension (I do patterns less well, but can navigate 3D space well, and can picture and manipulate 3D objects mentally with little effort. I also can superimpose mental images over what I see easily), I am artistic, and tend to remember visually.
I hate school. I hate, hate, hate it. I can do the math, I can comprehend the science, I have enough memory to do the history, I have a natural feel for english that lets me slide through english classes. But I still struggled in high school--not against the material, but against my hard to describe disinterest. Heh, extrapolate that through to college and you get where I am now: in between majors, trying to stay interested enough in physics to continue to do the homework.
So what's the problem? I think it is largely due to the way material is presented. I prefer being shown things rather than being told, but either way works (thanks to the duality I can access). However, it is very important that the teacher make the material interesting. If it doesn't strike me as being more worth my time than sleeping all day is then I won't put energy into it. End of story. I am not motivated by the logic of long term goals--i.e. get through the classes, get the degree, make money, pay off debts, become well established, and then do and take what you want to take, do what you want to do. That sounds great, but won't motivated me to get out of bed in the morning, let alone to do boring homework.
It worse for those without the same math and logic skills I have, they don't just
prefer the 'show me, then let me try' method, they don't necessarily know what to do at all with the 'tell' method. They probably have the same problems with long term motivation when there isn't some passion to drive them (and who has those in k-12?). My little sister is a great example; she is extremely emotionally and visually driven. Math and logic and science are foreign concepts to her. She tries in school, and is smart enough to do any subject if she tries hard enough, but comes home and is frustrated because she cannot understand what her teachers said, what they expect of her, etc. She cannot understand the 'tell' method. Don't believe me? Just try giving her some intructions--for, say, copying music to her I-Pod--and watch as she gets lost and confused. Show her instead, and she does much better.
These kinds of people will never be engineers, but they are capable of more than painting pictures; unfortunately they don't mesh well with the current methods of instruction. And I tend to think I have it bad because I
prefer what they often
need 
Definately should offer more than one methodology if and when we are able to on a public scale.
It is because even if they are really really good, their work has no market value until they die