America remains a scientifically ignorant nation for two reasons: the resurgence of fundamentalist religion during the past 40 years, and secondly, the low level of science education in American elementary and secondary schools, as well as many tertiary colleges.
While television ratings for Cosmos may have stunned media critics and your average fundamentalist, “Americans continue to poll more like Iranians or Nigerians than Europeans or Canadians on questions of evolution, scriptural inerrancy, the presence of angels and demons, and so forth."
http://www.alternet.org/education/results-are-america-dumb-and-road-getting-dumber
I think the problem is that children are taught to accept the things that are told to them as facts. Whether it's in school (2+2=4, George Washington was the 1st president of the US, etc.) or in church (God created the Earth in 6 days, Jesus died on a cross for your sins, etc.), we have been conditioned to accept information as fact by default. Does anyone remember being taught HOW to think in school? I sure don't. It wasn't until years after I was out of school that I started to question some long held beliefs. Not religious ones since I was raised in a secular family, but things like evolution and the origin of the universe. Even ridiculously simple things.
I broke my foot when I was like 9 years old and had a cast. When it was time to get it removed, the doctor (or nurse or tech, it was all the same to me at 9) brought out a saw and when I heard the noise of it and saw the blade, I was obviously not excited about it being put right next to my skin. The doctor told me, "Don't worry, this saw can only cut casts, not skin". I immediately relaxed and let him do his thing. It's not surprising that 9 year old me would believe this but the strange part is how LONG I believed this. I was probably in my late 20's or early 30's when I started to tell someone that saws used for removing casts can't cut skin when it hit me: THAT DOCTOR WAS FULL OF SHIT! :)
It's a funny story that I like to tell people but at the heart of it is what I see as the root cause of the question: we're taught facts, not how to think. When I was in school, there were 4 "core" class types that were taught every semester: Social Studies (History), English, Math, and Science. What if there had been a fifth one called Critical Thinking? It could teach things like logic, debate, and troubleshooting. If I had had that type of education, then 9 year old me might have told the doctor "That doesn't make sense, if the saw cuts through plaster which is harder than skin, then why doesn't it cut through skin?". Maybe he would have told me that he was just kidding and reassured me by telling me that he's cut off hundreds of casts without cutting anyone. Maybe it wouldn't have worked as well as the lie, but it might have been effective enough.
Maybe teaching Critical Thinking would be difficult to do since it's much harder to assess. You couldn't ask questions with solid answers like "What year did so-and-so do such-and-such" or "X=3Y/2, solve for Y". Maybe that's part of the problem? Maybe there's pressure from religious groups to not teach it since holy books are only useful if you don't start questioning them: Where did Cain and Abel find wives? If Noah's flood cover the Earth in salt water for a year why were the land plants still alive when it receded? These are the questions they DON'T want asked in Sunday school.