I do believe it has to do with the teaching process.
When pursuing a PhD in medicinal chemistry -- which stupidly enough I completed all the educational and research requirements for, as well as passing my qualifiers and having all the work related to my thesis published in peer-reviewed journals and writing half the thesis itself, I never did finish writing it and therefore never got the degree -- naturally I was required to teach the pharmacy students a lab course as well as general TA'ing.
The lab course was pharmaceutical analytical chemistry. Now while the official requirements were that they learn such and such procedures and blah blah blah, from my perspective the vast majority of pharmacists have no need of such things -- and the few who do will get much more specific and in-depth further training and experience -- but what every pharmacist and for that matter physician really, really, really ought to understand is what tests really are testing for, how they may be in error, how factors might cause an error and what direction the error would go in, and this kind of thing.
So that really was my focus.
What hard work this was!!!
The great majority of pharmacy students -- and these were not first year, they were actually in their first year past the bachelor's degree -- really cannot think, I found out. Well just barely in some regards, but the above kind of things were just obviously vastly beyond anything the educational system had ever required of them.
As a mostly-unrelated thing, I was also in an unfortunate situation where I was required to give the students quite high grades. They had a hard time in the lecture course, and the lab course counted as an exam in the lecture course grade, and rather than dumb down his tests the professor preferred to give the students an "easy test" by having the lab grade be high if they put in any half-decent effort. So I was instructed that 90% was pretty much the bottom grade for any student that did put in a reasonable effort.
Well it was quite hard getting their grades up there. First method I employed was a "splitting the difference" system where if they earned for example 80% on a quiz, they'd get a 90. Or if they earned a 90, they'd get a 95, and so forth.
That however was not enough. What did manage to get the job done was adding in questions that were deliberately ones that really and truly should not be missed even by them.
However because of their problems with thinking, and also on account of my not liking putting in questions that were just pointless, generally there really would be a point behind the "giveaway" question.
ANYHOW -- this obviously is turning into one of my long, rambling stories -- one day the lab work was determination of calcium content by EDTA.
Now, one thing about this which of course I made sure they learned and demonstrated understanding of and ability to think using this information, was that the analysis actually does not pick up only calcium but also other things, for example magnesium, and so if one does not know that other species that EDTA binds are not present, one actually doesn't know how much calcium there was, regardless of the name of the test.
But as it happened the big news story of the week was OJ's defense bringing forth the fact that the bloodstains on his socks had EDTA in them, and there was no reasonable explanation for this other than the blood not having been directly from a person, but planted after the fact from some forensic specimen of the person's blood.
So here was the giveaway question for them to think about: Suppose that it is true that the bloodstains found on OJ's socks contain EDTA, and suppose it is true that the only way this could be the case is if the police planted the blood on the socks. If so, would this prove that OJ did not kill Nicole?
I had actually, overoptimistically, expected that this would not be beyond their thinking capacity.
I was wrong. Quite a high percentage decided that this, if so, indeed would prove that OJ did not kill Nicole.
So you see what I am saying about ability to think. They had somehow got through 16 years of education, not counting kindergarten, without ever being required to think to the quite limited degree I was working to get them to do.
By the end of the semester I did make a lot of progress in their ability to reason things out. I have no doubt that if they had run into that sort of effort frequently in the previous 16 years of education then their abilities would be entirely different than what they were. But that clearly was not the case.
Getting back to the basic math, I will cut this story much shorter. My ex-fiancee's kid was doing badly in school and we were trying to get him into a private school that had a tough entrance exam. He really was way too far behind but it was worth giving it a shot until clearly impossible.
Now this was either for the first grade, his having just failed that in government-run education, or trying for the second grade after he had passed the first grade the second time around. Not sure at this time which it was.
I had no problem at all teaching him about numbers the way that ought to be the case. Ask him (then) about 81, for example, and immediately he recognized that as being 9x9. In the same manner as for example a kid could have an animal named to him and he could tell you immediately various things about it.
Now when having numbers in the mind this way, then of course when given a problem such as 81 / 9 = ? there is no work required, it's just obviously 9! Because it's something one knows about 81.
Well, they had an idiotic requirement for cursive writing as well which proved too much of a barrier. My ex-fiancee never did move in with me and did not keep up with me helping him with math or anything else. His loser teachers in the government schools of course did not teach in any effective manner. Soon he lost the ability to do the sort of thing I descibed. Sadly he will finish high school, if he graduates HS at all, as being of barely functional ability with regard to numbers and such things. Judging from where he is in the 5th grade, which is all he is at now after having failed grades three times now.
I fully expect that the teachers totally fail to do the relatively simple things that would have people just naturally, same way as being able to tell you that bald eagles have white heads and they are birds and that sort of thing, know that a billion was more than any number of hundreds of millions (unless more than 10 hundred million) and so forth. And other experiences in life don't do it.
Another way of perhaps explaining this is as follows. Have you ever noticed that if someone gives you directions and all the things named as reference points are unfamiliar, this is mentally difficult, hard to remember, and you don't necessarily manage to follow those directions? Whereas when each step, for example "Turn left at Elm Street" is referring to a thing you know quite well, that you already have a place in your mind for, then directions of perhaps the same general complexity are easy to understand. It is very hard to really grasp something new when it requires reference to things you don't really grasp in the first place.
For people in general, hearing $350 billion is rather like hearing "Turn at Princeton Street" when they have no damn idea where Princeton Street is. Yeah, they've heard it used by other people before but themselves, they have no idea where it is. So when getting such a direction, they have no idea if it is north of the railroad tracks (for example), or south. Similarly they don't actually know if $350 billion is less or more than some number of millions or trillions. At least this is my hypothesis, that despite years of "education" they actually don't have places in their minds, so to speak, for these things.
The fact that kids go through tens of thousands of hours of "education" in which so very, very, very much could be accomplished but so little is is a true tragedy.