That is sobering. Do you think any of the people in that borderline-remedial class may have been the victims of poor instruction, or do you think that they're all in the bottom 10% for native ability?
My hunch would be that it's more interesting than either of those. I once set an extremely simple percentage problem in an exam (accidentally - I was examining something else and this was part of the set up; it didn't occur to me that this part might be a problem to anyone!). Think "what is 40% of 10" - it was that level, requiring nothing more than an understanding of what "percent" means. Around half (I forget, now, whether it was a bit more or a bit less) of the students got it wrong. Now, admittedly, this was part of a stressful exam and it will have been obvious to the students that this sum wasn't the point of the question - but I was shocked that it was even possible for a substantial proportion of them to have got it wrong! The course these students were on requires them to have an A grade at A level mathematics, or equivalent; that puts them easily into the
top 10% of the population for mathematics achievement.
The spiral methods criticised by the author of that article are not widely used in this country, so we can't blame them here. I think there's a large group of people who can easily learn to apply a mathematical method while they're in the process of being taught it and tested on it, but who do not consider it worth giving brain space to afterwards. For me, and probably for you (dear Reader ;-) fractions and percentages form part of the basic mathematical language that it's hard to conceive of forgetting, but I think what's in that language and what's out is more variable than we sometimes consider. I noticed the other day that I have forgotten some of the trigonometric identities that DS is about to learn, which would have shocked me once, but does so no more!
