I know a lot of older kids who really, really, really don't get fractions. I think their native understanding has been destroyed by the way they've been taught. It's pretty funny to watch a bored 12 year old play with halvning and quartering etc things, and then not be able to work out that two quarter cups of flour is the same as half a cup, having physically done it, in measuring cups, twenty seconds earlier. (true story)
A 9 year old I know had a similar brain-freeze trying to figure out how far it was to go 2k twice, becasue he tried to do it as fractions and got all gumbled up in the terms "Numerator" "demonimator" etc. This despite having started by saying "well, the whole distance is 4k, so half is 2k" (IE: the problem was so easy for him [being 2+2, after all] he started by stating it in terms of the answer -- and then couldn't solve it becasue he got confused by LCMs)
So.... what I'm trying to say is... I, personally, wouldn't trust the "recomended" approach to fractions. (Or flashcards, personally, but if the kid likes 'em I guess that's a moot point)
