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JoshuaZ comments on Why do people commit mathematical mistakes? What are the mechanisms behind them? - Less Wrong
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There's a lot of literature on this. One thing that people have tried to do is look at specific common flaws and then try to figure out what kids are thinking. One very studied area has been students confused over how .999...=1. See this summary section in Wikipedia which gives a pretty decent summary of that literature along with references. I do seem to vaguely recall also additional studies that have shown a correlation between not believing the .999... and likelyhood to make algebraic mistakes, but that isn't cited there, and I don't remember the authors names or any other relevant search terms. Is anyone familiar with this?
People did studies on that? That just seems so frivolous!
It isn't an obvious thing. .999....=1 is a problem of understanding how the real numbers work, and actually goes so far as to sometimes impact otherwise good calculus students and the like. Algebraic manipulation is largely formal without regard to the conceptual meaning. While I would have guessed that there would be such a correlation the issue isn't obvious. So no, it isn't frivolous.
It seems frivolous to me too.
But I think if someone had a proper, almost religious respect and gut intuition for the separation of levels and meta-levels, it wouldn't seem so at all.
Can you expand on that claim? I'm not sure I understand your point.
The study is about people confused about something not worthy of further study. At first glance it might look like a study of the thing not worthy of further study itself.
Ah. I see. I don't think that was what was going on here. Wedrifid seemed to find it frivolous because he considered it trivially obvious that the two types of mistakes would occur together. I don't think for example wedrified necessarily consider it frivolous if someone did study which looked for a correlation between not understanding/accepting .999...=1 and say performance at dual-n back or some other task that is not as obviously related to mathematical ability.
Also because, we'll it'd be fun to do the study but I'm not quite sure how it got to the top of someone's research priorities! On the other hand I suppose it would be a cheap study to do and something to keep the post-grads amused.