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Comment by tgflynn | Hacker News Reader

Where in the paper is the distribution of answers over the four possible choices discussed ? The fact that the number of correct answers is close to what you would expect if the students were guessing randomly does not imply that the actual distribution of responses was uniform.

EDIT: In addition the conditions under which this test were given could matter a lot. How much time did the students have to answer ? Did they have access to scratch paper or did they have to do everything in their heads ? If they only had 5 seconds to answer I wouldn't find a random distribution of responses all that surprising.

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From https://www.jstor.org/stable/27962023

    1 ->  7%
    2 -> 24%
   19 -> 28%
   21 -> 27%
  IDK -> 14%    "I don't know"

At least they know the answers is not 1 (perhaps they thought the answer of a sum in never 1???), but ignoring the 1, it looks worse than random.

Linking to the cited followup study that ran 36 years later. Similar results are reported. https://files.eric.ed.gov/fulltext/ED565462.pdf

Well if these issues are as universal as they say, continuing across decades and very different cultures and educational systems, then it seems likely that it's just an inherent fact about humans that only about a quarter of them are able to understand the concept of rational numbers.

Well at least that provides more information than the OP's title or link, but since the paper is behind a paywall there's not much more I can say about it.

It is odd that 1 got the smallest number of responses, since it's by far the second best answer.

If you use a bad summation algorithm, 12/13 + 7/9 = (12+7)/(13+9) = 19/22, so 19 will be probably a common answer.

I can't imagine how to get 21. Perhaps 12/13 + 7/9 = (12+9)/(17+7) = 21/20 ??? It's somewhat like a bad version of a division, but I don't expect it to be so popular.

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