Is 1, 2, 19 or 21 closest to 12/13 + 7/9? [pdf] | Hacker News Reader

9? [pdf]

files.eric.ed.gov

4 pointsjethkl15 comments

I'd say there's a big difference between someone choosing one of the first two answers versus the last two.

Perhaps. However, if there were any evidence of 1-or-2 versus 19-or-21 type thinking, I would expect the results to be non-random. But the results of asking students who should know the answer were equivalent to random guesses.

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.

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.

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.

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.

Much worse is the example showing their inability to eliminate answers when multiplying decimals.

Yes. I interpret the results as evidence of serious and systemic problems.

In 1978, a US-based study posed this question to 20,000 8th graders. Just 24% selected the correct answer. This is basically equivalent a random guess. In 2014, the same question was posed to 48 suburban US students. Only 27% selected the correct answer.

That outcome also explains why the avocado toast propaganda worked. Propaganda isn't telling falsehood, it's omitting truth, math in this case.

The answer is so obvious that it isn’t even worth testing or commening on.

Did you guess correct one, btw?

I agree that this is a trivial question. But the linked pdf explains why it is an interesting question: it was posed to 20k US 8th graders in 1978, and the results were random. The same question was posed to 48 US students in 2014, and results were again random.

It seems like it's testing two very different things. If you choose the third or fourth answer it means you don't understand fractions at all. If you choose answer one it means that you either tried to do the exact calculation and made a mistake or else that you don't have much experience with approximate arithmetic, which really shouldn't be surprising since very little emphasis is placed on that in school.

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