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I'm an instructor of a College Algebra course and I noticed a problem with one of the computerized questions. I was going to ask for opinions here, but then I wasn't sure what was the proper forum for it....math.stackexchange.com? education? English? I'll put the question I was going to ask for context below in spoiler, please do not answer the actual question here, I'm just looking for advice on the proper forum to post it in the first place!

Computer question: Write the corresponding algebraic expression or equation for the verbal statement. Let x represent the unknown number. The quotient of one and five times a number.

The problem is where does one put in the pause in the English language. You could parse this as either "The quotient of one and five" "times a number" which gives you the answer of 1/5 * x, or the way the computer wants, "The quotient of one and" "five times a number", which gives 1/(5x). The computer only accepts the second interpretation, but according to my reading of the English language, either reading should be acceptable


From the comments, I decided English was the right place. In case anyone wants to participate in the discussion over there, here's the link. https://english.stackexchange.com/questions/496210/parsing-an-english-to-math-expression-question-is-this-ambiguous

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    $\begingroup$ I know you said not to answer the question, but who listens to people these days? There are many statements like this that are technically ambiguous, but are not ambiguous in mathematical language. I can't articulate why, but the computer is correct. $\endgroup$ – Matt Samuel Apr 25 at 21:05
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    $\begingroup$ @Alan Actually, there's even a third, which I also consider reasonable, interpretation. This is that the "one" and "five" both apply to "a number", which then gives $\frac{x}{5x}$ as the expression. I won't even try to answer which of these $3$ interpretations is most "reasonable". As for which site would be best to ask about this sort of thing, I believe it's more about how to parse & interpret an English sentence, than anything specifically to do with math, so something like the English Language & Usage site would be where I suggest you ask. $\endgroup$ – John Omielan Apr 25 at 22:29
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    $\begingroup$ "I was going to ask for opinions here...." Asking for opinions is not what math.stackexchange is for. Indeed, one of the standard reasons for closing a question is that answers are likely to be opinion-based. math.stackexchange is for answers, not opinions. $\endgroup$ – Gerry Myerson Apr 25 at 22:40
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    $\begingroup$ @GerryMyerson Yeah, I realized that before typing the question in, thus I figured I'd check the meta first for the right place to actually place the question. English language stack exchange it is! $\endgroup$ – Alan Apr 25 at 22:45
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    $\begingroup$ added link to the actual question in the body here, if anyone wants to participate in the actual discussion. Thanks all! $\endgroup$ – Alan Apr 25 at 22:50
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    $\begingroup$ @Alan I read your question on the English site. Regarding your statement at the end, I would suggest you contact the vendor to get the question removed/changed regardless of whether or not the responses there show a general consensus on how it should likely be interpreted. In my opinion, an average English speaker/reader could easily, & reasonably, interpret the question any of the 3 possible ways. Thus, if it's kept, it should be reworded to make the intention clearer. "A quotient of one, and five times a number" might be sufficient, but my suggestion is "One divided by five times a number". $\endgroup$ – John Omielan Apr 25 at 23:04
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    $\begingroup$ @Alan I just realized my second suggestion above could also be interpreted in more than one way. As I'm not an English linguist, I hope somebody at the other site gives you some more useful suggestions. I note that, as I write this, there's already $2$ comments there, both of which disapprove of the wording. I especially like Hot Licks comment of "It's gibberish to me.". $\endgroup$ – John Omielan Apr 25 at 23:10
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    $\begingroup$ The situation is made worse because non-technical society is very tolerant of linguistic ambiguity, but when the sentence concerns topics within a discipline perceived as "logical" then the layman (here including the test preparer) assumes the English sentence must magically become unambiguous. Nobody would complain that somebody answering "the color of Lucille Ball and Jimmy Olsen's hair" with "white and crew-cut", was unfairly marked wrong (the answer is "red"). But this is precisely the sort of construct that turns ambiguous when presented in a context-free environment, lik math. $\endgroup$ – Mark Fischler Apr 26 at 21:01
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    $\begingroup$ I somewhat disagree with Gerry Myerson. I'm pretty sure being "primarily opinion-based" is a reason for closure in all SE sites. Questions should draw on the expertise of the answerer base, not just poll them for opinions (see here for more). However, I don't think your question does this by any means. I think it fits on MSE, ESE, and MESE (matheducators.stackexchange), in increasing order of goodness-of-fit. $\endgroup$ – Theo Bendit Apr 29 at 2:30
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    $\begingroup$ @Theo, I can see that I did not make my intentions clear. What I meant to convey was that if OP is going to ask a question on math.stackexchange, the question should not be phrased as, "I'm going to ask for opinions here." Rather, the question should be posed in such a way as to have answers that are not primarily opinion-based. $\endgroup$ – Gerry Myerson May 7 at 13:13
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    $\begingroup$ @GerryMyerson Ah yes, then I agree. $\endgroup$ – Theo Bendit May 7 at 13:29
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If you want to know how English speakers would interpret the phrase, then English is the right place. If you want to know what the conventions in Math are, then you should ask in Math. This is not a "question of opinion", this is an important issue that mathematicians have come up with specific rules, called order of operations, for.

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