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A past question described a school where many teachers insisted that answers to algebra problems had to be phrased in set-theoretic language or notation. For example, when asked to solve $2x+3=6−x$, students were expected to say that the solution set was $\{1\}$, not that $x=1$. In a comment, the OP wrote:

I think that there is a history in my department of using a particular textbook that stresses this distinction, and that over the past several decades, it has crept into the culture here to the point where it is codified in course descriptions.

Now I'm wondering who the authors of such textbooks were. It feels like old math education, in the vein of New Math... Presumably the makers were American? Unless a school was importing their textbooks from overseas?

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    $\begingroup$ I've seen a number of College Algebra texts that talk about but do not focus on set-builder notation for solutions in their chapters on inequalities (openstax.org/books/algebra-and-trigonometry/pages/…, for example). To clarify, is your question about the phenomenon in the linked question, of the answer to a "solve" problem explicitly needing to be presented as a solution set? $\endgroup$
    – TomKern
    Commented Jun 1, 2021 at 5:55
  • $\begingroup$ @TomKern - Yes. "Solve" problems with their answers presented in set notation. $\endgroup$
    – Malady
    Commented Jun 1, 2021 at 13:13
  • $\begingroup$ Have you reached out to the OP from the linked question? He may have a list. $\endgroup$
    – Nick C
    Commented Jun 1, 2021 at 14:19
  • $\begingroup$ @NickC - How do I do that on here? $\endgroup$
    – Malady
    Commented Jun 1, 2021 at 14:36
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    $\begingroup$ @NickC - Comments don't bump questions up in the sorting? I thought it did, but I guess this stack is low traffic enough that I can't tell the effects of bumps vs edits... $\endgroup$
    – Malady
    Commented Jun 1, 2021 at 17:47

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It really depends entirely on what is being asked. I have often required set notation from my students (but I teach at the college level). Either is fine for me, but if the instruction is to define the answer within a particular form, then I do believe it is necessary. If the student did not follow the instruction, then I would most certainly deduct points. I have even deducted points for things like "put your first initial and surname" if a student puts the full name. This is to train them to be precise when asked to be precise. This is important because what if, for example, you have an absolute value equation?

Now, in response to your question about the book: Mostly in former Soviet textbooks will you see this as well as continental European texts. In the case of the US, I can definitely recommend you look at Dolciani's Modern School Mathematics (1960s or 70s version).

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  • $\begingroup$ Surely if they write their full name then they've written their first initial and surname! $\endgroup$
    – Thierry
    Commented Jun 7, 2021 at 0:26
  • $\begingroup$ Not at all. An initial is the first letter only (that is, to the exclusion of the rest of the letters in the first name), as defined in the English language. $\endgroup$
    – Wasp
    Commented Jun 7, 2021 at 0:35
  • $\begingroup$ Training them for precision or for accuracy? $\endgroup$
    – ryang
    Commented Jun 12, 2021 at 15:44

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