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One of my college students writes the Greek letter $\pi$ as a script n with a bar over it, like $\bar{n}$. [There is actual space between the letter and the bar.] I have never seen this before, and Googling didn't get me anywhere. I feel compelled to 'correct' him on this, but I wanted to first make sure this isn't, say, an accepted form of the letter. I am asking this here, as I am supposing mathematicians and math historians may have a better view of what and how symbols are used in the field (as opposed to a different site that focuses on Greek language).

Have you seen this symbol used in place of $\pi$? Did my student just make it up?

A more general question here: When should we correct students who use alternate symbols or form them in a new/strange way? Obviously, there are certain things I won't budge on, like using a symbol whose meaning has one standard use (e.g. $+$) in place of another (e.g. $-$). But where should we draw the line? [No pun intended]

[This question may be too 'opinion-based' and I understand if folks vote to close it.]

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    $\begingroup$ "Did my student just make it up?" Is your student's native language written in Cyrillic? Lowercase "п" (derived directly from π) is written by hand like a Latin "n" (in Russian) or like a Latin "ū" (in Serbian). $\endgroup$
    – Trang Oul
    Aug 29, 2023 at 5:15
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    $\begingroup$ Are you sure this is a "script n with a bar over it" and not "omega with a bar over it", i.e. $\varpi$ (variant pi)? $\endgroup$ Aug 29, 2023 at 8:39
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    $\begingroup$ Did you try asking the student about the strange symbol first? They may be able to explain it better than any Google search could. $\endgroup$
    – Zibbobz
    Aug 29, 2023 at 13:31
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    $\begingroup$ @Dominique It turns out you had the right idea about first language. This was the way they remember first learning it as a child in a Spanish-speaking country. $\endgroup$
    – Nick C
    Aug 30, 2023 at 4:12
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    $\begingroup$ It is a curious fact, that a brief lecture on common symbols is never a part of maths courses. Perhaps you (and all other maths teachers) should design such a lecture? Perhaps not just Greek, but also other font styles like blackboard bold and Fraktur - not to mention the occasional use of Hebrew ($\aleph$)? Knowing that these things exist helps a lot, I find, even if you don't remember the details. $\endgroup$
    – j4nd3r53n
    Aug 30, 2023 at 8:22

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Not sure if this is the case but: is this student a Spanish speaker? What they write looks like ñ, so if that's the case it could just be that they are interpreting 𝜋 as a letter they know, specially if they haven't been explicitly taught about the Greek alphabet or if when they were taught they were ill or going through a rough phase that made them unfocused.

So just asking "Hey, have you ever been formally taught the Greek alphabet? I notice for 𝜋 you write it like ñ, which could lead to confusion with other letters/symbols, or could be a problem if another teacher needs to replace me at some point as they could misinterpret things. Here is a good resource to learn how to (or improve how to) write them. I recommend you do some practice on this by X date, and I'll be happy to help as you require"

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    $\begingroup$ Update: It sounds like this was exactly the situation. $\endgroup$
    – Nick C
    Aug 30, 2023 at 4:10
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    $\begingroup$ Jesus H Christ, You're telling me there are math teaching professionals that actually teach the Greek alphabet? Sounds like a great idea. never had, heard, or have seen this happen... Many seem to take the entire zoo of write-only symbology in mathematics for granted, yet more do not even bother to pronounce the symbols they use, making it impossible to even google things sometimes. For the first 5 years after I was introduced to summation, I didn't hear a mathematics lecturer once utter the word "Sigma" let alone it's relation to the Greek alphabet... $\endgroup$
    – Krupip
    Aug 30, 2023 at 20:56
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    $\begingroup$ @Krupip my mathematical programming teacher called $\xi$ "kuhsee" and also wrote it weirdly. Took me a while to puzzle it out, and I only managed because I read the little notation blurbs in (some) textbook covers that list the Greek alphabet and their names - I don't think he knew it was the Greek letter $\endgroup$
    – No Name
    Aug 31, 2023 at 1:19
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    $\begingroup$ @Krupip Honestly I would assume you learn about the greek alphabet somewhere around grade 9 at latest. In college we were just told to brush up on it, since we would need more than just alpha/beta/delta Gamma. I mean how do you teach physics without greek? Even the basics you get in elementary are likely to have at least \rho and \epsilon. The fact you can in some way get to college without even knowing \pi seems completely insane to me. $\endgroup$
    – DRF
    Aug 31, 2023 at 17:26
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    $\begingroup$ @DFR Schools are quite inconsistent with teaching depending on the socioeconomic status of the area, so you can't rely on students having consistent 'basic' knowledge. Lower income kids often feel shame about asking basic questions that can be treated as 'stupid' by more privileged kids or even their teachers. Plus, in school you might learn pi, lambda and little else. In university you need to know all of the greek alphabet, both upper and lowercase. If a teacher doesn't have time to dedicate a full lesson to teach it, at least they should provide enough material for students to learn at home $\endgroup$ Sep 1, 2023 at 9:40
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Personally, if I can make up an ordinary math problem where the student's alternate/new/strange symbols lead to an incorrect response, then I think that's grounds for correcting the student. (Of course, I'd show them the problem I came up with so they understand why I'm correcting them.)

In the case of your student, the following problem would suffice:

Suppose that you have a collection of $N$ polygons, where $\bar{n}$ is the average number of sides per polygon. Prove that the sum of all the interior angles in this collection of polygons is $(\bar{n}-2) N \pi.$

In this problem, your student's notation would lead them to state that the sum of all interior angles in the collection of polygons is $(\bar{n}-2) N \bar{n},$ which is incorrect.

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    $\begingroup$ This seems like the most practical answer. I have seen many mathematicians write symbols in all flavors of strange and eldritch ways. Seems everyone has their own flavor of $\xi$. To me the questions are, "Are the symbols recognizable? Can they be disambiguated?" The value in your example problem is that it points out the student's writing does not pass check #2. At the same time, #1 may still be an issue if a reader would not understand that the student really meant $\pi$. $\endgroup$
    – Slate
    Aug 28, 2023 at 23:41
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    $\begingroup$ @njuffa Mark E Smith tried to make a go at popularizing eldritch $\endgroup$
    – D Duck
    Aug 29, 2023 at 11:09
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This isn't a moral conundrum, and your students shouldn't be snowflakes who freak out when they're corrected on something like this. They need your guidance in fixing their incorrect habits while they're still easier to fix, so that they won't become embarrassments to them later on. Here are some typical examples I see of students writing Greek letters incorrectly:

enter image description here

In most cases, what they're doing is to write the Greek letter as if it were some superficially similar Latin letter. In the case of gamma, I think some of them are responding to the fact that in some fonts (such as the default math font used by LaTeX), the bottom loop is very skinny, and it's hard to tell that the letter isn't in fact a y.

It's not OK to say that these are simply arbitrary codes. First of all, it's not a one-to-one mapping. And in many fields in the sciences, engineering, and statistics, the Greek letters have specific meanings. In engineering, ω is an angular frequency. In physics, γ is the Lorentz factor. In statistics, σ is the standard deviation. It's also common to hear students using the corresponding incorrect names, e.g., reading cos ωt as "cosine of double-u t."

Re the specific example you gave, there is some variety in how Greeks write π. For an unusual example, see the image on this page: https://en.wiktionary.org/wiki/%E1%BC%B5%CF%80%CF%80%CE%BF%CF%82 If your student might be Greek or might have grown up with the Cyrillic alphabet, you could certainly ask if this is some style of writing π that they learned in their home country.

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    $\begingroup$ I write $\sigma$ "incorrectly" as in your picture and I see no big problem with that. And FYI, that alternative way of writing $\pi$ has the TeX command \varpi, rendered $\varpi$, and I have indeed seen it used as alternative for $\pi$ e.g. to denote prime elements in number theoretical texts. $\endgroup$ Aug 29, 2023 at 2:44
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    $\begingroup$ @TorstenSchoeneberg I think the complaint is that it looks like a cursive o. In this day and age, when cursive isn't really taught, there isn't any problem at all $\endgroup$
    – No Name
    Aug 29, 2023 at 4:01
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    $\begingroup$ @TorstenSchoeneberg I can write in perfectly clear block script and replace all my E's with rainbows. Everyone will be able to understand perfectly what I wrote, but that doesn't make it any less wrong. As an educator it is your duty to correct this. $\endgroup$
    – user22808
    Aug 29, 2023 at 13:57
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    $\begingroup$ @NoName Cursive writing is taught and done in many places. $\endgroup$ Aug 30, 2023 at 9:08
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    $\begingroup$ @VladimirFГероямслава Fair enough. But it is being phased out in many others, including mine $\endgroup$
    – No Name
    Aug 30, 2023 at 9:11
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I think the real-world operational point is not that there is some sacred correctness to "orthodox" writing/font styles, but that writing in a very unorthodox style will cause one's readers significant difficulties, perhaps complete misunderstanding.

That is, conformity is not-at-all necessarily a virtue, except perhaps in communication with other people. Even then, there's not a universal, eternal "conformity", but, rather, of course, something depending on one's audience, and what year it is. :)

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These kind of syntactical glitches need to be corrected immediately, firmly, and clearly. As others have stated: it's immensely easier to fix these things earlier, rather than later when bad habits have set in. Take points off on assignments; that's frequently the only way to get students' attention on a matter.

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    $\begingroup$ I agree with this for beginning students. In my case, this is a student who somehow got through algebra I, algebra II and precalculus I, all without being corrected on this, so it got me wondering whether this was some alternative (for $\pi$) I've never seen. I definitely pointed it out to him, showing him two typical ways of drawing the letter. It's hard to imagine going so long without anyone mentioning it to him. $\endgroup$
    – Nick C
    Aug 29, 2023 at 2:49
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    $\begingroup$ @NickC: I'm not too surprised at this. Like you, everyone in the chain had probably never seen it/didn't know what to do/assumed it was someone else's job. And there's a lot of tendency to be "nice" and not address syntactical issues in any coursework. And many of those lower-level courses (where I am) are assessed entirely with multiple-choice tests. I've had remedial students blow a stack when I told them that something they'd been told in grade school (e.g., about fractions or order-of-operations) was flat-out wrong. Like, 6-8+ years without correction. $\endgroup$ Aug 29, 2023 at 13:11

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