Correcting how a student writes symbols

Question

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.]

Answer 1

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"

Answer 2

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.

Answer 3

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:

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.

Answer 4

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. :)

Answer 5

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.