Q&A: When (and How) to Correct Student Notation

Cross-posted from here.

Question

One of my college students writes the Greek letter $\pi$ as $\bar{n}.$

In general, 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 $-$). But where should we draw the line?

Answer

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.