I've noticed that many of my calculus students (all college students) will write, e.g., $1/3x$ to mean $(1/3)x$. This is an inherently ambiguous notation which I'd like them to avoid. Is simply pointing this out in class effective?
Edit: Here's a handwritten version of the ambiguous notation:
A colleague of mine includes on all his tests a line that reads (something like) "you will be graded on what you actually write down, not what I think you may have meant by what you wrote." He spends time carefully discussing what this means (examples like the one you gave are among them) before and after testing times. Normally after the second round (of four), students have developed the ability to reflect on how their own writing will look to others, and can avoid this type of mistake.
Many people simply do not realize that written math has notational conventions, and despite the fact that the algorithms and proofs are logical and complete, the notation is just a language and has holes and ambiguities like anything else.
As plenty of troll questions on Facebook show, many people will defend their interpretation of "what is the value of 5 + 1/2(6)" to the death, acting like PEMDAS is a complete mathematical rule handed down by the gods unto man and not just an incomplete (doesn't include juxtaposition!), arbitrary convention that makes it easier to figure out what some other person wrote.
The best way I've ever seen this solved is just to write a bunch of really easy but ambiguous expressions on the board. Tell the class to solve them on a sheet of paper, have them hand it forward, and then take a tally of how many completely different but still correct answers you get for each problem. Then use this as a learning experience about how math requires clear communication just like everything else, and that despite it being a logical field, not everything is an invariant theorem so you really don't know what they mean when they write confusing and ambiguous expressions.
I would take off one percent if I thought the wrong meaning was unlikely, and more if I thought the wrong meaning was possibly what they meant. I would write: "This looks like 1/(3x). You may have meant 1/3 * x, but it looks like your x is in the denominator."
At Warwick University then there were explicitly given 5 points per homework (out of 25, I think) for "Clarity and Style". By really emphasising this in the first year, I found that with my students (I was a graduate student at the time, so working as a sort of TA) then this sort of problem soon went away.
So I don't have an answer to the specific question ("Is simply pointing this out in class effective?"), but I can say that putting it in the rubric for homeworks and backing that up in tutorial time is effective.
I don't think the other answers answer what you have appeared to be asking so I will write my own answer. It looks like your question was whether pointing out the mistake is useful.
I think it depends on what you mean by pointing it out. Do you mean just stating that that's not how it's supposed to be written or do you mean giving a reason why that's not how it's supposed to be written? I think for some students, just pointing out that that's not how it's done might not actually work. I think some students when they're taught to do things a certain way will keep insisting on understanding why it's supposed to be done that way and of those students, the ones who wrote 1/3x to mean (1/3)x, they might need to have it explained that until other people are told how to do things, to them, 1/3x could either mean 1/(3x) or (1/3)x. I don't know if it's true or not but if it is true that by convention, 1/3x means 1/(3x), then they could be given that reason. It could also be explained to them that when they write the other notation for 1/3, others may take it as writing that notation and be confused because they haven't been taught to use the other notation to indicate that they mean (1/3)x and not 1/(3x).
