Others have already here pointed out that students can struggle with notation in mathematics. I can often think that the lack of proper notation gets in the way of solving a problem correctly.
Therefore, I would like a online free reference/resource about proper mathematics notation that I can direct my students to. I appreciate any suggestions.
I am not aware of the kind of notation reference manual you ask for. Although such a thing could be helpful, I doubt that alone will solve the problem. Something that might help is active discussion of notation with the students. I do not recall seeing a teacher engage in such discussion in all my years of taking math classes (including everything from elementary school to grad school).
I doubt that it would be of no benefit at all to occasionally take a piece of notation and discuss in which possible ways it could be interpreted. Does the notation serve its purpose if the class can easily come up with several interpretations? Do students recognize bad notation when they see it? (I have understood that recognizing words and non-words is a fairly good test of language proficiency; why not apply this test to mathematics?) If students are somehow forced to try to interpret their own (or their friends') notation and actively compare what they are trying to say with what they have written down, I believe something would go across. A notation guidebook might support this process well.
