I don't know if I can convince you otherwise, in that I'm increasingly thinking that it is a red herring, but I'll try to elucidate the original question a bit better.
We were thinking that one of the concerns some students have is that they will type something like sin(x) when the question asks for sin(t) and therefore get the problem wrong. We were thinking that if the preview automatically colored the independent variable in the problem it would provide a visual clue that they had the argument that they wanted in the problem.
That said, I think for the moment that the question is moot, because if they actually preview their answer and it uses an illegal variable (e.g., x instead of t), the previewer reports "Variable 'x' is not defined in this context," which should be obvious enough. I think some of my original thinking about this was informed by the original homework/testing software we were using being silent about variable errors (answering sin(x) instead of sin(t) would be marked wrong without an error message), and I think at some point I may have tweaked the grader we were using in WeBWorK to similarly ignore such errors, but that's obviously no longer the case.
More philosophically, we were thinking that there are three levels on which one could expect students to understand when they enter an incorrect variable in a problem: that they understand that the variable is incorrect if the system reports the error; or that they understand the error in the absence of warnings; or a middle ground, that they understand the error if they are given some visual clue short of an error message when they preview the problem.
I think a good analogy is probably the case of a student using correctly matched but incorrectly placed parentheses. The level of warning that is given now is that the previewer gives a visual clue that there's an error: it previews with the parentheses in the wrong place. If one decides that the error of using the wrong variable name is of a similar order of magnitude as mis-placed parentheses, then it would make sense to have the previewer give an indication of the error rather than simply return an error. But for the moment I think that's probably irrelevant.
Sorry that was so long-winded.
Features & Development
jsMath/previewing independent variables
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