Answer (spoiler, I was wrong):
I'd say they have 5 fingers on each hand.
There are 5 distinct glyphs, ⊙, ×, ⊓, ∿, ⊳. If we wildly extrapolate from human counting methods, there would be one number, and therefore one glyph, for each finger on each hand. They could also have 10 fingers and the puzzle only uses 5 of the values.
The aliens could also do something weird, like order their digits from the middle to the outsides, alternating left and right. This could be a haiku with zero mathematical intent. Etc. But I assumed on looking at it that it was intended to be a basic addition problem with glyph substitution.
Getting the correct answer:
Cheating a bit, I looked at Daniel's answer. He decided to try solving in base 6. I'm not that smart, so I wrote a program to brute force everything to base 12 (anything higher takes too much time).
It assumes addition (multiplication would probably add a lot more digits to the product, subtraction and division couldn't add any unless one glyph is a negative sign or decimal point). It tests both forward (treating the leftmost digits as most significant) and reverse (treating leftmost digits as least significant). The minimum possible base is 5, since there are 5 glyphs.
The only valid answer is if we reverse the digits left-to-right, and use base 6. Precisely the answer Daniel gave in a much more clever manner. I suspect that if base 12 has no solutions, higher bases won't either, because of something related to carrying in the left column, but I don't think I can prove that mathematically.