Would you expect a technologically advanced alien species to have an intelligence very similar to ours? Why or why not?
Rephrasing the question: In what ways, if any, would you expect a technologically advanced species to be similar to us? Why?
And in what ways, if any, would you expect (or at least not be surprised that) a technologically advanced species might be dissimilar to us? Why?
Since it was not stated, I'll assume technologically advanced to mean roughly as technologically advanced as we are.
This being the case, there are some commonalities we can infer. Our level of technological advancement relies on understanding various rules about how the universe works - in other words, physics. Additionally, in order to understand physics requires understanding the mathematical relationship between various variables, so their understanding of arithmetic and math would probably have to be rather similar.
So, their understanding of physics/math would have to be roughly equal to ours. In order to want to, and be able to, puzzle out math and physics, they would have to have some common intellectual/cognitive traits to us: logical reasoning, pattern recognition/classification, capacity for abstract symbolism, intellectual curiosity, a drive for problem solving, and a complex language which would allow for recording and communicating ideas, among others.
I concede that there may be some other fantastic way that a species could understand, develop, and build advanced technology without understanding math and physics, but I cannot fathom what it could be.