Yes, mathematics professors have been complaining about their students lack of algebra skills as long as there have been calculus courses.
No, we aren’t talking about a student who, in a moment of panic, decided to write because they were stuck on an exam. And yes, I once saw a professor walk into an analysis class, write on the board (while grinding the chalk into the board) while saying “the next person who makes this mistake will get an F for this class, ON THE SPOT! 🙂
But the weakness is more of the following: in class today, I wrote
The student actually understood the integration, but didn’t understand where the first equality came from! I said “it is just algebra” and he STILL didn’t get it.
I have a hard time believing that this student doesn’t understand the distributive axiom of algebra; what I think is going on is that they don’t have the concept as a regular working part of their math/science/engineering mind.