As someone who's often struggled with this, I'd disagree. "I listened to the lecture but I just can't understand how this works" is a different category of math mistake than "I added 36 and 9 and got 43." (I made this mistake on a test recently). I think math mistakes in schools break down to two categories:
Not understanding the concepts (or understanding them as magic, and blindly applying rules even where they don't fit).
Making stupid arithmetic mistakes (which seems to come from going too quickly or being tired or distracted).
Making stupid arithmetic mistakes (which seems to come from going too quickly or being tired or distracted).
More like not bothering to actively think about how to optimize reliability of problem-solving, as opposed to thinking about how to solve the problem. "Try harder" or "be more careful" is advice of very limited power, while there are many creative ways of ensuring reliability of results (for any given problem) that are much more powerful.
I'm mostly asking this open question to those among us who are well-versed in developmental psychology (I'm mostly thinking of children) . Although, failing the actual scientific research on the topic, I guess some testable hypotheses would be great too.