>Is the putative student "bad at math" or "bad at math the way it's taught in high school, perhaps even by a certain teacher"?
It could also be a mismatch between someone's personality and the sort of math kids get taught. I did poorly in most of my math classes in high school and college. After failing a few classes, decided I was hopelessly "bad at math", and left the topic alone. A few years I took an abstract algebra class on a lark and really enjoyed it. In hindsight, I did poorly in my earlier math classes because I was undisciplined and really disliked memorizing disconnected tricks and formulas. Abstract algebra, on the other hand, was more elegant, conceptual and fun to learn. Doing well in one class punctured my myth of inability and gave me the confidence to properly learn linear algebra (and take some other interesting classes).
It could also be a mismatch between someone's personality and the sort of math kids get taught. I did poorly in most of my math classes in high school and college. After failing a few classes, decided I was hopelessly "bad at math", and left the topic alone. A few years I took an abstract algebra class on a lark and really enjoyed it. In hindsight, I did poorly in my earlier math classes because I was undisciplined and really disliked memorizing disconnected tricks and formulas. Abstract algebra, on the other hand, was more elegant, conceptual and fun to learn. Doing well in one class punctured my myth of inability and gave me the confidence to properly learn linear algebra (and take some other interesting classes).