> The ability to get into a student's head and understand where their conceptual difficulty or misunderstanding is. I experienced that first hand as someone wh

> The ability to get into a student's head and understand where their conceptual difficulty or misunderstanding is. I experienced that first hand as someone who just enjoyed math and had several courses from uni, and tried to help my SO and a few friends which struggled hard with different pre- or entry-level college math courses. They all needed quite different approaches to be able to understand the material. For one I had to go all the way back and re-learn basic algebra as they had had a poor teacher which hadn't properly taught that. It would manifest in not understanding steps, not being able to solve equations properly and so on. One really didn't get the visual graph explanation of derivation of composite functions, and instead got it by deriving the formula and using it in several examples. An approach which didn't work with the others as they needed the graph as a reference or motivation. Was a very interesting experience, and as you say a very different challenge from just knowing the source material well.