I've been trying to teach my sister school maths, and one difficulty I find is, she is unable to state precise formulation of theorems, and sometimes confuse the assumption and the implication. This is not much of a problem because often the theorems in her life are two ways, the implication goes bothways, but generally this is not good.
I too remember personally have these problem when I was young. How can I help her/ other students generally the importance of remembering theorem exactly and also how to remember theorems exactly?
In my personal opinion, I think it maybe rooted from the lack of seriousness when defining the basic terms. For eg, we don't define what an integer or real number is in school, we just give an intuitive explanation which has to be rememberd. So, when suddenly a student reaches a class that they have to memorize exact theorems involving these objects, they take it with the same seriousness as they took the basics of it.