I think teachers make the mistake of focusing on the end goal, for example: “thinking in abstract terms”. A student starts in some state and that state may not

I think teachers make the mistake of focusing on the end goal, for example: “thinking in abstract terms”. A student starts in some state and that state may not have a direct transition to “understanding abstraction”. A teacher needs to understand the state the student is in and find a sequence of transitions that lead to the desired state. It’s difficult for teachers to do this if their expertise is limited to knowing what the final state should look like, but not being familiar with (or having forgotten) the state space that leads there.