What you wrote seems very similar to what I’d read about it in other texts; even when we went over it in the previous math course I just took where we went over these things, she used the same language you’re using.
I performed well on those tests because they were open book and I could look up the formulas.
I mean when I _see_ the formula, I do fine. But my problem is holding it into memory and some of what holds me back is the way math is talked about; these processes and properties are talked about as fictional mathematical objects performing duties and ending up with a result, but it never seems to hold in my head.
If I thought of them like machine parts performing machine functions it might help. Or using physics various analogies. But for some reason, the syntax used to describe mathematical objects, properties and functions so often doesn’t ‘hold’.
Maybe I need to nail down the lingo better. I understand the concepts but the lingo always leaves me with, “oh wait, what’s that again? distributive/ Oh ok, that’s over the parenthsies but what’s associative? hold on…” –