The time frames "currently" and "at the moment" can refer to a temporary situation, but they can also refer to a situation or action that might continue into the future.
Of the two, I would say that "at the moment" most often refers to a transient or ephemeral action/state, and yet, it most often takes present continuous.
But in some cases (with non-stative verbs) it simply cannot take simple present:
- Where are you going?
- At the moment, I go home (wrong)
- At the moment, I am going home.
"Currently", on the other hand, most often applies to actions or states that are continuing, and might continue indefinitely: :
- Who robbed the bank?
- Currently, we're looking into it.
yet it can reasonably take simple present:
- What inventory valuation method do you use?
- Currently, we use FIFO.
So, all I can say is that your prior notions about simple present vs. present progressive were much too constrained.
By the way, for what it's worth: "currently" extends a litlle into the past, whereas "at the moment" doesn't.
And, as you well know, one can say "I am going to school tomorrow." (But that's a different kettle of fish. Or maybe a horse of a different color. Or, more likely, a fish of a different color—namely, a red herring.)
Best Answer
"I have taught" doesn't indicate present tense at all. I think what you're actually thinking of is "I have been teaching". If so, then your guess is spot on.
"I have taught", on the other hand, means that you have had the experience of teaching them at some point in the past. You could use it to respond to a question like "Have you taught children before?"