I've always wondered why (and still do wonder why) we even have to call it the "square root of -1" at all [whether that's taken to be 'minus 1' or 'negative 1'].
Why not just call it, say, 'i'? [Which has the property i (x) i = -1].
Yes, it does indeed happen that i(squared) = -1 -- but so what? I don't believe there are any other consequences.
Then, we can define 'complex numbers' as 'entities' consisting of a combination of real numbers and real numbers (x)i. And also: just do away with the '+' sign in a complex number.
The complex number is simply: (a, ib) - and it obeys all the necessary rules for us to be able to treat it as a mathematically meaningful object.
Experts in pedagogy might like to investigate and pronounce on this suggestion.
I have not explored this idea in depth - but it might well serve to reduce (in some small measure at least), the difficulties of students struggling with the *complexification of thought* brought on by 'complex numbers' and 'imaginary numbers', etc. I seem to recall several of my classmates in school actually reduced to tears by complex number arithmetic!
Now, here is what I believe is a real 'pedagogical issue related to math' - of the kind that Haim claims does not exist!