I disagree. Two column proofs of the sort introduced in American middle school and high school mathematics programs are really just an attempt to introduce stud

I disagree. Two column proofs of the sort introduced in American middle school and high school mathematics programs are really just an attempt to introduce students to the beginnings of formal mathematical proofs and show that there is a world beyond prose proofs. No mathematicians actually use two column proofs (and even formal proof systems don't use two column proof notation). The state of formal mathematical proof technology is not currently at the stage where it makes sense for even professional mathematicians to be writing formal proofs, hence it's not even clear that two column proofs have a place in a future world where (hopefully) formal proofs become the norm in theoretical mathematics, depending on how formal proofs ultimately become structured. And the "third column" is effectively just comments, which are very easy to bolt on to any system after the fact. As it is right now, it is enough to know merely how in theory a prose proof could be reduced to a formal proof. And besides most middle school and high school students aren't going to be able to write even a rigorous prose proof. Trying to stack more stuff on the edifice of two column proofs seems like just saddling students with even more (from their point of view) tedious make-work.