EDIT: Ooph, he's running for the House of Reps in my state (http://www.bongino.com/)
Now, if children are being forced to use this technique throughout their education something is wrong. If this is a step on the way to the standard technique, then so much the better. I recall pre-calc: we were forced to do a bunch of cumbersome math to compute limits before being taught the 'easy' way, because the easy way, being symbolic manipulation, could obscure what is going on and keep you from learning the concepts behind limits. Same thing. I rarely do any math the way it is initially taught. When is the last time you wrote -3 = -3 on both sides of an algebraic system to move a 3 to the other side of an equation?
If you really want students to understand why they are doing it, I see no other way than teaching methods for proving the correctness of algorithms, i. e. Hoare logic: https://en.wikipedia.org/wiki/Hoare_logic