I’m not remotely arguing against encouraging kids to discover the mathematical principles themselves. I’m also not advocating teaching swapping + (1500 - 14) into -14 + 1500 by a careful application of the laws of commutativity. I’m saying that having a comfort and confidence with what summation is is way more valuable than learning that addition is a procedure applied to digits.
This very book argues against teaching these tricks without allowing the student to discover it themselves.
Why is 4 + 7 = 7 + 4? Is it a general phenomenon?