I'm not seeing any advocacy of memorization? The only thing you might have to memorize, out of what parent listed, is the algorithms for doing written out arithmetic; and that too is in fact an exercise in mathematical thinking. After all, there's a reason we teach these algorithms, as opposed to just telling kids that they can punch numbers into a calculator.
Quote: "Even for double digit addition problems they jump right into 'cool tricks' and 'mathematical thinking' while there are just really a few steps to memorize and, guess what, kids are great at memorizing stuff."
And rdtsc is entirely right about that. The Common Core math curriculum has been taken by many self-described "math teachers" and "educators" as an opportunity to just not teach the effective algorithms for doing arithmetic, and expect students to just "discover the results by themselves" via some mixture of trial-and-error, random guessing, and the rare "trick" or perhaps tiny flash of genuine "mathematical thinking". That was an unmitigated disaster, of course. It's probably part of the reason why Algebra is now being seen as way too difficult for Junior High students, and something that only HS students could approach effectively.
From your link, knowledge of the standard algorithm for addition/subtraction is only requested by Grade 4, and for multiplication by Grade 5. So the Common Core standard is basically relying on a hidden assumption that students can effectively learn all the other stuff that's expected of them up to Grade 4 and 5, without truly being fluent in addition, subtraction or multiplication! (I'm aware that the standards call for "fluency" slightly earlier, but that's mere wishful thinking until you teach the standard algorithms, or some cosmetic variant thereof such as lattice multiplication.) That's what so bad about the way CC is being applied in elementary education.
