Love this post. I agree that Common Core math, especially as explained here, points out a useful perspective on how we might better conceptualize computations for students. When I help my 8 and 12 yr old boys with math homework, I routinely impart mental math techniques, like the very ones mentioned here, as optimizations to problem solving. Perhaps, they’d be better suited starting with these techniques!
I must note, however, that having a rote-memorized, formulaic fallback is quite useful at times. I’m no professional educator but both problem solving techniques seem to have a place and, seems to me, there are lots of good arguments to be made for combining alternative approaches. So, if I could add one point to this wonderful, politically agnostic post, it would be this: Our current social fabric and context for learning needs to be taken into account when talking about how we adopt improved methods like some of those put forth in ‘Common Core.’
It’s worth separating noise about supposedly alien math learning techniques from other more policy-oriented Common Core complaints. As I suspect you might agree, it’s a bummer to see politics derail a potentially valuable leap forward in advancing the state of math learning.
Parents and traditional local institutions are (or ought to be) part of the Learning ‘Team’. The combination of roles they play (encourager, tutor, counselor, friend, etc), in the ongoing evolution of improved learning techniques needs to be considered. Politics and hysterics aside, the path to radically improved (or additional, complementary) methods, I’ll suggest, is not to abruptly force/coerce a new ‘common’ standard from one central decision making body (Common Core attempts this).
Instead, I prefer an approach that incentivizes getting ideas like this out there (like your post — thank you!) and lets people freely compete using different learning styles — where an infinitely variable and student-tailored Learning Team of parents and local organizations are empowered to decide what works best, how to incorporate new ideas and when they best apply them.