+10 Chuck-
....STEM is based on math. Students need to know not only "Plus, minus, times and gazintas" but they need to understand the associative and distributive law. They need to know logarithms. They as you so eloquently expressed, need to do proofs, and I'll add - derivations.
Teaching math is not a "learning how to think course", it's a years-long process in which the student acquires greater and greater skills, each course building upon the next. Sure, not everyone is going to have to tackle the Navier-Stokes equations to graduate, but the ones that do don't learn how to df it in one semester. They are prepared by years (usually about 16) of successive mathematics courses. At that point a student has acquired real skills that are useful for real problem solving.
And just as important, they have learned a method of applying them.
From my admittedly limited knowledge of CC, I don't see any emphasis on developing math skills for real problems. Even at an early age, you can ask a kid "Farmer Jones has 156 eggs, and his egg cartons hold 12 eggs. How many egg cartons does he need for his eggs?" or " The carpenter has 8 boards..."
This puts mathematics into a real-life perspective and teaches kids how to solve real-world problems. When you teach them that way the "light goes off". To me CC seems to be the "everybody gets a trophy" dumbing down of the core of what makes engineers, scientist, machinists,......
Common Core is what you get when you having 'educators' as opposed to teachers working with lobbyists to put together a curriculum. It looks good on paper but the way it's done leaves the teachers precious little room to adapt it to the kids they have to teach.
I was with my grandson over Christmas. He's a bright kid(10) and we were discussing school. He told me he was learning algebra- 6-x=2, what's x. So I asked him to solve 112+x=143. He laid it out in a number of columns and rows and figured out all the arithmetic somewhat as above, taking about 5 minutes. Then I showed him:
143
-112
---------
1
3
0
31
That triggered a subtraction contest where we asked each other simple subtraction problems and he quickly figured out how to do them in his head. He also showed me how they do long division estimating the numerals in the answer and checking them separately with the long-winded subtraction, somewhat as above, until you found the answer.
Common Core seems to be what you get when you task 'educators' as opposed to teachers to develop a curriculum with lobbyists. They use what they can remember from school, run it by teachers 5,10, 15 times until it all works, sort of, and then the administrators have to approve it, taking another 2-3 years of conferences.
Mathematics has been successfully taught using pretty much the same methods for centuries. I wonder why the methods had to be redone when they worked?