I get the sense that such rote methods are no longer encouraged and a lot of the "new math" in Common Core is aimed at approximation and reckoning so that students won't rely on memorization.
This aspect of the Common Core was about recognizing deficits in conceptual understanding resulting from rote methods of drilling arithmetic.
The empirical evidence is the opposite of OP's assertion, but the end point of giving students a better intuitive foundation for higher level math is indeed the goal!
Signed,
An elementary school math teacher who has studied the 60 years of math reform in America, internationally, and worked very hard to ensure all students have a foundation to succeed in higher level mathematics
Facility with those methods is then necessary to be able to adequately follow important proofs and gain understanding of more advanced concepts.
I don't know how you would teach people important results in their fields (physics, computer science etc., I'm not talking about actual mathematicians) without those skills.
I'm only good at _arithmetic_ because of making Warhammer 40k armies (true story bro).
I'm good at _algebra_ because I was taught well, on top of a knack.
Speed with basic algebraic operations was very helpful in many places but speed with arithmetic operations has only been helpful in board games.
I don't think anyone here would disagree with your point about algebra, but I think a lot of people such as myself would disagree that pre-K memorization of arithmetic helps with algebra later.
As I stated in another post, I don't know when it is neurologically ideal to learn arithmetics, it seems something that would be important to study carefully (personally I learnt before grade school, when I was 3-4 years old, but I didn't learn to read until I was 6, something that is often taught earlier).
10x+7 = -2x+31
Move 7 to the other side (picking up a minus sign)
10x = -2x + 31 - 7 = -2x + 24
Move -2x to the other side (flipping sign)
12x = 24
Recover 12*2 = 24 via memorization, quick division (though not long division), or whatever method
Therefore, x = 2. Then I drew a square and was done.
I don't get this part.
You mean to highlight the end result? In that case, it would, most of the time, be a rectangle (or try to be).
A cursory web search yielded nothing.
"∎"
I wasn't familiar with this, despite being a graduate. Its use might depend wildly on where.
Edit: thanks to the reply; HN ate my superscript 2. Apparently it doesn't like the unicode multiplication x, either: × ² ?
...but the only time I ever saw significant numbers when actually doing math was in toy problems that deliberately chose weird, big coefficients, where the arithmetic part was by far the least significant.