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.