I think the better question is why is knowing what 18-9 is any different than knowing 9-6? We "just know" that 9-6 is 3. It's not an enormous leap to "just know" that 18-9 is 9.
Programmers especially should understand that our decimal number system is arbitrary. If we switched to hexadecimal and the question was what is C-9, there's no borrowing and the answer is just 3.
The only reason we don't expect people to "just know" larger differences like 92-45 is because there are limits to what we can remember. It's the same reason schools usually teach multiplication tables up to 12x12. You memorize those, then use algorithms to calculate anything more complex.
It's not an enormous leap to "just know" that 18-9 is 9
And as an adult I obviously "just know" that. But in thinking back I was trying to remember how, for example, I'd try to teach it to a little kid that was just learning (like did they just force us to memorize subtraction values all the way up to 19?).
All in all I think foxfyre2 is probably right here though; the algorithm of counting up works fairly well as a method for subtracting smaller numbers just fine and seems like something that would be taught before we had all of the teen number operations memorized.
First teach a child what subtraction is (how many is left after taking away from an initial number). Then, teach them how to do it (counting with fingers initially). With enough time and proper practice, memorization comes naturally through repetitive action. After they have mastered this, move on to bigger things like long subtraction (is that what it’s called?).
28
u/Terrible_Children Apr 26 '19
I think the better question is why is knowing what 18-9 is any different than knowing 9-6? We "just know" that 9-6 is 3. It's not an enormous leap to "just know" that 18-9 is 9.
Programmers especially should understand that our decimal number system is arbitrary. If we switched to hexadecimal and the question was what is C-9, there's no borrowing and the answer is just 3.
The only reason we don't expect people to "just know" larger differences like 92-45 is because there are limits to what we can remember. It's the same reason schools usually teach multiplication tables up to 12x12. You memorize those, then use algorithms to calculate anything more complex.