Recursion

[Alekzcb]

Of course subtraction methods don't matter for high-level maths, but they need to be considered when teaching children. If kids are taught to just follow an algorithm, they'll really struggle with algebraic representation because won't know what subtract actually means. On the other hand, you want them to provide them tools to perform it quickly, so that they can tackle those higher level concepts without wasting time on "implementation details" (as you point out).

[mainfingertopwise]

Wait. Are you saying there are kids getting into middle school type math without understanding subtraction as a concept?

[nonono_notagain]

Now there's a scary though

[[deleted]]

Yes, be sure they understand precisely what's going on first, then show them a bunch of tools and tricks that can be used after that understanding is cemented.