[wiz21c]

On my part, I don't use that carry method at ll. When I have to substract, I substract by chunks that my brain can easily subtract. For example 1233 - 718, I'll do 1233 - 700 = 533 then 533 - 20 = 513 then 513 + 2 = 515. It's completely instinctive (and thus I can't explain to my children :-) )

What I have asked my children to do very often is back-of-the-envelope multiplications and other computations. That really helped them to get a sense of the magnitude of things.

[n4r9]

I have a two year old and often worry that I'll teach him some intuitive arithmetic technique, then school will later force a different method and mark him down despite getting the right answer. What if it ends up making him hate school, maths, or both?

[__s]

I experienced this. Only made me hate school, but maybe because I had game programming at home to appreciate math with

Just expose them to everyday math so they aren't one of those people who think math has no practical uses. My father isn't great with math, but would raise questions like how wide a river was (solvable from one side with trig, using 30 degree angles for easy math). Napkin math makes things much more fun than strict classroom math with one right answer

[cess11]

Commonly school is teaching a method. "Getting the right answer" is just a byproduct of applying the method. If you tell your kid that they should just learn the methods you teach and be dismissive or angry about school trying to teach them other techniques, that's probably going to cause some issues downstream.

Techniques of an "intuitive" character often lack or have formal underpinnings that are hard to understand, which means they do not to the same extent implicitly teach analytical methods that might later be a requirement for formal deduction.

[zeroonetwothree]

It’s valuable to learn different techniques to achieve the same result. That’s what math is all about.

[zeroonetwothree]

This doesn’t scale to larger numbers though. I do that too for smaller subtractions but if I need to calculate some 9 digit computation then I would use the standard pen and paper tabular method with borrowing (not that it comes up in practice).

[Izkata]

"Common core" math is an attempt to codify this style so more kids can get a deeper understanding of numbers instead of just blindly following steps. Like the people that created it noticed people like you and me (I do something similar but not quite the same) have an intuitive understanding of math that made us good at it that they want to replicate for everyone. But it seems like very few parents and teachers understand it themselves, resulting in a blind-leading-the-blind situation where it gets taught in a bad way that doesn't achieve the goal.

Also aside, in the method I was taught in school (and I assume you and GP from terminology), "carrying" is what you do with addition (an extra 1 can be carried to the next column), "borrowing" is for subtraction (take a 1 away from the next column if needed).