Parents see kids doing strange ways of subtracting 17 from 45 for example by thinking "17 + 3 is twenty, plus 20 more is 23, and 5 more makes 28" or thinking 45 - 17 is the same as 48 - 20 (add 3 to both parts) and so its 28.

Teaching that way blows my mind. When I help someone with math I guess I've always used the standard algorithm as a shared language but I know that when I've asked people how they resolve a problem in their head almost everyone does it differently. I've learned better ways of doing problems in my head by hearing how other people go about solving problems differently from me.

Feels like there is something useful in having a standardized way of expressing basic problems even if I know that most people will have a bunch of "tricks" they use to actually do math. It's kind of a strange paradigm shift for me to think about not teaching the way I was I was taught. Even with that I already planed on teaching my kid easier ways to get to their final answer.

Even in college mathematics I remember being penalized on tests and if I didn't work backwards to express things I had already calculated another way in standard notation. I don't think I even had a way to express how I calculated some things in notation, just little rule of thumb stuff.