At least in the UK, where we also learned these sorts of arithmetic tricks, we still learned the "harder ways". The point of these techniques wasn't to replace

At least in the UK, where we also learned these sorts of arithmetic tricks, we still learned the "harder ways". The point of these techniques wasn't to replace long multiplication or something, but more as shortcuts so we didn't have to do it if we didn't need to, and we could simplify problems if we saw a better way to do them. We also practiced this stuff regularly, and had mental maths quizzes at least once a week. And (at least when we weren't learning a specific technique), it didn't matter how we did the calculations, so if you felt more comfortable with the traditional methods, you could do that, you were usually just slower. (I was one of those slower people very often!) The point isn't to go "here's how you do maths, it's always like this". It's about (a) helping you do arithmetic more quickly, and (b) helping you understand why numbers behave the way they do, in terms of bases and pairs and factors and other things like that.