I don't really think the methods are important, what's important is whether students decide to learn more advanced math later (say at least up to Calculus), and

I don't really think the methods are important, what's important is whether students decide to learn more advanced math later (say at least up to Calculus), and more importantly whether they like doing so. Too many people say "I hate math", learning multiplication one way or another shouldn't affect that strongly. The article has a few nice quotes I like: "Computers do arithmetic for us, Devlin says, but making computers do the things we want them to do requires algebraic thinking." '"You cannot become good at algebra without a mastery of arithmetic," Devlin says, "but arithmetic itself is no longer the ultimate goal." Thus the emphasis in teaching mathematics today is on getting people to be sophisticated, algebraic thinkers.' While I can do multi-digit multiplications just fine and have a high confidence in my answer, I'd much rather a calculator do it for me, allowing me a higher confidence in the answer and just being done faster to use the result for some other purpose.