Ontario's 1990s curriculum was pretty awesome. The idea of dimension and sets were both introduced simultaneously and joined, using multiplication. Started in the 2nd grade and they just kept elaborating. Number lines and groups of items. (Tied it into geometry, too. Square numbers came up by at least 4th grade.) What is 3 x 3 but moving 3 units, 3 times in one dimension? Now, memorize these tables up to 12 x 12, you won't always have a calculator at hand.
I do though. I still blow minds when I put my iPhone calculator in scientific mode. Math education is important for many reasons. But teaching it as a practical survival skill using no tools does a disservice to the student. Either it is useful as a problem solving exercise or it is a practical skill that should take advantage of tools. "Just memorize this stuff" isn't useful because it backfires into hating learning. Nothing about math makes it ideal for memorization and none of my math teachers spent any time on study skills.
Nah. As somebody who ends up doing a ton of mental math, I think it's valuable. Yes, they should also learn how to use tools. But developing a feel for numbers is valuable, and I think that is much harder to do if one always relies on a calculator. (And yes, of course, this should be learned in a way that doesn't involve the kids hating it. But that's possible.)
Phrases like "you won't always have a calculator at hand" only serve to erode trust in the educator. It's simply not compelling, and for all practical intents and purposes is untrue. Even on backpacking trips I have a cell phone, even if it is off. If you believe mental math is useful then say that and explain the benefits. Students can smell a lie.
That sounds like an excellent thing to somebody who actually said "you won't always have a calculator at hand". Maybe you should find someone like that.
