If you don’t understand the mechanisms of arithmetic, algebra is going to be a challenge. If you don’t understand algebra, lots of other things that are applicable to daily life and trades are also out.
I use geometry and trig for gardening. I do unit conversions (algebra) in cooking. I use simple probablilty in gaming.
All of this comes down to my ability to perform arithmetic operations on abstract symbols. A calculator can give me the numeric results, but it can’t help me manipulate the equation to get the answer I need.
Your reasoning is also exactly why I don’t like the “You won’t have a calculator” excuse. It completely leaves out the importance of understanding the concepts of mathematics. If you don’t understand how the math works, you’ll have no idea I’d what the calculator spits out makes sense or even put it into the calculator in the first place. And even then some calculators do actually do things differently.
By the time I was in grade school we already had basic calculators that fit in pockets and that’s ignoring that pocket sized slide rules have existed for decades before that.
Of course. But this is about stuff like multiplication tables and things that are clear calculator fodder.
I can do stuff like 36 * 15 in my head if forced to, but my calculator can do it faster and more reliably then I can.
Also would you ever long divide 7/13 if you needed now? Of course not, use your phone.
A lot of that stuff is about internalizing rules. By doing times tables up to 10x10, you have just enough memorized to understand patterns of multiplication, how it behaves and how to manipulate it. By working out long hand you understand the patterns of positional notation and some mechanisms to manipulate it. Division long hand also gives you an opportunity to experience how division is the inversion of multiplication, as long hand division is literally running long hand multiplication backwards (it’s trickier cause you are more likely to run into a fraction tho) - and the concept of modulo is also incredibly useful for daily life.
Even these things are building foundations for later math. Times tables and long hand division aren’t the only way to teach math, but they are a way that works. It’s not directly relevant, sure, and hasn’t been for almost 100 years. But it’s a foundation and has importance in that way
