2 cents is all I have. I think older people should open their minds a bit, if they see that math is being taught differently when we were kids. When I was in high school the "affordable" calculators (like Texas Instruments) were just coming into the market and cost maybe $500-$600 in today's dollars. But, even it I did have that outrageous amount of money at my disposal, they weren't allowed in the classroom. Of course I'd learned to add, subtract, multiply and divide long before high school. But to learn algebra, geometry, trigonometry and all that, I still had to solve all those long, boring, arithmetic equations on paper, at the same time. I'm absolutely certain that the drudgery of solving those equations that I already knew how to solve, detracted from my ability to focus on the higher order principles I was being taught.
Flash forward to today though.......electronic calculators are so ubiquitous that I wouldn't be surprised to find one in a box of "Cracker Jack". Shit....if one of my grandsons asked me for a calculator, I could pull open my desk drawer and let him choose from at least a dozen! (Oh...I forgot. There's a calculator on my phone, too!)
So....much as we might like to, I really don't think we can make an honest case that a kid HAS to learn to solve big-number and fractional equations, on paper. Therefore, I can see how some in the know, might choose to skip that step at the outset and maybe come back to it later, as time and interest allows.
Here's how I see it....it absolutely IS essential for a learner of math, to understand the fundamental concepts of addition, subtraction, multiplication, and addition. For instance...take 15,634 + 7,256. It's essential for a kid to know that the sum will be a number greater than either of these two and it might help for them to quickly guess that it's around 20,000-something+.
But, assuming this equation is one part of a more advanced equation really.....is it necessary for the child to know how to arrive at the exact sum without a calculator?
Of course we used to say...."Yeah but, what if you need to solve an equation and you don't have a calculator?" But...c'mon...how often do YOU find yourself in a time and place today, where you needed a calculator and had no access to one? I still solve arithmetic questions with a pencil now and again. But to be honest, I only do so because I can, and I'm too lazy or it doesn't occur to me to pull my phone out of my pocket.
For me, this is similar to the questions we've been considering around "cursive". I think I can make a pretty good case for why it would be good, and useful, and illuminating for a child to learn cursive. But, is it absolutely necessary that a child learn cursive? I can't make that case.