Why do we still teach people to calculate?

Why do we still teach people to calculate?
freakonomics.com

Primary school teachers respect core fundamentals as kids acquire "mental muscle memory" and realize they have to both create some axiomatic knowledge (axiomatic in as much as you know 9x9 is 81 from rote recall, not because of a belief in inductive reasoning) as well as try to begin an uplift to reasoned knowledge (that 2^2 x 2^2 is 2^(2+2) is 2^4) and some coding/transcoding (1/2 == 0.5) Cuisenaire rods come in and out of fashion. Crows can count. Kids are sometimes dumber than crows.

Mathematicians are very much in davis/hersh "what is mathematics anyway" -I believe Hersh noted that you can be in a field where only 3 other people worldwide can talk to you cogently about your work, and peer review is meaningless.

Statisticians are very comfortable that approximations work, but are less concered with accuracy at times, and very much concerned with methodology. I've had quite remarkable conversations with them about sample size, and how UX people can survive on 5 responses. I neve predict which side of the problem they're going to respond.

Data scientists are almost intuitive at times. sometimes the reliance on codified knowledge (numpy/pandas) and a belief in the p-jacked value or an obvious excel error is frightening. I think they divide sheep/goats into the numerate, and the highly visual.

I consider myself semi literate, mathematically speaking but in fact, I stumble over basic arithmetic all the time, and I struggle with ideas behind complex numbers, trig. I have to re-prove things which should be known, re-induce belief in things which are based on inductive reasoning, I question commutation all the time. How the hell can 2 x 3 be the same as 3 x 2 there's a fundamental left-right ordering in my brain which at times I ask myself is this inside the farsi or hebrew or thai or boudestrophon flow texts, suggesting that not all right-to-left ordered languages obey it yet alas I do.

I also still don't entirely understand why school focussed on trig so much given that very few of us are navigating by sextant. I suspect at times it was dividing us into the ones which drink from the hand, and the ones which lap from the stream.

Do they teach decimal to octal and hex and binary in primary school yet? Will the world be different when the last of the duodecimal measurement learners have died?

I would say it is intended for everyone who can not figure it out for themselves.