Its kind of dumb how arithmetic is seen as a precursor to math when its really not. You could do an ENTIRE college-level course in linear algebra or calculus or graph theory or even combinatorics perfectly well even if you have no idea what 11*15 is off the top of your head and have to look it up every time.
Its just a ridiculously backwards approach to teaching. We don't teach CS by testing people on memorizing syntax and API calls - they are rightly relegated to "google it when you need it, eventually you'll remember it". Of course algorithms are more interesting and building things is more fun so we focus on that.
Current way of teaching math is just a historical accident IMO. No real reason it couldn't be conceptual and interesting from the start if there wasn't so much inertia around current systems.
Splitting out arithmetic from "Maths" doesn't seem terribly sensible to me. Times tables aren't really problematic, and they do provide opportunities to teach valuable concepts (5x6 = 6x5).
I'm honestly dubious of anyone who claims that the reason people hate maths is because of times tables.
If someone thinks of math that way, I can understand why it would be boring to them. Thats what I mean by blocked on arithmetic. If every thing is taught as a cookie-cutter process to follow its not surprising that people associate math with blindly following processes.
A hammer and a chisel are tools. You can use them to shave a bit of wood off the door, or you can use them to carve a beautiful sculpture. You can do neither without knowing how to use them.
I agree that too much of maths teaching is "here are 100 quadratics, go solve them" - which is obnoxious and dull. But "blindly following process" (matrix multiplication, change of variables/base, sum to infinity etc) happened throughout my degree and is a component of higher maths as well. Heck, most of the proofs I remember use "tricks" that any mathematician is expected to just know.
I sure as hell don't think children are taught maths well. I remember being taught how to take the derivative of x^2 without the teacher bothering to show where that came from or what it really meant. Heck - children are given the quadratic formula to memorise and basically told "it's magic, learn it" instead of showing them how you can trivially create it by completing the square.
But mathematics does involves a ton of following some process or other to get the problem into a format you can do something with. Probably by following a different process that you've done before. I'm not sold that you can simply eliminate that aspect.
The times tables are BS math? The thing I've used IRL literally hundreds (thousands?) of times more than I've ever used anything from, say, calculus? The thing that yes I could use a calculator for but damn would it get annoying because I use it so often? That's what we should stop teaching?
Math things I use a lot in actual real life: basic arithmetic (drilled skills/knowledge!), basic algebra, factions/percentages (converting one to the other, and scaling other numbers by them—the basic arithmetic stuff is also vital here), and generally how triangles work. That's... almost all of it, actually. Some high-school-level stats stuff from time to time, I guess.
Years later when I worked in a shop I used to cost complex print jobs in my head and co-workers though it was magic.
The way maths is taught in the UK is largely how and very rarely why.
On the other hand, I can't imagine anywhere that would expect one to know 11x15 off the top of ones head.
Learning how to perform mental arithmetic with the aid of pencil and paper was a way to escape from the grind of farm work. One could get a respectable job as a clerk. However with the advent of electronic cash registers and smartphones a way around this later form of grind has also been found. So no need to make it compulsory. Which isn't to say that people don't choose to practice specific things they personally consider useful. Even gamers do that.
So yeah, I think you still need to grind these multiplication tables, even if you have perfect version of Wolphram Alpha on your smartphone. It won't tell you what question to ask.
This is because coercion in education is: (1) painful, (2) prophetic, (3) it doesn't work!
What happens in real life is that if somebody needs to know something because they are keen to do something else then they will learn it efficiently, 'just in time' and precisely to the extent needed. Assuming their creativity is relatively intact...
But I can kinda understand why, you almost never have to multiply 9*7 by hand. If you're doing algebra or any symbolic calculations you rarely use digits other than 0-4.
In real world Benford's law + usual rounding greatly reduces the need to multiply by 7 or 9 (or 8 for that matter).
The way around is to just not do that.
Students get huge amounts of practice with basic multiplication if they are assigned more interesting problems/projects that use multiplication as one step, and will inevitably memorize all of the same basic facts, assuming they actually do the work.
Memorizing multiplication facts for their own sake is a soul-sucking waste of time that turns kids off from math for good.
Similarly, the way to get good at spelling is by reading engrossing books for hours every day and writing about subjects of personal interest. Studying lists of spelling words in school is beyond pointless.
These are not skills like sports or playing musical instruments, where there is a particular physical technique involving fine muscle coordination, where practicing incorrectly will establish wrong movements. Instead we’re talking about simple verbal/linguistic recall of previously seen information.
I'm just making things up tho
Just like in sports, where you must also do a lot of basic practise to get good.
Making the practise like a game can be done to done degree, but ultimately, a kid is going to see through that after a while, since it gets boring.