[SkyBelow]

Computation is quite important to understanding a problem. Often a more complex problem requires the ability to do simple computation and to build a intuition about numbers. Especially when we are talking things like simple fractions or rearranging basic equations. When a kid hasn't gotten a good grasp of fractions, they struggle to see why we can multiply both sides of an equation by x/x and then move things around to simplify the problem. To them, it looks like a magical step that follows no rules. Only with enough computation are our brains treat 7/7 as x/x as dx/dx as 1.

(I know nothing about the GP post, so I can't comment anything about them; I'm only relaying my own experiences from tutoring kids who struggle in math largely because they offloaded too much simple computation to a tool.)

[markgoho]

> Computation is quite important to understanding a problem

Your "problems" are just equations. 3x = 2 is not a problem.

Here's a problem: you and a friend have 15 dollars and would like to enjoy a day at the movies. Movie tickets cost $7.50. Will you have any money to spend on concessions?

The equation that you'd hope a child would produce is something like 7.5 x 2 = 15. And 15-15=0. Ultimately, no there's no money left over for concessions. That's the skill we need to teach. After that whether or not they know how to _compute_ 7.5 x 2 isn't a big deal. Give them a calculator.

It's crazy how indoctrinated we all are thinking equations are problems and teaching kids how to compute is "learning math".

[SkyBelow]

3x = 2 is a problem. Being able to abstract real world problems into math and being able to take that math beyond any real world problems one is familiar with is a major component of math. Often the real world problems are not found until after the math has already been researched. For existing knowledge, trying to learn the concepts and the math at the same time is much more difficulty and often the science for people who know the math starts out simplified to the point of not being applicable to the real world (perfectly spherical cow in a world without resistance).

>After that whether or not they know how to _compute_ 7.5 x 2 isn't a big deal.

If you want them to have a job with math any more complicated than counting out the exact change the machine tells them, they are going to need to understand equations. Kids who can blindly plug integrals into a solver but have no understanding of how to solve it also have no ability to take a real world problem and build an applicable integral to plug into a solver.

Modern education does often fail at teaching kids how to apply the equations back to real world problems, but that seems to be an issue where such problems are inherently harder and education is being dumbed down with many stakeholders feeling it is unfair for kids who 'know' how to solve the equation to miss a question because they don't know how to construct the equation given the problem (specifically because of the metrics that schools are measured by being gamed, Goodhart's Law being what it is).