What's wrong with the pedagogy is the idea that no one should be taught any material until everybody is capable of learning that material. Variable manipulation can be easily learned by 4th graders. But it can't be learned by all 4th graders, so everyone has to wait.

Just in case you think I might be misleading you somehow, here's a cheat sheet product for a "college algebra" course; again, "college algebra" refers to the material that would normally be covered in or before high school, except that it's being covered in college. So the idea of this product is that current college students will buy it to help them understand what's going on in class, or to review for a test.

https://www.amazon.com/College-Algebra-Quick-Study-Academic/...

> RULE: if a, b, and c are any real numbers and a = b, then a + c = b + c.

[later]

> Some equations require more than one inverse operation to solve.

> EX[AMPLE]: Solve the equation 5x + 3x - 1 = 15