This really has nothing to do with pedagogy and everything to do with the difference between calculations and mathematics. It's similar to the split between science and engineering.
In engineering, you're applying rules of thumb to get some desired outcome. Those rules of thumb may be based on math or science, but they could also be practices that have worked before. You don't have to understand why the rules of thumb work to apply them, although it is helpful, if you do.
What those kids are doing is something similar in the world of math. They have a desired outcome -- getting the correct answer, and they have a memorized list of "tricks" that get them to the correct answer quickly. They may or may not know why they work, only that they do.
None of that is really helpful for learning math in a school setting, which is not just about getting the correct answer, but about understanding why the answer is correct, and understanding why those various rules work or don't work. They don't usually even teach mental math tricks in schools because the point isn't being able to calculate quickly. Probably having a catalog of addition tricks makes it even harder to learn basic school arithmetic because you have to ignore what you already know to work back up from first principles.
In engineering, you're applying rules of thumb to get some desired outcome. Those rules of thumb may be based on math or science, but they could also be practices that have worked before. You don't have to understand why the rules of thumb work to apply them, although it is helpful, if you do.
What those kids are doing is something similar in the world of math. They have a desired outcome -- getting the correct answer, and they have a memorized list of "tricks" that get them to the correct answer quickly. They may or may not know why they work, only that they do.
None of that is really helpful for learning math in a school setting, which is not just about getting the correct answer, but about understanding why the answer is correct, and understanding why those various rules work or don't work. They don't usually even teach mental math tricks in schools because the point isn't being able to calculate quickly. Probably having a catalog of addition tricks makes it even harder to learn basic school arithmetic because you have to ignore what you already know to work back up from first principles.