So, the first one is because the kid is using the abelian properties of multiplication to solve these problems by switching the directions of the multiplication. The whole problem with this is that in the modern world, kids have to be ready to deal with things that aren't abelian. If the kids get used to using 5*3 = 3*5 before realizing that 5+5+5 and 3+3+3+3+3 are not conceptually identical then they are going to have a hell of a time when they get to 5^3 = 125 which is not 3^5 = 243. They're gonna have even more trouble when they get to matrices and linear algebra.

The whole point of math is to learn to think carefully and logically, not just to get the right answer. This has been a fucking problem since the 60s. We try and catch up with other nations in terms of education by redoing the fundamentals to allow kids to learn the advanced stuff better, but then people who don't have a damn clue about mathematics (Do me a favor, without looking it up, what's the fundamental theorem of arithmetic, the fundamental theorem of algebra, and the fundamental theorem of calculus?) come around and bitch about it, complaining that all the shortcuts they're used to aren't allowed and that their kids are being taught to truly understand that when they see 53*7 that there are all kinds of ways to multiply the numbers - 50*7+3*7, 53*2+53*2+53*2+53, etcetera. That's fucking important because when the kid's looking at x^3-x^2+x-1=0 they might be able to start to attack that problem with their mathematical arsenal and problem-solving skills rather than just having to whimper in terror at being presented a cubic. But hey, what do mathematicians and pedagogy experts know about teaching math and why they're teaching math? The important thing is for Baby Boomers to not feel frustrated by their kids homework.

Everyone where I work locks up when they start to realize that a problem is going to come to a quadratic equation, so they just make up some numbers that 'sound right'. Meanwhile I'm hopping on wolfram alpha and finding out answers for customers because I understand mathematics and can think rationally and quickly about a problem.