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It's because it's foundational. Sure, you can do this math problem in your head, but that's not the point of doing this math problem. The point is to teach you the procedure, not the answer. You need those procedures when you get to higher math. Karate Kid didn't need to learn how to wax a car, he needed to train his muscle memory with "wax on, wax off." If he would have just waxed the car any old way he would have missed the whole point of the assignment.
If someone would have explained that to 15 year-old me life would have been a bit easier.
Your point would be valid if math teachers actually taught the intuition behind why you're solving the problem in a particular way.
Instead, what we have is a system where you're taught to memorize a procedure and then carry out every step of that procedure, to the letter. The teacher doesn't give a SHIT if you don't understand the "why" of what you're doing. Only that you obey.
Great example: word problems. Every motherfucker has issues with word problems in math. This is because word problems require you to demonstrate an understanding of the principles of mathematics. Since these aren't actually taught, students always have trouble with word problems.
98% of math teachers suck dick. And no, I won't show how I got to the 98% number. I'm going to do what all "professionals" do and make shit up.
Instead, what we have is a system where you're taught to memorize a procedure and then carry out every step of that procedure, to the letter. The teacher doesn't give a SHIT if you don't understand the "why" of what you're doing. Only that you obey.
That's because the teacher doesn't understand why either. It's a universal truth that when people don't understand the assignment they're more strict about adhering to the 'book.' Not just teachers, but bosses at work, too. When you don't understand what you're asking someone to do you can't judge whether they're accomplishing all the necessary components they're supposed to accomplish. You have to insist on managing/grading them on something you do understand: does what they're doing match what I see in the book.
A teacher that understands the mathematics and what you need to know for the higher math to come later on will know if you understand what you need to understand. Even if you do the work differently than the book they'll be in a position to understand your thought process and whether that will suffice or hurt you.
In the world of education these uneducated teachers are due to two things: pay and education requirements. I can get a Master's degree in applied mathematics and I'm still not "qualified" to teach grade school math. For that I have to go to school for another two years to get the necessary courses for a teaching credential. All of those courses are liberal hogwash liberal arts shit. What mathematician wants to take two years of that shit just to earn less than they would make elsewhere? Almost none.
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