> It reads like you see my opinions are black and white and yours as spectra. No, we're talking past each other. Your claim is the current system is "broken"

> It reads like you see my opinions are black and white and yours as spectra. No, we're talking past each other. Your claim is the current system is "broken" because you think teachers believe the "answer" is the ultimate goal. I refute that. The teacher does not believe the "answer" is the ultimate goal, they are teaching you techniques on how to solve problems, and the answer is the standard upon which you are being measured in correctness. This is why "show your work" exists, your steps to get to the end (the answer) is employing the techniques, they measure how effective you are at getting there. The best teachers even mark you down if you make a mistake somewhere, but still get the right answer without proving it fully.