That’s a bad example I guess. For something I struggled more with, take history. When I was in school it had a huge focus on trivia like dates, while I’m now fascinated by it, focusing on the cause and effect of things. But you can’t easily assess someone’s understanding of that side of things in a standardized manner, so it gets short shrift. Success is defined by the factors that least matter, and students, wanting to spend their efforts efficiently, will focus on the measures that define success.
As for the “most people can’t derive the quadratic formula,” you might be right about my blind spots, but I think it’s equally likely that I’m right and have the necessary point of view to see that most people can’t do it because it’s taught and tested poorly. Both explanations would equally explain it being easier for me to derive the formula than memorize it.
History is certainly a better example, but dates DO matter - You can't talk about cause and effect if you don't know when things happened. Now perhaps the minutiae isn't quite as important - but what better way to learn the chronology than knowing the dates? It's fundamental to it.
> to see that most people can’t do it because it’s taught and tested poorly.
Or they just don't want to learn it. Some people don't like math. Or maybe people are lazy - they like it but can't overcome procrastination to really learn it. Or they are more focused on something else, like I was as an adolescent (computers.) There are certainly people who got sick, or went on vacation during that week of school, etc.
My point is, we always like to blame things that aren't actionable, i.e. "the system." It was just "taught poorly." There are certainly cases of that being the truth, but if you look at the time constraints and all other details, it's hard to just blame the system. How do you actually fix the system?
> There are certainly cases of that being the truth, but if you look at the time constraints and all other details, it's hard to just blame the system. How do you actually fix the system?
Yeah, given all the constraints, I agree completely. My complaint is that there is a giant emphasis on testing in really scalable manners that take people and dialogue out of it. So which constraint is the system (the way things are taught and tested) most sensitive to? I expect that it's teacher to student ratios, which my thesaurus says is a synonym for money, simultaneously the easiest and hardest constraint to change :-(
As for the “most people can’t derive the quadratic formula,” you might be right about my blind spots, but I think it’s equally likely that I’m right and have the necessary point of view to see that most people can’t do it because it’s taught and tested poorly. Both explanations would equally explain it being easier for me to derive the formula than memorize it.