“Know how to solve every problem that has been solved.”
That seems a reasonable goal.
That seems a reasonable goal.
He thought everything settled about physics should be teachable in the freshmen introductory series, and if he couldn’t make it fit that meant we didn’t really understand it yet.
I personally like the idea of upper level classes being about things we are still working out. That feels more like preparing people for the real world, where your job is to figure stuff out they couldn’t teach you in class because you and your coworkers are going to write the “book”. Or at least make money because not enough people have figured “it” out to make it cheap.
I think you are describing undergrad vs graduate, not intro vs upper level, and even that is optimistic. Even tenured professors are still learning new things about what is already known to the world at large.
Reductionism can lead to simplification, which will take less time to teach and learn.
Take planetary orbits as an example. There was a time when people would have spent a lot of time learning about all the complicated movements the planets make through the sky, "spheres within spheres", retrograde movement and so on. These days we teach Newton's laws of gravity and a heliocentric model (both of general application). The motion of the planets then pops out almost for "free".
It's only when one moves away from these principles to something more subtle or less well-understood that the education becomes hairier. But as these are further characterized, compression again becomes possible. Landau & Lifshitz, for example, attempts to do this at a graduate level. Many concepts they discuss are increasingly available to the advanced undergraduate due to better compression and better physics principles / pedagogy.
Today, we can go directly from New York to SF in a straight line.
Also, we shouldn't be so quick to throw away the original process of discovery. If our goal is to make scientists that can discover i think it'd be best to expose them to some of the real discovering. Like, the way fermi-dirac statistics is presented typically leaves out the rich process of discovery and understanding that took place, similarly with einsteins field equations. It leads young students into the thought that the big names are great, eldritch gods, completely incomprehensible in their genius. It begins to feel like you could never ever have made the discovery, because what you learned was not the discovery, it was the sum of 70 years since. I felt a great weight lift watching the sean carroll talk about _how_ Einstein made his equations. He explained the logic of each step, the assistance he needed to reach critical points, and generally made it human. I believe it was an RI talk. Then i remember some video about the process to find FD statistics to resolve the ultraviolet catastrophe and it was so enlightening. They aren't old gods, they're people that worked for decades to reach completely reasonable goals and we just don't teach it like that at all. It's incredibly discouraging to new students to never see that these people were mere mortals.
It's also possible that he meant every problem in your domain. That would be slightly more reasonable, and something I could agree with.
That's how a modern school system ought to be designed, imo. There's so much wasted time, and so much unused potential.
And if that involves rote-learning at times, fine, but can we at least make that smarter too?