The technology that everyone is using is built on math.
The new technologies that will be created and depended upon in the future…will depend on math.
But math doesn't depend on showing your work. You can shortcut tf out of it and get the same result. Additionally, some people who take the shortcuts can make the high-level connections because they don't get stuck in the details. They may actually end up understanding the subject and concepts
better, but end up hating math class and math. If you look at it close, in many ways at those levels (dealing with kids), showing work is close to tedious brute force memorization. At those levels showing work is supposed to be for the problem solver/student to reference their steps, not for the teacher to determine pass or fail.
I think you'd be surprised at how many professionals don't know how to do basic integrals, differentiation, etc. yet are involved in making some groundbreaking tech because they know to get the answers one way or another (which is what the real world values). I know how to solve the integral of (xe^2xy)dxdy, but pretty sure 98% of the people I've worked with don't.
I honestly think the world needs a revamp on math education (and education in general) to be honest. We may be wasting time on too much old-fashioned ceremony that really isn't doing as much teaching and skill-building as we think it is. Do we know for a FACT that showing your work is
really producing and training the talent? Is it
really the cause of a good math student? Are we sure it's a necessary procedure and not a time sink just because it's been passed down as an "accepted" practice and rigor?
I don't even want to get started on musical education and how many hours, maybe years, people have spent on ear training for marginal benefit because it's the accepted ceremonious "rigor" we think is making better musicians. This dude here is an accomplished violinist (who picked up guitar), got absolute pitch and by using modern tech basically shows why the age-old advice of learning to sing what you play (a practice many people have passed on through the years) is BS:
Now, in most musical educations (especially on the collegiate level) there are sometimes 3 semesters worth of ear training courses. Imagine how much time could have gone into other more useful skills as a player. Think of every single person who took those courses, that's decades worth of time. shyt, maybe even a century's worth if you add the time everyone has spent doing a task that is outright wrong. Similarly, he said the best musicians he plays with professionally would basically fail all those ear training courses as well.
That's where going with traditions without verifying if they're really as effective as we think is going wrong. It's "rigorous" and difficult so we think it's raising our abilities, but is it really efficient at increasing skills and is it really in
correlation to what we're trying to accomplish? A lot of curriculums are basically passed down and simply accepted because "somebody told somebody" and they started to pass on that advice.