I think that is part of the reason school and education is still important even though there isn't as much emphasis on those things anymore. I remember learning to find the slope of a line the old fashioned way. It wasn't until we learned derivatives that we realized just how easy it can be, but you still had to know that old way for any of it to make sense. If you learn one piece without the other, there is a huge disconnect. I think of the people who never went on to take calculus and they are missing out on half the story by not ever learning about derivatives. Of course, they probably don't care, but looking at it from my point of view, it's a little sad.
Correct. And it is also important to realise that the brain develops based on exposure and repetition - it doesn't grow its structure by just having answers. People sit their kids in front of a screen, and the cost to the brain is immense.
Very true. My wife and I were just talking about this with her sister and brother in law the other day.