If a new concept or method can be clearly explained to me that has obvious advantages over its predecessor, then in my opinion it should be adopted. Period. Status quo and its length be damned (even in such a case as "it's been that way for centuries" or perhaps — especially in that case?)Stumbling across Professor +njwildberger's YouTube channel several months ago (a treasure trove of mathematical instruction if there ever was one), it seems I found perhaps the single most pragmatic and practical professor of mathematics one could ever hope to meet.
It is simply not possible to too strongly encourage you to watch any one of his many series of lectures.
Math Foundations, for example, will at the very least force you to reconsider closely many of the core concepts of mathematics, such as real numbers and set theory. While Rational Trigonometry will have you asking yourself, "Why... why couldn't I have been taught trigonometry with this method when I was a student?!" And his lectures on The History of Mathematics are easily the most in depth and interesting I've yet found.
This is but the tip of the iceberg. There is much, much more. I hope you'll enjoy the channel as much as I have. (And given the sheer volume of uploads there, I'm sure I will be for quite some time to come!)
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