Your coffee cup example - if math were taught more that way rather than a dry list of mechanical actions I think less people would dread it. I have nothing but hatred and horrible memories towards my grade school maths education.
I can only study this stuff in my spare time so my knowledge is very patchy. But when I see stuff like eigenvectors I associate them towards a much more powerful concept of invariance - which I see everywhere. Recursion, programming, Machine Learning, dynamical systems, physics. And I feel on the edge of an epiphany but do not have sufficient knowledge to fully grasp it.
But it makes me think that all these things that appear over and over again in different guises, the subject is taught far too inefficiently. I feel there is a much simpler way to teach maths and have it flow and be holistic rather than a replay of history: disjointed and disconnected.
This is one of the reasons I'm creating a web site intended to show the connections between topics, and through that, how wide-spread the applications of the mathematical ideas are. Math should be taught with connections, applications, examples, demonstrations and, above all, by knowledgeable and enthusiastic teachers. Most high-school teachers don't know more than they have to teach, don't know the connections between topics, and don't have time to deviate from the prescribed curriculum.
I can only study this stuff in my spare time so my knowledge is very patchy. But when I see stuff like eigenvectors I associate them towards a much more powerful concept of invariance - which I see everywhere. Recursion, programming, Machine Learning, dynamical systems, physics. And I feel on the edge of an epiphany but do not have sufficient knowledge to fully grasp it.
But it makes me think that all these things that appear over and over again in different guises, the subject is taught far too inefficiently. I feel there is a much simpler way to teach maths and have it flow and be holistic rather than a replay of history: disjointed and disconnected.