>>> Meaningless symbols that need to be manipulated to arrive at some mysterious answers.
I get what you're saying, and agree but with a caveat: Please don't take this away completely. There's always going to be a few of us freaks who came to math because of this feature: Math as an exercise in pure abstraction. We have no other refuge. As I've mentioned in this thread and others, proofs were what made math come alive for me. And I didn't struggle with applied math at all.
Agree! And that's because there are some who just get this and are able to explore this in the space of ideas the same way we all have very different tastes in music and literature. Math has both practicality and poetry and many problems are introduced when the focus is one on. What one responds to is personal.
Abstraction can be learned with purpose, eg if they want to program physical movement in a game, X and y need to be variables, not because we are just using abstraction for the fun of it. Even proofs can have meaning and purpose if you can show how they are useful. Algebra, calculus, liberal algebra at least, all make more sense (and easier to accept by new learners) when you actually use them to do something.
I get what you're saying, and agree but with a caveat: Please don't take this away completely. There's always going to be a few of us freaks who came to math because of this feature: Math as an exercise in pure abstraction. We have no other refuge. As I've mentioned in this thread and others, proofs were what made math come alive for me. And I didn't struggle with applied math at all.