Stepping off a polygon

[Jon]

From my own experience, teachers fail to answer what the first slide in any presentation should be: Why do you want to learn this? Admittedly, in math it's difficult to answer if the student doesn't yet know how to use what's being introduced but, by re-answering the question as each bit of new knowledge is presented, some degree of communication can be effected.

Agreed. They have also failed to address the reasonable question posed by non-technical students: "When will I ever use this in my life?"

When I hear kids asking this, I say: "If you're asking that question, the answer is that you will probably never, ever need to use this specific bit of mathematics in your entire life." This backs them into saying: "Then why am I wasting my time learning this?!"

Then I explain that, for non-technical people, the benefit of math is not necessarily the math itself, but the problem-solving techniques:

-Acknowledging the existence of a provable, immutable, and universally-accepted answer, devoid of nuance and opinion.
-Using knowledge as stepping stones, where each level builds upon the previous one.
-Understanding that some components of life are mechanistic and deterministic, and you'll never change that.

And the most important:

-Doing something difficult, hating every second of it, and completing it anyway.