The Best Way to Learn Math Is to Learn How to Fail Productively

The gist of this article is contained in this sentence:

> _Students who are presented with unfamiliar concepts, asked to work through them, and then taught the solution significantly outperform those who are taught through formal instruction and problem-solving._

I obviously haven't done the research, but for myself, I find this to be true with almost everything, not just math. I learn to code in new libraries better if I struggle with them first and _then_ have them explained to me, rather than someone explaining them from the start. I find that this even applies to techniques for physical activities such as cooking and rock climbing.

I find that I'll understand a clever solution best if I first understand why the intuitive (but wrong) solutions don't work.