>> Based on my own experience as both a student and a teacher, I have come to the conclusion that the best way to learn is through "guided struggle". >This is t

>> Based on my own experience as both a student and a teacher, I have come to the conclusion that the best way to learn is through "guided struggle". >This is the only way to "properly" learn mathematics or science. Anything else is only making you think you've learnt something. I agree with this statement but I think it misses the point entirely. Guided struggle is indeed necessary, but learning some theorem without seeing the impetus for its discovery is like learning how to play an instrument without understanding that the intent is to make music. Yeah, with enough time and struggle, you might be able to go through the motions and play some scales, but most people don't learn to play instruments that way, they learn to play a simple song or two, then go back and start with the scales and building musical theory. Math textbooks sometimes try to do the same thing, but it seems like they always come up with the most inane and pointless exercises. All of this is just to say, learning they why of math can help someone learn the how.