Originally Posted By: Dottie
Excellent thoughts, but if my calc student doesn't buckle down and just memorize a few basic trig points, she is going to lose too much time deriving them on her upcoming test!

That's exactly why I said that rote learning can be a valuable tool for increasing fluency. And fluency is important, not just for tests, but to allow a person to glide over those concepts that have already been reasoned out. If you can't do that, it overtaxes your working memory when you're trying to reason out a new concept that builds on the old ones. Once the pathways are laid down in the brain by that initial "aha", they need to be reinforced by practice.