How before why
The algorithm comes first, and understanding comes later. Mathematics simply is. It cannot be negotiated.
This comes towards the end of a forceful but, I think, well-reasoned post which I found via Mathematics Weblog. As I understand it, the gist of the post is that in mathematics we need to learn how how before we learn why — even if it is the why which we ultimately find satisfying, and which allows us to remember the how.
My own not-entirely-coherent belief is that the way to learn mathematics is to `induct’ up from a bunch of examples: which raises questions as to how one teaches pure maths (say) under constraints of curriculum and audience background. One reason for starting this weblog is to explore this contention further (as well as to link to better-written arguments than mine, obviously).