Tim Gowers offers what he considered an uncontroversial pedagogical principle, examples first. He discovered, though, that on the internet there are no uncontroversial topics.

When I started reading Tim’s post, I expected to agree completely with his point. I think I understand subjects almost entirely through examples. I expected him to advocate putting examples before theorems, but he’s actually advocating putting examples before definitions. I dislike that style fairly strongly; it’s like being led down a road by someone who already knows the destination, but they won’t tell me where we’re going until we actually get there.