Michael T. Richter wrote:
On Tue, 2007-10-07 at 20:59 +0100, Andrew Coppin wrote:
But it rambled on for, like, 3 pagefulls of completely opaque set-theoretic gibberish before I arrived at the (cryptically phrased) statements I presented above. Why it didn't just *say* that in the first place I have no idea...
Because the overwhelming majority of people who teach math know math well, but do not know teaching well. Sadly it would be better for all but the highest levels of education to have that reversed. My own long-standing, deep distaste for the "chicken scratchings" of the pure maths stems from incredibly smart teachers who had no idea how to communicate what they knew to those not already there.
At the risk of becoming tangental... When you are really *deeply* knowledgable about something, it can become seriously hard to even realise all the things you're constantly assuming your audience knows. It's so obvious *to you* that it never even crosses your mind that you might need to explain it. Heck, you don't even realise that what you're talking about relies on this concept, since it is so deeply embedded in your mind. I see this *a lot* with computers. People who know lots about computers forget that some people don't know that a "megabyte" is (considerably) bigger than a "kilobyte". Or that having a faster CPU doesn't make Windows load faster. The number of technical documents I've seen that make perfect sense to a knowledgable person, but would be utter gibberish to most normal folk... I've also come across no end of product websites where the authors are so keen to tell you how brilliant their product is and all the cool features it has that they completely forget to explain WHAT THE PRODUCT DOES! For example, FreeNX. I spent *hours* trying to figure out what that actually does...! (In the end, I had to ask somebody. Turns out it does nothing of any interest to me, but still...) I like to think that I'm quite good at explaining technical things using non-technical (but not patronising) language. But I'm probably just kidding myself...