[j2kun]

Ellipses aren't functions :)

I think if everyone agreed that the goal is to teach critical thinking skills, and have the factual knowledge be a byproduct (and elementary facts are very easy to pick up if you have critical thinking skills), then it would make a world of difference.

As to the motivations, after the students get going they don't need more real world motivation. They seem to be interested enough to ask their own questions about graphs, try to answer them, or come up with their own relations to the real world. This is where I think a lot of the critical thinking happens, not in learning facts about graphs. The facts (what degree means, what planar graph means, etc) come as a byproduct of following these paths of thought.

[acjohnson55]

Ellipses can be functions, if plotted using polar coordinates :)

[j2kun]

Touche. Do they teach polar coordinates in high schools these days? I vaguely remember fiddling around with the option on my calculator and plotting cardiods. Speaking of which, I got a nontrivial amount of programming experience by totally ignoring my math lectures and trying to write programs on my calculator.