I'm very surprised that we don't teach basic graph theory in <= high school education. It has such a nice, gradual slope from puzzles and pictures to proofs, algorithms, and all sorts of science. I've done activities/lectures on the topic to all levels of high school (some with notes [1]), and it is routine to see amazement and engagement. And Hamkins shows it can go all the way down to eight-year-olds. It seems like a win-win to include it in every math teacher's repertoire. It can go as deep as the students want it to go.
I found your site through HN a while back, and since then I've sent a link to your site to pretty much every math/STEM teacher I meet (and I encounter quite a lot of them). Many of them have specifically mentioned to me what a great resource you've created for teachers and how you got their kids excited about math. I hope you know that your work is having a tremendous impact on math education and that impact will grow exponentially.
Agree, This applies to pretty much every topic. If you make it relevant, interesting and create a safe environment where mistakes are ok a lot can be taught to kids.
I was fascinated as a kid from various types of sailor knots. I was in the air modelling, then computer club, and our neighbours were the young sailors, but I've never got into it.
But I know kids around me were fascinated by them too (it could be that we were after all living in a fishing/sea town with lots of big ships, etc.).
But then even for girls (knitting, or other activities) - there is something about graph theory to be found there. Just wondering...
I faintly remember that we did `use` graph theory in our HS assignments, but haven't actually touched hypothesis or proofs, that I now associate with it.
I remember we wrote programs to higlight a graphs skelet, find shortest path, search for components, e.t.c.
Discussions on correctness and efficiency were informal.
[1]: http://jeremykun.com/2011/06/26/teaching-mathematics-graph-t...