I met Colin Adams when I was giving a lecture at Williams college a few weeks ago. He showed me some of the work he’s done on knots and it looked like there would be some fun projects for the boys hiding in that work. I ordered his book Why Knot? right after our conversation and it arrived yesterday.
This morning instead of the review work that they’ve been doing in algebra and number theory I had the boys play around with the book. No help from me today – just open the book and go.
Here are their thoughts.
First – initial reactions and a simple knot:
Second – an attempt to construct a slightly more complicated knot. This task was harder and, in fact, we didn’t quite complete it. Something to work on later today, though:
So, a good start, though this is probably a project that needs a bit more adult help than I provided this morning. I’m looking forward to exploring this book with them over the next few days.
Mike's Math Page 
A long time ago in a galaxy far away (when I was in my early twenties in NJ) I worked with older elementary children spending time with them in a wilderness environments, where knowing how to tie good knots comes in really handy. I was still completely oblivious to learning differences in kids, but even so it was remarkable to me how some kids learned knot tying with ease, but others, it was like they just couldn’t see the relationships that needed to be created to make the knots. I wondered (even back then) if there was a connection between the minds that couldn’t grasp knotting and that couldn’t grasp math. i’m beginning to think about knot tying and origami in the same way, thinking that they are good preludes for young minds to become accustomed to the kind of thinking that is useful with math. One the things that is mostly appealing to me about knots is UNtying them. BTW I had heard of something called Knot Theory and was surprised amused when I realized that it was a branch of math that actually had to do with knots!