I don't know how other people function, but I'm all about collaboration. When I get weird ideas, I like other people to play along with me. One idea evolved like this:
Luke and I were interested in dot and line games a few years ago. We puzzled over what types of stars were made by connecting the dots in circles of different numbers of dots in different ways. Luke came up with a theory (probably while I was changing Seth's diaper) and he ran with it.
I won't bother explaining the theory here (figure it out yourself!) but we both did a lot of productive thinking--mental calisthenics--to go along with the development of this theory about connecting dots.
OK, so what?
Well, several years later I wanted to pull together some of our favorite math activities and write a book about them. But I wanted the book to be useful, interesting, and very original. While chatting with several family members, I had an epiphany to have each math concept or activity introduced through a magical creature who plays games which incorporate the math principle. I knew I wanted to include the circle-dot-line game and encourage other kids to use their own brains in some open-ended thinking about this. Thinking of dots in circles reminded me of how much we enjoyed the "fairy ring" of white mushrooms that would pop up occasionally in the back yard in our first home when my big kids were small. So I asked one of those small-now-big kids if he'd come up with an image that showed fairies dancing on spider webs strung between mushrooms. Since Quinn has a beautiful, unusual mind, he drew a beautiful, unusual picture:
I love the perspective, the position of the fairy's hands, and the swirly skirt that echoes the underside of the mushrooms. This drawing was included in the first printing of Magical Math. But I just received, from Quinn's sister Adrianne, a color version of the drawing, and I love her additions so much that I had to write this post.
Check out the phosphorescent glow from the mushrooms, and how they shine off of the fairy's arms and legs. Nice touch!
So that's why I love collaboration: everyone contributed to this little piece of Magical Math (even the one who required a diaper change). As John Donne said,
"...Every man is a piece of the continent, a part of the main;
if a clod be washed away by the sea, Europe is the less,
as well as if a promontory were,
as well as any manner of thy friends or of thine own were;"
I am so much "less" without my family and friends, who've given me feedback and encouragement all along the way!