I’m in NH at a conference that I had the pleasure of attending last year. Constructing Modern Knowledge is a “minds on” conference where we are encouraged to put on our learner hat and take off our teacher hat. I have two paths that I want to follow over these four days; I want to look at my new iPad and find ways to make it a tool to put learning in the hands of my students and not just another fancy pencil, and I want to find ways to understand the underlying geometry to the amazing tile, plaster, and wood patterns in Islamic Spain.

Today I started with the tiles. I used Turtle Art, a visual programming language that allowed me to construct, or try to construct overlapping geometric figures. The language is easy enough to understand, especially if you have played with Scratch as I have, but my personal learning issues have to do with spacial stuff (which way does the turtle need to turn to be facing the right way to make the shape??). So there are challenges.

I started with a square and serendipitously ended up with a square with a tail which, on eight repetitions, created a familiar pattern. It took me what seemed like forever in trial and error mode to figure out how far the turtle had to move to begin creating the circles and how big the circles should be. All the scripts that it took are floating there above the figures. Here it is, on its own:

I was happy when it worked (audible ‘yea’ was heard in the room) and I decided to leave that for a bit and try and other set of geometric intersections, inscribed squares.

Here are the images with scripts and without. This had me really trying to understand the ratios between the inscribed circles and squares. I think that Gary Stager has me convinced that to make the patterns scalable and capable of reiteration, then I need to move from Turtle Art to MicroWorlds and the logo programming language.

A colleague that is here with me was equally frustrated and was trying to think of alternate software or instructions for the process.

I think that is missing the point for me. I want to struggle with this. You can see that I don’t yet have it right. Where is that line heading??

There is no end to the things that I do not know. But there is also no end to the things that I can learn. If my students and I engage in shared inquiry, if we work together to solve some common problem, I think that the equality of scholarship will change the dynamic in the classroom for the better. And maybe, just maybe together we can sort out the underlying geometry of this: