Which is the more mathematical approach to attributes - systematic or playful?
In my program Math in Your Feet (
www.mathinyourfeet.com) elementary students use "movement variables" to help make up their percussive dance patterns. These movement variables are actually a collection of attributes (5-6 options in each of the follwoing 3 categories: foot position, type of movement, and direction). I'm wondering if using variables/attributes like this in a systematic way (like how you go about determining combinations, for instance) makes it more mathematical? Or is it simply that when you are working to solve a problem (like making a dance step) you manipulate the variables/attributes to suit your aesthetic or needs, with one or many possible agreeable solutions? Let me know if I should clarify this further. :-)
There is a certain tension here between free and open math exploration - and being systematic. I want the two to be balanced. I want kids to play with variables freely, trying this and that. I also want them to notice patterns in what they try, then explain patterns, then try things more systematically based on patterns. Both are math activities! Different people have different personal preferences, too. I hear Einstein played a lot before, during and after working systematically. ![alt text][1] [1]: /storage/temp/22-einsteinteasing.jpeg
