I like the fact some of my classmates thought that constuctionism is a new concept and others a familiar one. I think one of the points made was that we live in such a technological world that it is difficult to take ourselves away from it and the idea of tinkering and making is a way to do this. Well, in the physical aspect. We can tinker and make using technology, its just a different perspective. I mentioned programming in my high school course back in the 80s. That was “tinkering” and “making” in a virtual world.
One of the ideas that I have been thinking about recently is the concept of creativity. I know that math itself is not creative. You can be creative in attaining a solution. There is definitely more than one way to solve a problem. But I have been struggling with how to stimulate student’s creativity in math art. At the end of every year, I usually have time to indulge in these artistic pursuits (Escher type tessellations, mandalas, perspective drawings). Some students thrive and love it. They don’t see it as math, but they ARE using math concepts. Students generally get a mental block and can’t think of how to create a design. For example, one of the procedures to making an M.C. Escher type tessellation is to cut out a curve from the bottom of an index card, tape it on the top side of the card, then do the same for the sides of the card. You generally get a shape that looks like nothing recognizable, but the shape itself tessellates. The problem arises when you now need to draw some detail in the shape to make it look like an animal, object, person, or anything you “see”.
Here is a link to the procedure.
It’s been an interesting challenge to get students to go out on a limb and be creative mathematicians. I’ve allowed them to Google images to see ideas, but they usually end up trying to replicate the pattern they see and call it good. Not very creative, but they tried.
As the semester progresses, I look forward to the ideas that come up and I can hopefully use them in the class!