Thinking beyond Conventional Standards: A Tool to Face the Challenges of a New Century

In order to find clues about how to face the challenges that the new century present us, we can take a look at the man’s mental development, as well as the revolutionary moments in the history of humankind, in particular the history of mathematics. We can examine more closely the different mental stages we all go through (according to Piaget), in order to have a better sense of human potential. Two of the innovative moments in the history of mathematics are the creation of non-Euclidean geometry by Nikolai I. Lobachevsky (1793-1856) and the formalization of the concept of infinity and the transfinite numbers by Georg F. Cantor (1845-1918). These achievements were the result of efforts performed by minds working against traditional ways of thinking, freed from the concrete reality where so many mathematicians before them had been stuck. As mathematics teachers at the beginning of the most demanding century ever, we ought to better know our students’ potential, and grant those students who think differently all the attention and support that likely creators of changes in history command.

Polyhedral Crafting

I started the year once again feeling unsatisfied with the spare, utilitarian look of my classroom.  So, having given up on finding math-related posters I liked, I decided to head over to Math Monday to look for some cool looking thing I could make this weekend.  The result:

Tensegrity polyhedra, made from 3/16″ dowels and standard rubber bands, based on this little article by George Hart.  The coolest thing about them is that no two sticks are actually touching each other (which makes me wish I’d used different color rubber bands).  Or maybe it’s that they can collapse like this…

…and then snap back into shape.  Or maybe that they bounce. (Yep.)

In any case, they were really fun to make–the dodecahedron turns out to be a great spatial reasoning puzzle as you get close to the end–and I think they’ll make good toys or decorations.   And there’s tons more inspiration for mathy crafts at Math Monday (as well as at georgehart.com and vihart.com).  Maybe I should crowdsource this by offering it as extra credit–that ought to get the classroom looking good in no time 🙂