There are a couple of things I really want to focus on in my undergraduate Teaching Elementary School Math and Science course this semester. I want my students to be able to see the relevance of school mathematics. I want them to see that it isn't just a means of balancing your check book or working out how to solve mathematical problems. I want them to go beyond the "do the math" syndrome that our culture seems to have fallen into when it comes to any form of quantitative experience. I want them to see the poetry and creative writing equivalents in mathemtics.
I want my students to appreciate the aesthetics of math in the same way that Vi Hart does. I want them to see how wonderful it is when you add two successive traingular numbers such as 3 and 6 and get a square number. Imagine three small wooden blocks next to each other so that a stack of 2 is next to 1; like a step. Now add a third stack of 3 to make another step and a total of 6. If you take another 3-step and invert it, it fits with the 6-step to make 9; two successive triangular numbers make a square number. You can make triangular numbers just by adding an additional step. 6 plus a stack of 4 is 10. Just like this: invert the 15 and it will fit with the 21 to make 36, a square number.
Isn't that just way cool?