You Can Dance If You Want To, You Can Leave Your Friends Behind...

So here I am, updating my Math blog, even after MAED 314A has finished. I decided that I will keep this updated for some time. This is about my professional growth as a math educator, so why not keep it fresh?

Today, I went to my practicum school to visit my sponsor teachers and hang out in the class. According to my sponsor teacher, I picked a good day.

Sponsor: "So, Paul, did you bring comfortable shoes and comfortable clothes?"

Me: " Uhh, yeah. Why?"

Sponsor: "Because today, in class, we're gonna dance. Didn't you see it in the curriculum?"

She really had me going for a moment. I was pausing to think about how dancing could possibly make its way into a math class, with the exception of some form of interpretive dance (like the short movie we saw in MAED 314A class). Once I figured out what the dance moves were, I thought the idea was brilliant! The "dancing" had four moves, all based on the orientation of polynomial functions on the Cartesian plane.

For odd degree polynomials with positive leading coefficients the dance move was this...
....O
.._|_/
/.. |
..../\
because the function is plotted (from left to right) from quadrant III to quadrant I.

For odd degree polynomials with negative leading coefficients the dance move was this...
....O
\_|_
....|.. \
.../\

For even degree polynomials with positive leading coefficients the dance move was this...
.....O
.\_|_/
.....|
..../\

For even degree polynomials with negative leading coefficients the dance move was this...
.....O
..._|_
./.. |.. \
...../\

The purpose of all of this was to get students to recognize what the general shape of the polynomial is before hitting the [Graph] button on their graphing calculators, so that they know whether what they see on their screens is truly representative of what they should expect to see. All in all, I thought this was a great activity, but only if the students are willing to try it out. This might not work right away with me, unless the students feel comfortable enough with me to act a little foolish. But hey, it's in the name of education!