Let me say this about Phillips Exeter Academy – the showers in the dorms are FANTASTIC.
I wrote a note to myself this morning to share this fact. After living in an old house for years, and vacationing in rustic cabins for even more years, the strong steady water pressure with adjustable but stable temperature (uninterrupted by sudden flushes) is just one more bonus to this conference, whose end is, sadly, in sight.
Leaping from the start of the day to the end, Dan Meyer (@ddmeyer) spoke [inspiringly] this evening about Perplexity. I am an avid follower of his blog, dy/dan (http://blog.mrmeyer.com/), and an advocate of his approach to infusing the classroom with an empowered spirit of inquiry as a means to meet the myriad challenges of teaching math in an era of omnipresent, rapidly and continually changing technology. But in addition to engaging (in the best sense of the word), perplexing, and enlightening his audience, Dan gave us concrete suggestions (thank you!!!) for how to categorize/organize/efficiently store the overwhelming amount of information streaming toward us, how to employ readily available technology (e.g. our phones) in service of that process, and how to enliven our own spirit of inquiry in order to provide ‘perplexing’ opportunities for our students. It was yet another mind-expanding event in this week of continual enrichment and enlightenment. Did I mention he has a great sense of humor?
Other highlights of the day included a great lesson on Parabolic Art in Desmos by Mary Bourassa (http://mathgeek.ca/), putting together a chapter for a class iBook project on Louis Kahn, the architect of the Exeter Library (which, by the way, has a grandfather clock in the lobby and a grand piano upstairs), and some great group work in Number Theory, during which I actually articulated and modeled a pattern for one of the problems (a major academic breakthrough!). I am preparing a very brief presentation on Flatland for Friday’s class, and learned that the author, Edwin Abbott Abbott, was not only a mathematician, but a celebrated classicist, theologian and Shakespearean scholar. Not bad for the son of 1st cousins (hence the 2 Abbotts). And in my work on the Louis Kahn book, I discovered that the Trenton Bath House which he designed in the mid 1950’s is neither in Trenton nor a Bath House. It did, however, have an incredibly mathy design and mural.
In my Higher Mathematics course today, we were discussing the Socks and Shoes Property, a way of explaining inverses – in order to put on your socks and shoes and return your feet to their normal barefoot stage again, you must complete the actions in reverse. Our quantum mechanist posited the idea that if the sock was ‘fundamental’ [to be honest, I’m not sure what he meant by that] then you wouldn’t be able to tell which sock you put on first, whether both socks were on the same foot, or whether you could even tell them apart. He admitted that this did make him sound like a bit of a wingnut, and then tried demonstrated this with pieces of paper. Following this, we began a discussion in which we imagined ourselves fleas crawling around on a surface, not being able to tell whether it was flat, or a torus, or indeed how many holes were in the torus, and how we might use a string to help us determine that. This discussion intrigued all of the wingnuts in the room, myself included.
One final bit of entertainment, a video in which exponential growth is illustrated in one of the most entertaining ways I have seen. Enjoy!