My leap into regular blogging took place a year ago, when I had the opportunity to attend the Anja S. Greer Conference on Math, Science and Technology at Phillips Exeter Academy. The experience of the conference was personally and professionally enriching, so much so that I was overflowing each night with ideas and reflections, and managed a detailed daily post. So affected was I by the opportunity provided by the conference to learn, collaborate and connect that I spent a lot of time and energy trying to get back there this year. Last week that happened, and it was as wonderful an experience as the anticipation warranted.
I attended the conference this year with a friend and former colleague, which added another dimension to the experience – sharing something wonderful with a friend. You don’t really know how well you get along with someone until you travel together, and I learned how compatible we actually are – our conversation flowed continually, tangentially, and effortlessly, making the road trips there and back easy, and we shared both ideas and new acquaintances as we experienced the conference separately but in tandem. Another big plus this year was being reunited with a kindred spirit on the Left Coast – someone who I met last year but felt as if I had known for a very long time. So, before even thinking about the rich professional and mathematical experience that the week provided, my soul was personally soothed and enriched.
At the Exeter conference, participants take 2 week-long courses, sit in (voluntarily) on 45 minute stand-alone sessions which run throughout the day, and attend evening programs with speakers. This year, Geometry was the ticket for me – my 2 classes were ‘The Geometry of Origami’ with Philip Mallinson, an Exeter instructor, and ‘Geometry Labs’ with Dan Butler, a public school teacher from Minnesota. I came away from both of these hands-on classes bursting with ideas and energy to push the geometric envelope a little further in my classroom.
In the origami course, we began by doing some proof regarding folded paper, and I learned an amazing fact about A-size papers – which may be common knowledge, but not to me – that the ratio of the sides in all of them is 1:√2! Think of all of the math problems we could do with PAPER ALONE if we used these sizes! But I digress…we explored patterns created by ‘flattening’ folded figures, the ratio/relationship of the number of mountain versus valley folds, and finally, did some origami. The conversation in the class, expertly and humorously facilitated by the teacher, flowed easily – participants posed questions and made conjectures which the rest of the class immediately explored. I have since purchased Project Origami by Thomas Hull, some origami paper, and will be engaging in some folding on my own very shortly. As a result of the infectious enthusiasm of my instructor, I went to see the Surface to Structure exhibit at the Cooper Union, which was nothing short of awe-inspiring and mind-blowing (images at conclusion of post).
Last year, I became friendly with someone in the Geometry Labs course, and was completely envious; my experience this year confirmed exactly what I had imagined the class would be, and it was, from start to finish, a delightful and enlightening experience. First and foremost, the instructor, Dan Butler, has an open, warm, and engaging teaching style. He very rarely gives answers (someone after my own heart), but rather prods students into working through their wonderings. He is continually good humored and generous with both time and supplies, and has a way of making every student feel acknowledged and heard.
Our activities during the week included hypothesizing why a snail ball won’t roll down a ramp, calculating the distance required to have a marble sent down a chute land in a cup, problem-solving with Taxicab Geometry, discussing the implementation of Gateway Exams to ensure basic skill competency, identifying changing patterns and shapes created by the shadow of a stellated icosahedron, and modeling with Geogebra. And in between activities, or waiting for class to start, we attempted to solve cube puzzles made out of tetrominoes. We spent one full class period working on the multi-level Goat Problem – how to determine the grazing area of Billie the Goat as her tether was repositioned relative to barns of various shapes.
Dan offered an extra-curricular activity as well – creating our own stellated icosahedra. Using string and straws from the 99¢ store, he opened his classroom for three afternoons between class and dinner, and coached us through their construction. [I do not have written instructions for this project, unfortunately, but there are a number of examples out there on the Interwebs.] There were always other participants in the room – discussing problems from class, working on other experiments, or just hanging around. It was easy to envision Dan’s classroom at school filled with students all day long; he creates that kind of welcoming space in which everyone feels comfortable and wants to participate on some level. At the end of the week, Dan held a lottery for his samples which were created with FANCY hard plastic straws (from Party City), and which he did not want to fly home with. Lucky me! Lots of geometry swag for my car.
Another highlight of the conference (I really should have written some interim posts; I see that clearly now..) included a lecture on The Future of Learning by Alan November – a thoroughly engaging speaker who explored increasing students’ abilities to self-assess and teachers’ skills in providing meaningful feedback. Alan is one of those people who spout ideas as quickly as you can write them down (for me, anyway) – including resources like kaizena.com, clubacademia.org, and mathtrain.tv. He reminded us of that which most math teachers have – The Curse of Knowledge – and probed the eternal questions of how to (a) motivate students and (b) get them to do more than you actually ask. This RSA video by Dan Pink reflects a lot of his thinking.
I also attended a CwiC session (Conference within a Conference) offered by Frank Griffin of the Cate School which was chock full of tips on ‘Animations, Simulations, and Visualizations.’ While many of the resources Frank presented were ones with which I was familiar, he showed specific applications of particular features which enabled me to actively envision using them in my classroom. A partial list of these resources includes SmartBoard algebra tiles, Proof of the Pythagorean Theorem on hotmath.com, the Wolfram Demonstration Project, and some spiffy uses of TI Smartview. This was another workshop which had be writing as fast as I could.
If you’ve managed to slog all the way through the content, now I’ll tell you about the magic of the conference. Phillips Exeter Academy is in a picture perfect New England town and we were blessed this year with lovely cool weather. The school itself is beautifully maintained; the dorms are basic and clean, the academic facilities are state of the art, and filled with visual and academic surprises (see my posts from last year for some of these). There were 5 different education conferences running simultaneously: the math conference, a biology conference, a writers’ workshop, a humanities conference, and a diversity conference. We wore nametags all week, and each conference was identified with a different color lanyard. This year, the main dining hall was under construction, and meals were relocated to a smaller facility, which was a bonus in disguise – there was much more inter-conference mixing and discussion than before. I loved hearing about how the writing teachers had to awkwardly share their own work, or sharing concerns about identity with the diversity conference participants. On the last two evenings, we ate dinner out on the lawn in the quad – and it was a sight to behold.: 400 teachers, all engaged in intensive professional development, having the time of their lives. We all deserve – and need – opportunities like this. We can most effectively help our students learn when we are better prepared and engaged as teachers. And being sent to conferences like this gives teachers the message that they are worthwhile, that their ongoing professional development is critical and that their role as educators is as highly esteemed as it should be. Children are the future – how the ongoing education of their teachers can this be any less important?
Attending the conference this year was not easy – I had to search for funding, and fight for the days to attend. When I first arrived, things had a bittersweet feel, because attendance a third year in a row seemed impossible. I left with the conviction that it is mandatory.
IMAGES FROM SURFACE TO STRUCTURE EXHIBIT