# Day 5, 6, and 7 – Connections, Karaoke, and Fireworks

[NOTE: After spending the better part of Sunday morning writing this post, WordPress decided to delete it when I began to upload photos. If you have any dissatisfactions with this post, I assure you, the previous version addressed them all. I am rewriting this post as I comfort myself with a completely decadent cinnamon roll from the Zermatt Bakery.]

It seems impossible that we have been here at PCMI for a week. Impossible because we just got here a minute ago, and equally impossible because so much has happened – so much thinking, connecting, bonding and laughing – it feels as if it has been much longer. And in case you are wondering whether any of that gratitude for having made it here has faded, it has not.

In our final problem-solving session of the week, the connections between the problems given to us by Darryl Yong and Bowen Kerins had been working on all week deepened, sometimes in intriguing ways. For example, the same side lengths of a prism that give an equal surface area and volume (disregarding squared versus cubed units) are the same regular polygons (by number of sides) that when abutted around a single vertex add up to 360˚. WHAT? Why? This is a delightful mathematical mystery (at least, to me it is) that I am still pondering. Some teachers wondered whether all the apparent connections were meaningful – as my new sock shopping buddy, Jennifer Osgood articulately put it, “Just because my shoes fit you doesn’t mean my shirt will fit you as well.” In the coming week, we will be joined by some high school ‘Math Camp’ students; I wonder whether this line of inquiry will continue or resurface – what do Darryl and Bowen have in store for us all?

We became a group of 6th graders during Reflections on Practice, up on our feet, working in pairs, creating graphs with chart paper and post-its (for data points) given a set of scoring constraints about a soccer tournament. Once our graphs were complete, we were charged with determining which of the resulting 9 graphs depicted the ‘fairest’ tournament, in which teams were most evenly matched. It was a great activity, hitting multiple learning modalities – visual, kinesthetic, logical – and Cal Armstrong eavesdropped on our conversation to determine the direction and depth of our understanding, just as any teacher would (or perhaps should). We debated what fairness meant in terms of a soccer tournament, and how to ‘calculate’ that fairness given the graphs in front of us, and being 6th graders, our language wasn’t always mathematical. Finally, Cal asked us if there was a mathematical method for definitively describing the level of fairness in each scenario. When the term “Mean Absolute Deviation” was offered, there was the briefest of silences as many of us thought – 6th grade? Mean Absolute Deviation? But the fact is that this concept is included in the 6th grade math curriculum – at least it is in New York. It seems as if this is a huge idea for 11-year-olds to find through inquiry, but as one teacher pointed out, it may be more important to get students to want a tool than for them to actually discover it, echoing Dan Meyer’s recent series, “If Math Is The Aspirin, Then How Do You Create The Headache?”. This activity beautifully created the headache for finding reliable statistical measures, and modeled how students might function in a similarly well-designed activity, and how powerful the results might be – a huge takeaway to finish the week.

Our working group struggled with the sequencing of the online geometry course we are developing, as we debated the topics on which teachers might need direction given the curriculum shift that will accompany the full implementation Common Core standards in Geometry, and the logical order for those topics to be addressed. Clearly crafting an effective learning experience with these objectives in 4 sessions is a huge challenge. On Monday we will be meeting with teachers from other professional development groups for feedback, and I anticipate that the ‘outside’ perspective will be instructive. My partner and I are working this weekend to clarify our own session, which is the first one of the course. How much to include when introducing a topic, and what groundwork needs to be laid to prepare the participants for the second session are large questions we are trying to address.

The final formal session of the week was the Cross Program Activity: How to Make Sculptures of 4-Dimensional Things, featuring Henry Segerman, an assistant professor in the Department of Mathematics at Oklahoma State University. I must confess that
most of the presentation was beyond my mental capacity at the time, but the images he presented were quite beautiful, and I plan to attend one of his workshops next week in which I will hopefully learn how to use the incredible 3D printer that is available to us during the Institute.

And thus the weekend began.

After a leisurely dinner in Midway during which I was forced to rein in my New York tendency to insist on immediate and swift service (mostly because we were ignored for 30 minutes! – to my credit, I think I behaved well), I participated in the largest game of Cards Against Humanity I have ever witnessed – close to 20 participants! Each turn took close to 5 minutes, and one of our players (who may or may not have been one of the authors of the Common Core State Standards for Mathematics) had an uncanny knack for offering the most appropriate answer for each of the game’s inappropriate cards. The game left us all with an odd sort of bond – we ALL think nasty thoughts – and we hear them with good humor and tolerance. A perfect lead in to an evening of karaoke, skillfully hosted by Bowen, during which we discovered that not only do many of us have hidden (and not so hidden) performers within, but that also among our numbers are truly wonderful singers, rappers, interpretive dancers, and go-go girls.

On Saturday, the work on our parade ‘float’ came to fruition as we participated in the Park City Annual 4th of July Parade. I haven’t been in a parade since I was in a marching band uniform, which is more years ago than a lot of my colleagues have been around, but I don’t remember EVER having as much fun as I did yesterday. The Park City parade is a bit eccentric and very enthusiastic. Among the floats and participants included a snowplow, an antlered hedgehog, and grown-ups in tutus. Where else would you find a band of 60 to 70 math students and teachers, walking along waving geometric structures, chanting math slogans and being cheered on by the spectators with shouts of “Math Rules!” and “I love math!”? I was ‘officially’ a Marshall for our group, keeping us a pace, but you know what they say about herding cats? Luckily, the group immediately in front of us in the parade line-up was a 6 piece New Orleans jazz band, which not only kept us stepping in time, but provided musical accompaniment to which some our members danced and leapt for joy (truly!). After a lunch to rest our feet (and arms – waving Zome tool stars takes a lot more energy than you might think), I spent the rest of the day roaming around town, helping the local economy, which I actually don’t think needs my help. It was one of the loveliest 4th of July’s I can remember.

After a dip in the pool, and a little quiet time (what’s that?), the day finished, appropriately, with viewing a fireworks display from atop the crater across the road. There was a local show, and off in the distance we could see four or five other firework displays like small showers of sparkles across the dark horizon. It was a perfect end to a great day, and a great week. At the risk of maudlin redundancy, I am thrilled to be here, to meet these people, and do this work. I can’t wait to see what the coming week brings.