The Anxiety of Influence: PCMI, TMC15, and [Trying to keep] Moving Forward

IMG_5793I returned from Utah 2 weeks ago, and am about to embark on my ‘real’ vacation – 2 weeks on Lake Dunmore, Vermont (aka heaven).  My final recap and reflection has been on the to-do list since July 18, but my return to Brooklyn was accompanied by a delayed crash from the end of the school year, some home disaster and drama, and my envious observation of TMC15 as it appeared in my Twitter feed (which I couldn’t always bear to look at) and blog reader.11782342_10205542168927228_3163533859352772846_o

11412004_10205487182992614_2989034904136514571_oPCMI was a gift for which I am deeply grateful on many levels.  The scholarship enabled me to attend, got me to confront a long-lived phobia (flying), placed me in the company of like-minded teachers who became dear friends that I know I will see again, and restored my teaching soul more fully than I thought possible.  The challenge I face in the coming year is maintaining that restoration and energy in an environment which, while personally supportive, pretty much works in opposition to many of the mathematical and philosophical teaching practices to which I aspire.11709954_10205462851144333_210506142907498134_o

As wonderful as PCMI was, the emotional backdraft from Twitter Math Camp is overwhelming. One by one, I have been reading everyone’s blog posts, getting a keen feeling of what I missed in California.  (The top hit for this, by the way, was Fawn Nguyen’s keynote, the slides and notes of which I read in their entirety, IMG_5880hearing Fawn’s voice loud and clear.)   But there has been a bonus for me – everyone’s heartfelt and articulate writing has left me with some TMC takeaways, and I wasn’t even able to attend.  And these takeaways reflect and magnify my experience in Utah, creating some kind of ultimate fractal/exponential virtual math professional development effect (there’s an acronym or hashtag in there somewhere – I’m sure of it).  Here’s what I’ve gleaned and what I continue to ponder:

  • Mary Bourassa wrote so eloquently about the growth of her participation in the MTBoS and how she finally felt she made a ‘real’ contribution with the Which One Doesn’t Belong website.  I’ve participated in workshops Mary has run (at Exeter), and thought she was the cat’s meow way before Which One Doesn’t Belong.  I share resources and participate as constructively as I can generously on Twitter; I would love to be able to create something as broadly useful.
  • Darryl Yong was awesome as the co-designer of the morning math problem sets at PCMI, but his post on Radical Inclusivity spoke directly to my heart.  I have a personal goal to speak out against the pervasive tacit racism at my school, and to try and start a diversity committee. Darryl’s post eggs me on.
  • Julie Reulbach and Anne Schwartz, two women who I really would like to see again after meeting them in Philadelphia at TMC13, both wrote about hesitancy in attending TMC after personally and/or professionally difficult years, and the restorative power of this community.   I know that at the end of the school year, I felt quite spent in both of those arenas, and approached PCMI with trepidation.  I was thrilled to find myself recharged within days (even amongst ‘strangers’), and I was glad to hear the same was true for Julie and Anne.
  • Megan Schmidt, my favorite person who I have never met, looked another scary issue squarely in the face in her post Safe Spaces at TMC15.  Megan’s posts speak directly to me, every time, and this post was no different.  The personal issue I dealt with at PCMI was the baggage I carry and the isolation it occasionally forced on me; it was difficult (I found it impossible, actually) to talk to anyone about the ravage alcohol abuse has wreaked on my home life or the ever-present watch for cancer recurrence that has become routine for me.  I’m not sure how to create those safe spaces wherever I go, but I love that Megan articulated the need for them, because there are times when group hugs just don’t do it.

In addition to the aforementioned keynote by Fawn Nguyen, there were two other quotes (below) that appeared numerous times in the blog posts that sum up, for me, not only both conferences – PCMI and TMC – but how I view my involvement online and why I continually seek these opportunities, and relish them so.

from Lisa Henry: “It’s the community, stupid!” (quoted from Dylan KaneIMG_5780

from Christopher Danielson:  “Find what you love.  Do more of that.

Thanks to everyone who shared, and you can bet you will see next summer!



PCMI Day 12 Here Come the Kids (and then there was the weekend…)

just another gorgeous shot in utahIt’s Sunday afternoon, and Friday seems like a long time ago.  Typical of intense self-contained experiences, time has taken on a paradoxical quality.  To paraphrase a colleague of mine here at PCMI, I feel as if I just got here, and if I’ve been here forever.  And I know that just as quickly, I will be going home.  So I’m glad that every day seems like a week, and that the intense experiences of the weekend make Friday recede into the past.

salt pyramidSpeaking of Friday, during morning math, we were joined at our tables by the students attending the High School Math Camp, as we experimented with pouring salt and the shapes thus formed.  They worked hard and enthusiastically, using what they knew to make the connections that solving the problems we are given each day require.  Their presence added some excitement to the room, I thought; as exciting as it is to access our inner explorers as we problem solve each day, it is even more exciting to see a student to light up with discovery.salt ellipse

We finished our week of Reflections on Practice by grading sample student papers, and crafting feedback that would hopefully move learning forward for the student who had made either a conceptual or mechanical error.  Seeing the actual student handwriting on the papers, and witnessing errors I have seen frequently in the work I grade ‘for reals’, added a touch of reality to the work we are doing.  In pairs we discussed not only how would we grade the work in front of us, and what feedback we would give, but whether that feedback would actually have an impact – we all agreed that students, receiving their papers, would immediately compare grades, calculate percentages (when grades were not out of 100 points), and, in the case of failing papers, crumple and toss.  Regardless of our shared occasional pessimism, I know that going through these exercises re-energizes all of us aspens[participants] to go back to school (when it is time – not yet! not yet!) with the energy and positivity to bring our best game once again to our classrooms, to engage in those best practices we discuss every day, with the goal of __________. (Fill in: raising student achievement, creating lifelong learners, increasing conceptual understanding and appreciation of math, whatever your personal pedagogical goal may be.)

planksAfter some ‘pre-lunch plank’, followed by the meal, our working group continued to progress towards a consistent product with which to complete our task for this conference – content for an online Geometry course for 8th grade and high school teachers shifting to the Common Core standards.  It’s been a challenging process, not without its frustrations, but I personally feel like we have completed a lot of work in a short amount of time, and that perhaps the task is too large for the allotted time in which we have had to work, and I would like to have the opportunity to continue this process to its fruition, which will surely be after July 18.  We presented our work to some visitors, who asked pointed questions about our goals and intentions, our resources, and even our vision of the final product.

game show screenThe cross program activity on Friday afternoon was a presentation on the Math Behind Game Shows by none other than the Amazing Kreskin Kerins.  Bowen’s presentation modeled perfectly what makes an engaging lesson – a topic about which you are intrigued and want to know more, enthusiastic participation from those engaged in learning, and PRIZES.grant deal no deal

The final ‘official’ activity I participated in last week was a meeting with two teachers from Monument Valley High School in Kayenta, Arizona (Kayenta is a census-designated place which is part of the Navajo Nation and is in Navajo County, Arizona); they had reached out to PCMI through Herb Klemens of the University of Utah for help with rich tasks to engage their at-risk students.  A group of us had compiled a list of tasks and resources to share with them; we were aware of some of the challenges these teachers and their students face, and we were also aware that their issues and needs were, for most of us, beyond our purview.  But we met, we shared, we discussed, we offered our suggestions and insights, and they were accepted graciously.  At the close of the meeting, Herb suggested that lines of follow-up communication and sharing be created and maintained; I certainly hope that is the case.  Although I am aware that the circumstances in which these teachers work and students live present huge challenges, I would like to find some way in which my experiences and knowledge could be of benefit to them.  It was a humbling experience.

And then the weekend began!

nutmeg lampFriday evening brought a lovely dinner with some new friends at The Farm at the Canyons, a restaurant that took its ‘farm to table’ philosophy very seriously.  After we finished a deliciousperfect eggdinner, we wandered around a bit and into the lobby a hotel which had decor that actually competes with our home-away-from home, the Zermatt.  The staff was so cordial that they didn’t seem to mind that I was snapping photos of their light fixtures.  Hmmm.  When we returned to Midway, I caught the tail end of a repeat karaoke session, and had the pleasure of being part of a highly dramatic performance of Bohemian Rhapsody.

Now, THAT'S a chandelier!

Now, THAT’S a chandelier!

Saturday brought even more fun – thanks to MaryAnn Moore, I had the opportunity to volunteer at an outdoor concert at Deer Valley and see Smokey Robinson with the Utah Symphony for free (plus a t-shirt)!  It was a beautiful night, and my job was to distribute programs as patrons entered the park, a plum job – everyone was excited to be there, and happy to receive a free program.  My official duties were by the intermission (which was before Smokey came on; the first few numbers were entirely orchestral), so I saw the smokeyconcert from a lovely perch on the hill.   And he is amazing – spry and cheery and wearing a metallic green tux as he danced around the stage!  The crowd was, of course, loving it, and many people got up and danced.  It was another special evening.

aspensAnd to top off a wonderful weekend, I hiked Park City Mountain (I couldn’t quite figure out whether that mountain has another name) with an intrepid crew.  The hike went much further than we initially thought, but we persevered with good spirit and patient navigation, and made it up to the only running chair lift on the mountain, which also happened to be the one at the highest altitude.  crew on a mountain I had to fight with myself to keep going – I’m not normally outdoorsy and have a couple of decades on the people I was hiking with – but I persevered and accomplished yet one more thing on this trip that I had not before.*  If you’re still reading, I apologize for saying this again, but I continue to be grateful for this experience.

And so the final week begins.

Mathness on a Mountain

PCMI Day 10 and 11: Tripling your fun

Hint of a rainbow

Hint of a rainbow

This post will be brief but I want put down some notes, if only so to remember the details of this great day myself.  Working backward from a jam-packed evening:

I have just returned from Line Dancing taught by one of the Undergraduate Faculty participants, David Nacin.  He has been generously giving his time in the evenings, giving us the opportunity to bounce around the dining hall doing jazz boxes, Monterey turns, and coaster steps.  We’ve been having a great time and trying to figure out the appropriate time and venue in which to show what we’ve learned this week.

hotsnlots photoPrior to that, we had a Sharing session, which was an opportunity for participants in the Teacher Leadership Program to share some of their best practices with the rest of the group.  I led off the evening (which I was pleased to do, being pretty nervous) with my end of term differentiated assessment for my Geometry class.  It was wonderful to be able to share this project with an audience of appreciative peers.  Getting my presentation out of the chris plickway allowed me to focus on the interesting ideas my colleagues had to share, including a demonstration of Plickers, a program to enlist students as teachers, engaging ‘synthesis’ tasks which require multiple problem-solving strategies as well as broad content knowledge, and an engaging marketing/statistics project which resulted in Bacon, Mac and Cheese pizza being conceptualized by 8th grade students and test produced by Pizza Hut. I am in awesome company here.
getting there foldAnd prior to that, Ashli Black, math teacher and folder extraordinaire taught us how to fold fabric in order to geometric designs.   So therapeutic to work with your hands, and so engaging and challenging that it is fabric and math simultaneously!  I think I may have more of a chance finishing this in a timely fashion than a quilt.

What a finished product might look like.

What a finished product might look like.

All of the above happened after 4:30 this afternoon.  That’s how full the days are.

Before 4:30, we had our regular programming – morning math problems, Reflections on Practice, lunch, professional development groups.  And just before lunch, a group of teachers decided to do three minutes of plank for core strengthening.  (This took place in a corner of the dining hall.)  At first, I volunteered to be the timer, but watching their effort, I had to join in – so I only had about 1 and 3/4 minutes of plank.  Hopefully tomorrow I’ll make it for all three.

I should probably be writing about all of the math we’ve been doing (discovering the relationship between complex numbers and Pythagorean triples, and constructing ellipses and hyperbolas), all the reflection and sharing that has been going on (examining feedback and types of listening the teacher can do in the classroom, developing the all important hinge question), and the progress we are making – inch by inch – in our professional development group.  But the hour is late, and I’ve got a bunch of math to do in a few hours!

The Zermatt Resort has footmen.

The Zermatt Resort has footmen.

Day 9: Almost Hump Day!

rainWe were reminded this morning that tomorrow is the halfway point of PCMI!  How can this be?  Time has begun to take on that quality of seeming to speed up when you want to slow it down.  This post may be a little shorter because (a) I don’t want to spend time writing when I should be experiencing and (b) I only want to write what might be meaningful to say.  I also want to point out that anything I write here reflects only my experience at PCMI, and how I am processing all the activities in which I am participating and everything that I am learning.   Just a caveat to my readers.

We were put into new groups in morning problem-solving, which I have just reminded myself is called Developing Mathematics.  At my new table, I met someone who teaches in the same building in which I used to teach in Prospect Heights, Brooklyn (the building houses 4 schools), and the stories this teacher has heard recently about the principal I and most of my colleagues ran away from in 2011 continue to substantiate everything I remember as driving me out of the school.  Luckily, he teaches in the most functional school in the building.  Although hearing about the continued outrageous behavior of this woman is somewhat validating, there are 400 students who are being educated under her inversemisguidance, which is sad and unconscionable on the part of those who supervise her.  The work pace at my new table is quite different – I am sitting with a group of people who appear to work much faster than I do, and with more on-going discussion.  My discomfort is a challenge to me – how can I produce good work and participate in this group in the most meaningful way possible?  And how can this discomfort illuminate my understanding of student behavior and performance when I want them to work together in groups I have selected?  One of the many wonderful features of this conference is the many layers of learning that are presented to us.   The actual problem set is terrific – we are exploring complex numbers as rotations, an idea I have never completely understood until now, and the skill with which the progression of problems has been designed takes our understanding deeper as we work through them.

Meghan’s Eye View of the Crew

Meghan's Eye View of the CrewOur Reflections on Practice session was a little shorter today because of the group photos being taken.  – Nonetheless, it was very fruitful with takeaways large and small.  We shared new ways to collect evidence of student understanding – Plickers, Desmos Teacher Tools, Jeopardy – and how some of those tools provide data from more open-ended questions than others. Plickers does not require technology except for the teacher’s phone, but it is collecting answers to multiple choice questions.  One teacher suggested a tweak on the speed-dating activity using whiteboards (another suggested call the activity Meet and Greet to avoid discomfort with the ‘speed-dating’ title) for sharing solutions to a range of problems, and yet another teacher pointed out that good old fashioned eavesdropping on student conversations about their work could provide meaningful formative assessment as well.  We looked at the activity “Two Truths and a Lie” as applied to mathematics:  students are directed to write two mathematical truths and a lie in any order; the lie must be well written, and in a way “which would challenge your last year’s 2 truthsteacher”.  As we reviewed some examples in our groups, we saw how rich discussion could result from this activity.  We finished the session by learning about a “Hinge point” question: it is a carefully crafted check for understanding midway through a lesson to see if students grasp the central concept, need to have it briefly clarified, or need the teacher to start all over again.  This idea, written about by Dylan Wiliam in his wonderful book, Embedded Formative Assessment, is simple yet powerful.  As teachers, we check for understanding throughout our lesson, but how intentional are we each day when we do this?  By examining this practice, and crafting our hinge questions (and potential responses to the results) while planning our lessons, we can do way more than pay lip service to the idea of regular formative assessment.

The features of good hinge questions as described by Wiliam are:

  • They are concise; students should be able to answer them in under 2 minutes, and teachers need to decide on a response to the results in 30 seconds.
  • The questions can’t be answered correctly for wrong reason; common errors and misconceptions should be visible.
  • Teachers should be able to see responses from every student using some method of data collection.

As Cal Armstrong put it, the goal of the Hinge Point question is a quick read of the classroom, “taking the temperature, not doing an MRI.”

[so much for a briefer post]

I finally feel on track in our professional development group, and managed to craft a solid framework of a draft for our portion of the course.  My partner and I are still working on adding activities to our lesson, but the structure exists – essential questions, learning outcomes, and content.   I am relieved; it felts as if we were floundering for a few days, but I suppose that was part of the process of allowing our ideas to coalesce.

RNDC2-624x841The rest of the day was filled with enrichment: a visit to the gym, a Cross Program Pizza and Problem-Solving session in which the High School Math Camp participants gave us a big run for our money, and a Line Dancing Workshop run by David Nacin, a professor at William Patterson University and participant in the Undergraduate Faculty program here at PCMI.  Who knows – maybe there will be a talent show at the last night in which we can perform our group tango!

And shameless promotion of my super-talented child (or a minute of video entertainment for my readers):

PCMI Day 8: Hooks and Provocative Problem Posing

quilty mountSo week 2 begins.  Today was jam-packed with activities – the regular classes, some enrichment, some special interest grouping, and some hands-on geometric fun – math teachers at play!


Dan loves gummi candy while he does math.

Day 6 of problem-solving aka Heavy Rotation was filled (as usual) with rich problems moving in a different direction: transformations.  There were seriously intriguing problems involving unusual combinations of transformations that resulted in figures that looked different but still had mathematical relationships, and a dilation of a parabola that had simultaneous intuitive and counterintuitive results.  Once again, there is a promise of patterns that will emerge throughout the week; today’s set provided a great hook.  The group I am currently working with (or was working with until the end of today’s session) had a good work symbiosis.  We seemed to complement each other well, working solo and then sharing, always respectful of each other’s work pace and need to discover solutions on our own.  I hope my next group works as smoothly.

In Reflections on Practice, we switched rooms, tables, and mixed with other people, but ourthsthe routine of working problems, sharing strategies in small groups, and then with the whole room seems familiar and flows easily.  Today we examined a range of student solutions to a fraction problem, in which they needed to identify 1/4 of a compound shape, and then modeled an activity designed surface both evidence of understanding and misconceptions, in which students were given solutions and asked to design problems to accompany them.  The activity – entitled Jeopardy was a well-designed bit of work; it included problems on elementary, Algebra 1, and Algebra 2 levels, and was a much richer task than the usual ‘Jeopardy’ that is frequently used for exam review in classrooms.

The afternoon working group session finally felt (to me) like concrete progress was being made.  We split into two groups, and each had the opportunity to present the overall plan for the online course to a different professional development group; the act of having to explain our structure and strategy was enlightening in itself.  The feedback we received was helpful and clarifying, and pointed us toward a wealth of new resources, including Henry Picciotto’s website, The Math Ed Page.  When the Online Geometry Course group reunited and shared ourJen feedback, the path we need to take to solidify the proposed first three days of the course finally became clear to me.  It was helpful to discuss the strategy for the first of the four days, the portion of the course for which my partner and I are responsible; we had been going back and forth regarding the level of familiarity with the transformations content we should assume on the part of the participants (my partner is a sixth grade teacher and I teach high school), and some outside perspective lent clarity to that as well.

The rest of the day included optional activities, starting with attendance at a Cross-Program lecture on problem posing by Judah Schwartz; he talked about the power of visual representations, and using them in unexpected ways to explore problems.  Schwartz says the essence of teaching is posing provocative and engaging next questions at the proper moment – such a succinct and articulate phrase, and such a huge challenge.  His demonstrations opened a little bit of a door in that direction.  Following the lecture, people from the Teacher Leadership Program met in small ‘special interest’ groups.  I gravitated MPj03988190000[1]toward the group for ‘At Risk Students,’ hoping to share stories and resources for dealing with my most challenging kids.  What I found instead was the opportunity to participate in a unique collaboration – two teachers from Monument Valley High School – a school on the Navajo reservation in Kayenta, Arizona, will be visiting PCMI on Friday in the hopes of gaining some resources and support for teaching math to their highest need students.  These teachers had shared a list of standards for which they wanted resources, but as we began to discuss how we would assist them, larger questions emerged – for example, what resources had they already tried?  What cultural issues did we need to be aware of?  Finally – how could we help them without hearing them speak about their students and their need first?  We agreed to collect ideas in a Google Doc, but not to share anything until we had the opportunity to speak to them directly and hear their story.  I am looking forward to meeting these math teachers, who are willing to travel far to meet with us in order to find solutions for their students.  I do not feel like any kind of an expert, but I know that having someone listen and really hear you, and then make suggestions, can be enormously beneficial and supportive.

phiolaThe evening was just plain old hands-on fun (at least for math teachers and students).  Carol Hattan, one of the directors of the program, sponsored a Math Building Party – basically Origami Fun Time.  We began to create modular structures – first cubes and then icosahedra constructed of similar units.   As she instructed uslotsa foldingin the folding of the basic unit, Carol pointed out how much mathematical language could be used with students in completing this soothing and satisfying activity.  And as we chose our colors and folded our papers, we shared stories of school and home, deepening the bonds that have been forming since the program began.   Despite my quilting, folding paper is not something that comes easily to me, so I am very proud of my progress, and am looking forward to completing my icosahedron next week.  Of course, I have to figure out how to get it home….



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

yodelay[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.sculpture

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, CJHbT68UcAAI2PqJennifer 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?

graphsWe 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. cal on a chairWhen 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.

geometry groupOur 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.

exceptionsThe 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.printer

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 cardsmost 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.

better bannerOn 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. CJFY3_UUsAUQkO7on the moveThe Park City parade is a bit eccentric and very enthusiastic. Among the floats and tutu1tutu2participants 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 bandMarshall 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 hedgewas 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 theamy 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.

blurry worksAfter 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.gals in stars

Day 4 – Regrouping

holly's quiltToday, after 4 whole days, things are beginning to feel comfortable and familiar.  Even though we switched groups during our morning problem-solving session, our routine of working in pairs and trios, and then solo resumed quickly.  Geometry was always my first love in math (hence my quilting), so the growing connections among the problem sets this week are deeply satisfying.  When Bowen intoned “Take a break!” at the midpoint [ouch!], I wasn’t ready to stop working, nor again when it was time to transition to our next activity.  I need to think about the takeaway from this feeling – is it possible to recreate this drive to explore in my classroom, and for more students than just my uber math geeks?

During lunch today, I had a conversation with several teachers who were either National Board Certified, or working towards that through their Math for America fellowships.  Obtaining this certification is a large undertaking with many facets, not the least of which is a whole class video, something of which many teachers are leery.   Today’s Reflecting on Practice session was a perfect example of why this is so.  Although neither of the other classroom videos we watched depicted a perfect lesson, today we witnessed a host of missed opportunities in a TIMSS video of an eighth grade math class from 1999.  It’s so easy to spot problems from the safe position of fountain boybeing an observer.  But even as I ticked off the moments in the video when I saw areas in need of improvement, I knew that I make just as many grievous errors in my own classroom, sometimes in the name of expediency or pacing or classroom management.   We worked on plans to remedy the shortcomings in the lesson we saw, and Cal Armstrong thoughtfully reminded us that in spite of any criticisms we might have, the teacher in the video opened her classroom for the entire world to see and learn from.  A word to the wise: the video is 16 years old; what goes on the internet stays on the internet.

Our afternoon working group has begun to assume a productive structure after exploring some big ideas about transformations; my partner and I are outlining the first day of the proposed online course, in which the definition of rigid motions is clarified and teachers are provided with some exploratory activities for themselves and their classrooms.  Every step in our planning requires conversation, debate, pushing back and forth to refine and clarify the experience we envision our lesson to take.  Two hours of work flies by pretty quickly, and each pair in our team seems to be going through the same process.  I know we won’t have a completely finished product at the end of PCMI, but I feel like we will have a solid framework of high quality.

evelynIn the later afternoon, I attended the Cross Program activity (open to the undergrads, graduate students, Research program participants and the teachers), a talk by Evelyn Lamb, a professor at the University of Utah, on the value of the online math community.  Evelyn is an unassuming and entertaining speaker, and she spoke with insight and humor.  Her presentation was organized into the purposes of Online Math Communication – talking to ourselves [reflective blogging, for example] and talking to others [chatting on twitter, reading and commenting on blogs].  She broke this second category down into further subdivisions: talking to other math researchers and educators, and then talking with people who either tromp l'oeilwondered about the life of a ‘math person’, or wanted to relate their own personal tale of math horror.  She told some stories about unlikely connections she made through her blogging and tweeting, and shared some personal truisms and myths of the online math experience, two of which I am paraphrasing here (as well as I remember them):

  • Myth all bloggers need to remember: If you write a blog post, people will read the whole thing.  Remember – readers are not your students, and have no obligation to do so!
  • Myth of writing posts: “Any sacrifice of accuracy, rigor or generality is unacceptable.”   This is a good thing to remember [Wendy…] for those of us who agonize over every sentence as if it were our graduate Statement of Purpose.

Here’s my personal favorite of Evelyn’s Big Ideas about Blogging:  Why should the math internet be different from any other internet?  Use cats liberally to please and entice readers.323 - cat experiment exponential ilolled math whatOne final note related to Evelyn Lamb’s talk – the Ballroom had some prime examples of Zermatt decor, such as a trompe l’oeil tapestry, and this Merry Band of stained glass windows, pointed out to me by the observant Ashli Black.merry band

The day finished with the final touches of 4th of July parade preparation, complete with tangrams, pun posters and all manner of Zome creations.  Who is this masked man in the patriotic Zome tutu?  You’ll have to attend the parade on Saturday to find out!masked man