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

It can’t only be Day 3! Patterns and Park City

archesI’m writing this for myself as much as for you, dear readers, because each day is filled to the brim with mathematical, pedagogical and interpersonal stimuli.  I am certain that when I return to Brooklyn, I will not remember half of what seems so clear and immediate today.  As the days go by (all three of them), fewer people show up early to breakfast.  I love coming in and sitting with someone different at each meal.  Today the conversation ranged from state assessments to finding thrift stores in Park City (I found some kindred spirits ready to go on the hunt with me).  loosey

pencil caseDuring today’s morning math session, I felt that patterns that have been spiraling the problem sets each day begin to take shape in my mind, and had a burst of insight.  When we discussed some examples as a whole group, I saw that there were more mathematical dances going on in the work than I had currently grasped.  I think I need to take some other time out of the day to continue working on these sets, but choosing what NOT to do in order to find that space in the schedule?   Hard choices, but lucky ones to have to make.  Tomorrow we switch groups, and the work habit adjustment will begin again.  I am discovering that I like to work through things by myself, I think.  It is challenging to work on a math problem, develop insight into it, and formulate a solution at the same pace as anyone else, and the admonishment ‘not to teach our colleagues’ in the norms we were given proves difficult to follow.  I wonder if there will be a conversation about this at some point during these morning sessions.

explicit recursiveInstead of watching a video of students solving problems in our Reflection on Practice session, today WE were the students, and worked first solo and then in pairs on several problems that appear regularly in middle and high school classes.  I unwittingly provided a sample of a typical student misconception in the first problem (it involved working backwards using fractions and a bag of marbles, a word problem subject of frequent choice), and got a completely wrong solution, much to my chagrin.  As a group we explored different types of solutions – mostly correct ones – and discussed the conflict between how the Common Core standards view fractions (along a number line) and the area or ribbon models which can be effectively used to create visual representations that are not pizzas.   Our task for pair work was to develop both explicit and recursive sequences for the Handshake Pascal et alProblem, and then to choose from among the various solutions three to present to a class (and to justify those choices) to further a particular lesson goal.   Tomorrow we are moving on to formative assessment (I should be doing my homework reading right now…).  I’m looking forward to really digging in to that conversation.

enrouteThere was no formal programming this afternoon, and buses ran back and forth to Park City.  As lovely as the Zermatt Resort is, it was equally lovely to move off the grounds of this Tyrolean Wonderland (with its varied amenities, including goats and footmen) into the semi-real world of Park City. IMG_5353 My colleagues and I roamed the center of town and made our contributions to the local economy, and enjoyed speaking to the shopkeepers, many of whom were transplanted from elsewhere but did not live in town due to the high real estate values.   Main Street in Park City is a super clean version of a Western town – a quaint and upscale commercial strip with unusual boutiques and art galleries.  My friend Irene almost scalded herself wood beartrying to embrace this fellow in the 85˚ heat, but found someone a bit more accessible in one of the shops.

wool balsThe Kimball Art Center was a highlight of my day; it is a cultural center which runs, among other things, art classes for children and adults, exhibits of photography, mixed media and other art, an annual art festival and other events.   The current exhibitions included a series of reproduction WPA-commissioned posters for the National Park Service and a quilt and felted wool exhibit by Faith Hagenhofer, an quiltartist who explores issues of culture and contested land, and uses wool from her own sheep in her art work.

On the bus back to Midway, our bus driver advised us to keep our eyes open as we drove back; he claimed he had seen a lot of wildlife on the move that evening.  And sure enough, we were treated to an elk.  We shared stories of our day in Park City, and in doing so, shared even more of ourselves, moving from tales of the classroom to tales of our lives.  What a rich, rich day it was.

More de

More decor!

PCMI Day 2 – Transformations, Standards and Groceries

Raised by a cup of coffee

Raised by a cup of coffee

What an auspicious beginning to my day with this cup of coffee!

Another beautiful day in the mountains began with sharing over breakfast – swapping school stories (good, bad and humorous) with teachers from different cities, and different types of schools.  The underlying commonality we share includes being committed to improving our practice regardless of our length of service, and giving our students, thus, a better experience in the classroom.  It is clear from talking to my colleagues that our desire to help our students goes beyond their understanding of mathematics, although this is the key we use.clouds

Our morning problem-solving session felt more comfortable today; the sequence of the daily questions not only builds on ideas in each set, but also hearkens back to emerging patterns from that of yesterday.  I was again reminded that the personal adjustment period in our experience mirrors the same phenomenon in our classrooms.  I discovered that another teacher at my table felt a discomfort similar to mine with respect to the different speeds and work habits of everyone at the table, and knowing that, felt more comfortable.  How often have I told my students not to be afraid to ask questions because if they have a question, at least one other student, and probably more, has the same one.Screen Shot 2015-06-30 at 8.51.57 AM

We ‘observed’ a Calculus class in today’s Reflection on Practice, examining student response, participation, and body language as the teacher led them through a problem solution.   We sympathized with the silent girl in the video who we all felt was lost in the exercise but clearly didn’t feel safe or comfortable enough to voice any of her confusion or ask any questions.  We collectively cringed when the teacher asked, “does everyone understand?”, knowing full well that a student who didn’t understand was unlikely to admit that in a room full of peers who apparently did.  As we worked at our tables to craft questions that would probe and push student understanding, I thought how much easier it was to do this exercise with another colleague at a workshop but perhaps not quite so simple on my feet in the classroom.

sconceAlthough the specific objectives are a little unclear in my afternoon group – creating an online Geometry course for teachers, my partner Irene and I had a blast exploring as many possibilities as we could in reflecting a line segment, so much so that we found it difficult to stop when we were told to take a break.   Irene is a 6th grade teacher, and I love how her style, which is well-suited to the explorations her students need to make in learning this content for the first time, illuminates my own.  It forces me to be more methodical in my approach, which I can see is necessary for my own high school students, many of whom may not recall the content well from middle school or who may not have mastered it at that time.

imgresThe special treat of the afternoon was a session with Bill McCallum, one of the authors of the Common Core State Standards in mathematics.  Bill walked us through the re-design of the Illustrative Mathematics website, and tried to answer our questions about the implementation of the Common Core standards and curricular resources.  He is an eloquent and engaging speaker, although the theme that the standards are not curriculum seemed to emerge after every question or two.  From a teacher’s perspective (if I may be so bold to speak for some of my colleagues as well as myself), the implementation of the new standards, especially at the high school level, is hampered by a lack of choice in curricular resources that are fully aligned and easily usable. [Note: I use the word ‘easily’ because while clearly has fully developed rigorous curriculum for Algebra 1 through PreCalculus, many teachers find the organization of the materials challenging, and the scope of each lesson ambitious for most classrooms.]  The frustrations that were surfaced through this session, however, serve as action points for teachers seeking solutions for their classrooms and students.  We were exhorted by the inspiring Gail Burrill to advocate for change, particularly around creating support for students who begin to fall behind in elementary school.    I left this optional session feeling ready to tilt at a few windmills.

forced entryThe day finished with something New Yorkers love to do – shop in a supermarket outside of New York City!  The Riddley’s in Midway was not only spacious and filled with all manner of comestibles not frequently seen in my local grocery store, but also had some 4th of July treats.  Interestingly, everyone we met knew we were with “the math group.”  Huh!FullSizeRender (1)

 twinkies  jawlipops

Day 1 of PCMI 2015

11707937_10205349155822021_6184387136337970008_oA day that begins with this view on the way to breakfast is full of promise.  And my first day at PCMI was full of a lot of math and a lot of collegiality.   I’m still trying to sort through it all before the next one begins.  It’s late, and this is unedited.  I’m trying to document this whole experience for myself, so I apologize for any typos or rambling sentences.  I always try to make my posts ‘sing’ a bit, but I’m don’t think I’ve hit that mark.

The morning session – “Some Applications of Geometric Thinking” – had participants working on some interesting problems, looking for patterns in simple problems which were clues for more challenging questions.  I love the way the problems were scaffolded.  It was interesting to note the different work habits and paces of my colleagues at the table, and I encountered my own frustration at having some ideas and discoveries shared before I was able to work towards them.  An important part of this process is not only to do math, I think, but also to simulate a problem-solving classroom environment, so this frustration provides an opportunity to gain some insight into the student group work experience, as well as my own ability to counter it in myself.  I’m looking forward to digging into it again tomorrow.picket

The second half of the morning was spent on “Reflections on Practice”, the theme of which is Eliciting Evidence of Student Thinking.    We analyzed a video-taped rich middle school classroom activity in which students explored how changes in the shape of a quadrilateral affected its area, similar to a problem we had explored in the morning.   Student thinking at several levels was apparent throughout the video, and we discussed and shared this evidence in both small groups and as a whole class.  We examined some written student work, noting the difference in our own styles of analysis.  I’m looking forward to seeing where this conversation goes.

In the afternoon, we were broken into working groups – I have been assigned to a small group that has been tasked with framing an online Geometry course for teachers to address the some of the content shift in the Geometry Common Core standards – to alleviate some teacher anxiety, address some possible misconceptions or murky areas, and provide ideas for weaving these ideas into the classroom.  Today we played explored transformations with patty paper – trying to stay away from coordinates – and examined how transformations could be used to prove theorems.   The challenge of reshaping proof as it is taught in high school to include transformations as well as forms other than two columns is another big issue for many teachers, and a topic we are going to continue to address.

lotsa white zomesThe rest of the day was devoted to self-replenishment and fun.  After a rousing session of creating stellated figures out of Zomes for the PCMI float in the Park City 4th of July parade, I managed to get to the gym at this lovely resort and take a dunk in the pool (although at 95+ degrees all day, the water is more like a warm bath).   The opening dinner was followed by even more bonding over Zome

There are so many nuances that I am processing – the wide range of attendants at this huge math event which from undergraduate math students barely older than my own, graduate students and math professors, the teachers from all over the country who readily share their stories and ideas, and the warm and welcoming organizers of this event who make even the newcomers like me feel as if they have been attending for years.  But I have 3 weeks to make sense of this wonderful experience, so I’ll stop here for now.


Haven’t even checked in yet!


So I got on the plane, took my happy pills, drank some wine, and just by putting one foot in front of the other, arrived in Salt Lake City.  Being late was actually a hidden bonus – the rooms are not ready at the resort, and the folks who came on the 7 am flight have been sitting in the hotel lobby since noon.

The Zermatt Resort in Midway, which is all things Tyrolean, is approximately an hour away from Salt Lake City.  I rode over here in a van filled with undergrad and graduate math students, who were interested in hearing how a high school teacher keeps her students airportengaged in an age of cell phone ubiquity.  I shared my strategies for using cell phones for instructional purposes (which, truth be told, only work some of the time), and had the pleasure of turning them on to Desmos and Kahoots.

tyrolOnce we arrived at the resort, I immediately began chatting with other teachers – a surprising number from New York – who were waiting for their rooms. (The front desk keeps giving away banana bread in lieu of room keys.) Conversation was easy and interesting – we all teach math, we’re all engaged in our teaching of math, and motivated to share and improve the quality of the experience we give our students.    The math students, on the other hand, are busy doing math already – reading papers, sketching out problems and proofs.  It’s a major nerdfest here in the lobby of the resort, and I’m loving it.


PCMI Bound

Barely decompressed from the end of a harrowing school year, I am off to Utah for PCMI, the mega Math Teacher conference.  I’ve been fortunate to be accepted with a scholarship after my second go round at applying, and thus am waiting at the airport for my rebooked flight to Salt Lake City.  Why rebooked?  A series of unfortunate events, as they say – a wrong turn on the way to airport, almost putting me on the Verazzano Bridge rather than the Belt Parkway, which made me miss baggage check, and a double scrutiny by security – those graphing calculators, you know – caused me to miss my flight, the first I have taken in many years.  Yes, dear readers, I am a flying phobe.  I had picked the earliest direct flight possible to avoid having an expanse of time at the airport during which my anxiety could begin to brew.

A kind agent rebooked me on a flight not too far in the future, and waived the rebooking fee as I somewhat hysterically told her my tale of woe at security.  My husband returned to the airport with my large bag (he was going to somehow figure out how to ship it to me), which as it turned out was overweight.  We tried removing things, but worn out by the mornings events, I opted to shove everything in to the bag and pay the fee.

So I have re-checked in to my flight, bag all tagged and on the vast conveyor which will hopefully put it on the right plan, using my complimentary 30 minutes of wi-fi to write my first post in 2 months.  I purchased a book of Sudoku which are too difficult at the moment, and I am debating the timing of using my happy pills so I can be preferably asleep for the bulk of the flight.

Menard UND Transcript copyIt’s been a year in which I tried to do too much – way too much – and achieved a bunch of it at the expense of my free time and personal life.  I completed an online Multivariable Calculus class, earning me enough higher math credits to apply to the Math for America Master Teacher program.  I met several financial goals required to maintain my home [long non-bloggy story] through a lot of private tutoring and per session work for the Department of Education.  I improved the Regents performance of my Algebra 2 students – a goal which was important to my school, and to my students’ transcripts.  And my Geometry Fundamentals class – all three sections of it – completed the Mondo Choice Board final, further refined from last year’s launch.  Oh – and last but certainly not least, I have made my attendance at PCMI happen.

As I mentioned, this all came at the cost of my personal life, the reparation of which will take time, but the summer is long (although never quite long enough…).  I’ve learned a lot this year about what works and what doesn’t, what I can do and what I can’t, and I’m ready, for the moment, to set all the what ifs and ‘what I should be doing’ thoughts, and immerse myself in what I am sure will be an unforgettable personal and professional experience.

I just have to get on the damn plane.


I only spent a few days getting to know @sophgermain at #TMC13, but finding a kindred spirit who worked at Hogwarts-in-Troy prompted me to join her #shutupandduckface Instagram event last March and this, my discomfort with selfies notwithstanding.  So when I read her blog post Things that scare me, I somehow began typing this, even though it is Sunday evening and my work is not finished.  I used to be afraid – truly anxious – of so many things.  I still am, but I have faced a lot of scary stuff, and realize the fear is a construct that I have some control over.  But there’s still a list, for sure.  So here I go.

  1. I am afraid I’ll never be a really good teacher.  No matter how hard I work, how many resources I hunt down, how many blogs I read and ideas I try to incorporate into my practice, I frequently feel like I am not doing enough, reaching enough students, eliciting enough critical thinking, or raising student achievement.
  2. I am afraid I will run out of time and have worked too hard. I love my job, and I love math.  But I also love quilting, and spending time with friends, and reading, and movies, and exercising (well, I love its effects, anyway).  But I spend way too much time on those first two – work and math – and I know very well that our time is not infinite.
  3. I am afraid of the world my children are inheriting. This world is a scary place.  Nothing gives me greater joy than their talent and success; the flip side of that is a fear of the problems they will face.
  4. I am afraid of severe weather.  I think this is a result of watching This Wizard of Oz as a small child.  No shit.
  5. Speaking of running out of time…I am afraid my cancer will recur.  I have wonderful health care, and an oncologist I might run away with some day.  But anyone who has ever had cancer lives with this fear, and some of us have more regular reminders of it than others.  The good news is that the fear keeps me honest, and forces me to confront things I might otherwise avoid if I was under the illusion that I had time to spare.

Thanks, Annie – love your posts, and love that you get me to try things.