My experience at Phillips Exeter Academy

IMG_3595

To build upon my experiences this summer at the Exeter Mathematics Institute and to improve the newfound problem-based classroom, yesterday I paid a visit to the renowned Phillips Exeter Academy in Exeter, New Hampshire.

I observed six mathematics classrooms, had a private meeting with some students and had lunch with a few Exeter teachers. In between all of that, I also had some time to roam freely about the leafy campus, spending a good chunk of time at their library. I was on campus from 8am to 5pm.

I tend to process experiences pretty slowly. I say that because I know that I won’t be able to fully synthesize this visit for at least a few days — especially after I’m back in my own classroom. Nonetheless, I’m going to get out my immediate reactions with what else? Isolated bullet points whose main ideas are scattered and disorganized. Clearly, I still blog for myself.

  • This place is very old. Some of the classrooms looked like they hadn’t been renovated since the 1800’s (see photo above). The look and feel aren’t for everyone, but I found it charming.
  • The teachers were so welcoming. Each one mentioned my presence in the room and had every student introduce themselves. I shared the purpose of my visit and thanked them all for allowing me to share their space for the day. I got the vibe that they are accustomed to having visitors almost every day, but I still loved their transparency. One of the teachers valiantly tried all period to get my last name right until the moment I walked out of his classroom. It was a small thing, but I really appreciated that.
  • The students were highly motivated. I fully expected this. Maybe what I didn’t expect was how helpful and respectful they were. I got lost several times while on campus and each time I was politely helped and redirected. They also gave me some student-driven advice on how to encourage buy-in from my own students in this type of learning environment.
  • Most all of the students I spoke with came from a traditional learning setting and they all enthusiastically preferred the problem-based, discussion-based environment that Exeter has pioneered. Their families are also paying upwards of $50K a year for tuition, so yeah, there’s that.
  • In terms of instruction, I saw the same thing in every class. The period opens up with kids spending about 10 minutes putting up the homework problems (~7) on the boards around the room. For the rest of the period, the students present their own (or someone else’s) work and/or solution and the class discusses and draws conclusions. The onus was put on the students to push the lesson forward. This confirmed what I’m doing in my own classroom.
  • Every teacher spent a good amount of time sitting at the Harkness table with the students. I don’t have a Harkness table nor would I want one (give me couches and coffee tables instead), but actually sitting amongst the students during class has been a game changer for me.
  • With that said, just like in any class, there was some variation to how teachers enacted this structure. Some teachers assigned students to certain problems when they walked in by having their names on the board. In others, students openly chose their own problems. In some classrooms, students could not present their own work; they had to present someone else’s.
  • In a couple of the classes I visited, when the class got stuck, it felt like the teachers wanted to lecture — and sometimes they did…for like 15 minutes. Maybe it shouldn’t have, but this was surprising given the completely student-centric classroom that Exeter pushes.
  • This made me think about the problem sets. Every Exeter mathematics teacher uses them and they all did while I was there. If the need for direct instruction was as evident as I witnessed, are the problems scaffolded enough? How much flexibility do the teachers have when it comes to class time? Must it always be problems, problems, and more problems? Or can they filter in occasional days of enrichment based on the concepts learned from the problems?
  • Desmos was widely used in the class discussions around the problems. Most all of the classrooms had a slick setup with an Apple TV and Airplay where students could easily toggle between whose laptop/tablet screen was displaying on the projector. Other than that, there was no sign of using Desmos Activity Builder or any other structure to help maximize its obvious benefit. Maybe a problem requiring Activity Builder to answer it?
  • A few teachers used doc cams for student work. Nice.
  • I constantly saw kids taking photos of the boardwork with their phones. Since my kids can’t use their phones, this affirms why I now have a class iPad and a volunteer that snaps photos of the boardwork and emails it to everyone at the end of each class.
  • I only spent one day on campus, but if I’m honest, I felt a gulf between the teachers and students in the classrooms I visited. The focus at any given time (even at the onset of the period) was overwhelmingly on the standardized problems and less on the individual students in the classroom. Shouldn’t the problems be supplemented with other materials/resources for different classes based on the needs of the kids? Again, my sample size is incredibly small, so I may be way off.
  • From what I saw around campus, Exeter seems to be in touch with the revolution that is happening in our country right now around race, gender, sexual orientation, and other social issues. The library was exceptional on this front. At the same time, students of color were disappointingly scarce both on campus and in the classes I visited.

 

bp

The need for estimation and the estimation wall

For the last few months, I’ve really been buying into the power of estimation. It has changed how I teach in a dramatic way. Let me set the stage.

In December, I gave my students this problem on a checkpoint:

screen-shot-2016-12-24-at-9-54-32-pm

I wish I would have taken photos of some of their work. A few gave answers like $340. Others were in the ballpark of $34,000. To say I was disappointed is an understatement.

But to make a long story short, too many of my students made absolutely no sense of the problem. Sure, they knew that a given formula needed was to be used, but in terms of logical answers goes, they were lost. Key skills like using context clues and relevant information, compare/contrasting, drawing from prior experience, and – most notably – number sense, were completely absent in their responses.

Upon handing back their papers the next day, I did everything but rip the SmartBoard of the wall. They felt my disappointment in their responses. I made sure they did. The most disappointing part was the fact that I’ve seen this sort illogic amongst my students for years and have never strategically addressed it…until now. One student even boldly asked, how do you expect us to think logically if we don’t practice doing it? She was SO RIGHT. I was expecting them to do something I hadn’t outwardly emphasized or taught. More on this situation here.

Around the same time, I attended a workshop led by Dan Meyer and remember him asking for estimates for the answer to a problem. It wasn’t his goal for us to better understand the usefulness of estimation, but somehow that was a big takeaway for me. I think it had much to do with the context Dan created and how worthwhile the too low, too high, and just right estimates were to help us make sense of the problem.

Ever since, I’ve been opening class with an estimation challenge at least three times a week . Estimation 180 has been my go-to. The kids love it. Besides addressing the issues I described above, I’ve been intrigued by how the estimation process itself leads to a variety of other conversations related to the context.

For example, this estimation on the capacity of the soda can prompted a meaningful discussion around why the soda can contains more than the stated 12 fl oz that’s printed on the outside of the can.

7886532_orig

What’s the capacity of the can (oz or ml)?

Could it be manufacturing error? Or maybe the carbonation bubbles are causing the measured volume to be greater than expected? Or better yet, maybe Coke is out to get us all by covertly filling our cans with even more sugar or, in this case, artificial sweeteners? (Conspiracy theory anyone?) These sorts of tangents abound whenever I post an estimation challenge.

Anyhow, take all of my in-class success with estimation coupled with my knowledge of Jonathon Claydon’s estimation wall and I decided create a space in the hallway outside of my classroom to encourage the entire school to dive in. Hence, the estimation wall (first edition):

IMG_1115

The wall consists of several estimation challenges and their associated question, each taped to piece of construction paper. Underneath the construction paper is the answer.

Soon after I completed the wall, here’s what could be seen. Woohoo!

IMG_1226

The creation of the estimation wall also served a different, much bigger purpose. It is much bigger than myself and it revolves around school culture. I realized pretty quickly this year that beyond high-stakes exams and AP courses, my school has no real mathematical identity. There are no mathematical initiatives, no clubs, no field trips, no electives. Though it has mathematics in its title and its one of its founding principles, mathematics is not publicly championed at my school for its creativity, wonder, beauty, and usefulness.

I’m on a mission to change that. The sort of cultural shift I’m envisioning at my school will take time, but we’re a small school…so I’m determined to make a difference.

bp