I have fewer desks than students. On purpose.

There is a growing number of shared public spaces that are popping up all over the world.

 

Cars, bikes, motorcycles, and pedestrians are forced to govern their own behavior. They have to make eye contact and acknowledge each other’s presence. There’s an inherent faith that folks will slow down and pay attention to each other. I bet they even greet one another way more than they would otherwise. It all makes for a more trusting and human experience. And, from what I’ve read, the number of injuries in these spaces has even decreased significantly.

Why can’t we operate on the same principle in our classrooms? Can we somehow use shared space in our classrooms to create a more personal and humanistic learning environment? Call me idealistic, but I’d like to think so.

That’s why last week I asked the custodian at my school to remove several desks from my classroom. I wanted to ensure that I had fewer desks than students. I didn’t want each student to have their own desk. Instead, because I have the room set up in groups, I have intentionally removed 1-2 desks from each group — but left the seats. The result is 6 groups of 4 desks with 5-6 chairs each. Here’s an example of one group:

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It’s a small change (unlike removing all street signs from a busy intersection), but the idea is that in order to navigate their group’s space, students must purposely engage with one another on a regular basis. It creates a more communal learning environment and helps them take ownership of their workspace (and our classroom). It can get messy because they rub elbows, get in each other’s way, and have to constantly negotiate how they should use the space. But in the end, I 100% welcome these inconveniences. (Honestly, living with the ungodly congestion of NYC, my kids probably don’t even realize these things.) They create a greater degree of collective energy each day. Ultimately, my hope is that they will be more mindful of each other, to be more present.

A side note: This line of thinking is also reflected in the large whiteboards that I began using last year to de-front the classroom. These are communal spaces around the walls of the room that students used to publically display their thinking at any time — unlike having one greedy board at the front of the classroom that screams for attention (and a lack of optimal engagement).

In some ways, I see desks as imposing segregation on my students (and me). Despite being organized into groups, desks still create distinct social spaces for students to think individually. There’s a clear end to my space and a start to yours. Can this subconsciously establish a greater sense of independence from others in the classroom? Tables would probably be the best physical solution for helping create a more personal, humanistic classroom, but I doubt that I’ll ever convince my principal to get me those.

 

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I have a senior in my fifth period algebra 2 class

I have a senior in my fifth period algebra 2 class who, after failing 3 of the 4 marking periods, has lost all hope in earning credit for the class or passing the Regents exam. Neither is going to affect whether he graduates or not, so over the last few months there has been a slow, gradual decline in his effort and overall concern for our class. It’s come to the point where he comes to class and simply puts his head down for the majority of the period.

I’m horrible and very awkward at outwardly motivating students, but I’ve tried by encouraging him to take pride in his work and preaching the importance of finishing strong. During these one-on-one conversations, he smiles, nods, and looks right through me. He doesn’t care and is very open about this fact.

I’ve also called home. Nothing. I’ve asked other teachers in my school for advice how to reach him. However good natured, they laughed at me. I’ve made it personal by asking him for a copy of his college admissions essay, reading it, and being genuinely blown away. This yielded insight into who he was and a personal connection between the two of us, but there was still no change in his attitude.

So this is exactly the point in this blog post where I’d love to start transitioning into a description of something awesome I did to get through to him. That magic trick that, according to mainstream media and most politicians, all teachers are expected to perform with every student. Well, I haven’t been able to do that. He’s still very much uninterested in our class and I’ve done nothing to change this.

There are lots of issues surrounding his struggles, but I can’t help but look in the mirror. In many ways, I’ve failed him. I could’ve poured more energy into him and his situation earlier and more often.

I’m not proud of it, but there were days when his head was down and I looked the other way, when I made a conscious decision to focus on the other 23 students who were alert and attempting to understand (many half-heartedly) the mathematics at hand. In those moments, I mindfully refused to address his lack of motivation and interest. The truth is, I was at a loss. I just didn’t know what to do. I felt handcuffed. I was frustrated at him, at me, at the situation. I still am.

And I’m not tap, tap, tapping these thoughts out on my phone’s tiny screen on airplane while chaperoning a trip over spring break as a cry for help or to earn sympathy. At least I don’t think so. This just seems like a deed that needs to be done, for myself. It’s to hold myself accountable to never give up on this kid – or any kid like him.

Or it could be because I’m 33,000 feet above the Atlantic Ocean surrounded by 24 teenagers with nothing better to do than think about my students.

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Why isn’t there more public-private collaboration?

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Definitively, I can’t say much about the success of my problem-based learning this year. Mainly because I’m still trying to figure out what the heck I’m doing.

Because of my ineptitude with the PBL structure I’ve adopted, naturally, I am seeking out others that are doing a better job than me with it.

Enter: private schools.

Or are they called independent schools? Or prep schools? Boarding schools anyone? I’m  confused on what to call them — I think it depends on the individual school, though. Either way, in my brief experiences with problem-based learning, it seems like these schools tend to use problem-based learning (or at least how I understand it) more than their public school counterparts. It helps that they usually have much smaller classes.

For this reason, I’ve been exposed to private schools in ways that I have never been before. This exposure has inspired me to get out of my classroom.

In October, I made the hike to New Hampshire and visited Phillips Exeter Academy. Then last week I squeaked out a visit to Horace Mann. The takeaways from each were awesome and unique. But as a public school teacher planning and making these visits all on my own, I couldn’t help but think about the generally nonexistent collaboration that exists between public and private school teachers. Maybe I live in a bubble, but in all my years of teaching (besides my recent experiences), I’ve never actually collaborated locally with a private school math teacher.

I do have a tendency to isolate myself, so I’ll own it. At the same time, there have never been deliberate, organized attempts by my bosses (or my bosses’ bosses) to help me learn from the private sector (or have them learn from me). And that’s a shame because there’s so much to learn from each other. Besides, I don’t care what anyone says, the public and private worlds aren’t really all that different. Math is math. Kids are kids.

Through all my complaining, I don’t want to discount online communities like MTBoS that help teachers from every school type learn from one another. Through it, I’ve connected with folks spearheading great PBL work like Carmel Schettino, Joseph Mellor, and Johnothon Sauer — all of whom I’m indebted to for helping me create and iterate my PBL classroom. That said, all of our interactions have been online.

There’s an annual Twitter Math Camp (free) in the summer that I’ve attended twice. There’s also NCTM conferences (not free) that I’ve never attended. NCTM may be regional, but neither one of these is truly local. The MfA Summer Think that helped plan last year is only for MfA public school teachers.

The closest thing locally I can think of that allows public-private collaboration is Twitter Math Camp NYC, which is local, free, and open to all. I have been once. But even TMCNYC isn’t deliberate about connecting public-private teachers. If it happens at the conference, it’ll be coincidental.

I don’t think things will change much. Most teachers, like me, live in our worlds — public or private. With the day-to-day grind that teaching requires, it is really hard to physically get out of our own classrooms.

But I’m not going to give up. I can dream. It’s fun visiting private schools and classrooms, and enlightening! And to speak to the individual, there are folks like Sam Shah and Michael Pershan who both teach at private schools (I think) and who are two of most thoughtful teachers I know. Best yet, they both teach here in NYC. I wish I could visit their classrooms. Maybe I should ask?

 

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My experience at Phillips Exeter Academy

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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.

 

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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:

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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.

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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):

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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!

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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.

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