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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The case for disorder in the classroom

I’m going to go ahead and say it.

I think there needs to be more disorder in our classrooms.

By disorder, I don’t mean kids throwing chairs and running amok. Instead, I’m thinking about those instances when teachers give students largely unstructured time and space to land on their own ways of thinking the content. Those instances when the teacher, by design, fails to impose a rigid learning structure on student learning.

This is not a popular idea. It goes against pretty much everything teachers are told must happen in their classrooms every minute of every day. We must have structures, routines, and systems. We need tidiness. Students need to learn concepts linearly, there must be an obvious beginning, middle, and end to everything. It is our job to provide managed, predictable spaces for our students to work together and exchange ideas. For if we don’t do these things, our students’ will be distracted. They won’t learn. Unless its art, a mess is not welcome in the classroom.

Now I’m not saying that there’s no value in structured pedagogy. There is. I have lots of structure in what I do with kids. This includes approaches that range from “traditional” teacher-directed lessons to instructional routines to Desmos Activities to debate-oriented strategies like Talking Points. These are great and serve a purpose. They work to establish outlets for students to explore concepts in safe and dependable ways.

Yet with all the value of structured time, I would argue that messy, unpredictable time is equally important to our lessons and student learning.

By consuming ourselves with algorithmic structures, we teachers sometimes take away opportunities for our students to face problems openly. At times neutralize their brilliance and rob them of their natural inclinations — both intellectually and socially. By giving my students pedagogically less and expecting more individually and collectively, I’ve realized the importance of allowing my students to own their learning — to own our classroom.

For example, it’s now a regular thing for me to give my students a set of carefully constructed problems, whiteboards, and random groups as a means to learn new concepts. They are free to do whatever to understand the problems, including each other and the internet. If it was up to me, I’d even let them leave the classroom. Nonetheless, they are out of their seats for the entire period. I will aid with the math, but I indirectly encourage struggle. I’m there to help, but mainly around to support them to summarize and reflect on their work. It is their energy will make or break the room. It’s on them.

The result is often an untidy and confusing classroom. The uncoordinated, ambiguous, and disoriented learning environment it creates relies heavily on the cognitive diversity in the room. It’s an intentionally unpredictable and flawed approach, but something I’m learning to be good with. For me, it’s worth the tradeoffs.

Rarely does it end in rainbows and butterflies. But that’s kind of the point, though. Often times the kids walk out more confused than when they walked in. We might not get to an answer, let alone a correct one. This usually means that they don’t like me for a while (sometimes all year), that I won’t be on their list of favorite teachers. But in long run, it’s my belief that their discomfort will not only help my them understand the responsibility they have to themselves and their classmates when it comes to learning, but also the responsibility they have to make our classroom go.

Formal schooling sucks the instincts out of our kids. I teach high school and by the time my students get to me, they’ve internalized the classroom as a place where the teacher is supposed to direct their every action. They lose their ability to sense-make because they’re only concerned with “doing school.” They would probably stop breathing if I told them to (and then run to the principal’s office).

So while we thoughtfully select safe and comfortable approaches to student learning this school year, let’s make sure we don’t deprive our students of something they desperately need, which to experience disorder and be pushed out of their comfort zone. This means that they’ll be more tension, messy interactions, and awkward moments in our classrooms. And this will most likely require us to be pushed out of our comfort zones. And that’s a good thing.

 

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Why am I all about chalk and t-shirts this summer?

I need to let this out of the bag.

This summer, I have had two things on my mind more than they probably should be:

  1. using sidewalk chalk
  2. buying t-shirts

Why? Hang on.

First here’s some of what I’ve done with the chalk:

And these are the t-shirts that I have bought:

Through both the chalk and shirts, I’ve found myself publicly advocating for math like I never have. Obviously, I’ve always been a proponent of math in my classroom, but now through what I subtly wear and create on the pavement in my neighborhood (and around my school), I’ve found myself attempting to transfer this passion more broadly…to the general public.

With the awakening of my social conscience during these last few years, I am more mindful of the damaging stereotypes and inequities that exist in and around the culture of learning math. Far too many people in society are put off with math as being a cold, lonely subject that is reserved for the elite. The reasons for this vary, but, as a math teacher, I think I am really coming to grips with the responsibility I have in reversing this trend, even if most of my effort goes unnoticed. There’s something bubbling up inside me to find and create small, practical ways to promote math as an accessible, friendly science…that go beyond the scope of my classroom.

It’s a very steep mountain to climb, but the hope with both the sidewalk math and my new t-shirts is to promote equity, access, and exposure to math in unique ways and to spark meaningful conversations about math (potentially with perfect strangers). Along with this comes helping to shift the mindset of how other people (young and old) view learning math and their own mathematical value.

I’d like to think it has worked…as both the chalk and shirts have elicited reactions from people I’ve encountered this summer. Two other teachers even liked my t-shirt so much that I went ahead and got them one. I guess that’s a good thing.

Come to think of it, this is really no different from Sara VanDerWerf’s call for math teachers to identify themselves evangelists.

 

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Teaching & parenthood

At day 2 of the MfA Summer Think yesterday, there was a teacher poetry circle. The following was the result of the free write at the end.

Early in my teaching career I never thought that about being a parent. As time-consuming and energy-consuming as teaching is on a daily basis, I never thought that I would be capable of being a parent, fathering a child, tending to the everyday needs of another human. I, along with most other teachers I know, are completely drained at the end of a school day. As a parent, I would then have to go home and do something even more involved? Nah, I’m good.

I was so wrapped up in my own professional cocoon that I would privately question teachers who were parents. Was there’s a conscious decision to start the journey into parenthood? If so, WHY in the world would they do it? And how do they maintain their own sanity on an everyday basis?

Well, two and a half years ago I willingly turned my personal life upside down and became a dad. In addition to being the most awesome and adventurous ride I’ve ever been on, it also spurred a dramatic change in me as a teacher.

Before my son arrived, I was an impassioned teacher. I had the career that I had wanted since my junior year in high school. I loved my students, I loved my job. But after his birth, the love I developed for him was deeper and more compassionate than anything I had ever known before. For any parent out there reading this, you know what I mean.

Slowly, during that first year of my son’s fragile life, I began to see my students differently. This was both amazing and unexpected. I realized that the same love I had for my son was also felt by the parents/guardians of my students. In addition to every other aspect of their lives, these parents sent their children to my school, to my classroom, each morning wanting nothing but the absolute best for their kid. This desire was no different than what I felt for my son from the minute I held him in the hospital for the first time.

As a result, I began to see each of the 34 students in my class from the eyes of a parent, not just a teacher. This triggered a shift in mindset that transformed how I felt about teaching mathematics and, coming from a single parent household, why I taught. Because he gave me this beautiful gift of perspective, each one of my students has become a version of my own son.

So, now, while I fail often at meeting this standard, I teach my classes as if he was on the roster. I simply know no different.

 

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PBL v2

So my yearlong experiment with problem-based learning has concluded.

After attending Exeter Math Institute last summer, I decided to overthrow my units and use problems as the foundation of how my kids learned each day. Throughout the course of the year, week by week I wrote a bunch of original problems, edited others that I already had, and stole the rest. In the end, there were 349 problems which I would classify as mediocre at best. These problems (and other practice, including DeltaMath) were the vehicle that my students used to learn algebra 2…and be adequately prepared for the Regents exam on June 14. The 12 whiteboards wrapped around the walls of my classroom provided the platform for my students to dig into these problems each and every day.

It was idealistic, but this change was inspired to help my kids be more independent and interdependent problem solvers. I took a huge risk because I didn’t know what heck I was doing. Despite some early struggles, I stuck it out because I believed in the process and knew that real change would take time. I constantly adjusted to support my kids as they pushed themselves out of their comfort zones. There were tears. There were instances where I felt like I bit off more than I could chew. Despite support from my admin, I still felt alone because I was doing something so different, so radical, from the rest of my colleagues. It wasn’t their fault. I was hard to relate to. Mine was a messy, nonlinear pedagogical stance to teaching mathematics and, as such, others stayed away. In the end, although folks wished me well, I had no one to talk to about the day-to-day, nitty-gritty roadblocks that I ran into. Other than an independent trip to Exeter and an awesome visit from one of their teachers, I worked in isolation. This only intensified my struggles.

Anyhow, the result of all this was an uplifting, rejuvenating, and stressful school year. I have some major takeaways that will inspire next year’s work, PBL v2. I’ll let them breathe here.

  • Don’t think that students will value my perspective on learning simply because I say its valuable and worthwhile. There was going to be a natural struggle involved with learning through problems, but I did a poor job of setting them up for dealing with it. Next year, the first 1-2 weeks will be all about helping them meet my expectations. This may include modeling how they should approach the problems using prior knowledge and independent research, encouraging uncertainty, showing them how to document their thinking, and how to use classmates as resources. I also want to present the research behind how and why I’m structuring their learning experiences.
  • A more diverse set of instructional routines to discuss problems. This year I used student-led Harkness discussions, rotating stations (group speed dating), Desmos Activity Builder, structures unique to the specific problems, and traditional, teacher-directed lessons that focused on anchor problems. Before the year began, I was worried about having the right problems as they are so pivotal in this setting. As the year progressed, I realized that I overlooked the pedagogy behind implementing the problems. Even with a focus on small groups, uniform Harkness discussions simply won’t cut it for a class of 30 every day. While it is and will continue to be a foundation of what I do, students quickly tire of the routine. I’m also thinking that exploring the use of protocols may be worthwhile.
  • Better engagement during group work. On most days, I gave students lots of freedom when discussing the problems of the day. For much of the period, they were on their own to construct their own (with guidance from me) understanding of the problems and the related concepts. Trust was baked into each day’s discussions; their thinking inspired the success we had each day. Some days were great, but on plenty of occasions, they did what teenagers do: be lazy. I’m wondering what else I can do to foster more consistent engagement during these small group discussions.
  • More metacognitive journaling. I did one in the spring and I liked it. They chose a recent problem and analyzed their own thinking around it. They told the “story” of how they arrived and understood the solution. They were a lot to grade though. Maybe one per marking period?
  • Be better with parents. I need to have a much more transparent and stronger relationship with my parents. I almost got around to inviting one into my classroom. Nonetheless, I need to clearly communicate how students are learning, why it’s important, and how I will support them along the way. Some parents had reservations about my approach and they definitely didn’t hold back from sharing their thoughts.
  • Use standards-based grading. Because I didn’t have explicitly defined units for students, when they encountered the problems, they didn’t have the crutch of knowing they were working on “section 2-4,” for example. They needed to use the context of the problem (and work done on previous problems) to discern what to do. I really like this because it made more challenging for students, but it handcuffed me when because I couldn’t find a way to accurately identify and document their understandings on exams, other than a vague, overarching percentage like “74%.” I thought deeply about this a lot and decided I will need to sacrifice a little PBL to assess meaningfully and authentically. Next year, I still don’t see having units, but I do think I will attach concepts to problems, at least to start. At the start of the year, when I give them their problems, I will also give them an exhaustive list of concepts that the problems elicit over the course of the year. I will number the concepts (eg 1-52) and each problem will have an indicator showing which of the concepts the problem connects to. Maybe over time, I can move away from this and students can make the problem-concept connection on their own. Either way, with well-defined, itemized concepts, I should be able to assign qualitative measures to each student’s understandings (needs improvement, developing, proficient, mastery). Whew.
  • The above would allow for more meaningful retakes of exams. With “corrections,” this process was a joke this year. There was no meaningful learning and we were all simply going through the process of applying an informal curve to their exam grades. With SBG back in the fore, this means that my post-exam procedures will look more like last year.
  • A nonlinear approach to learning mathematics. A huge plus of the PBL as I implemented it was that it gave me the opportunity to interleave concepts like never before. Not only did I marry concepts together in natural ways that are harder to achieve with discrete units, but I was able to space out concepts over the course of several months when it would traditionally be crammed into a three-week unit and subsequently forgotten. The most obvious example of this is trigonometry. We did many problems over the course of four months, each being a small step that got us closer to learning all the concepts from the unit. All the while, students were learning about other concepts as well. I can definitely improve my sequencing of problems but, again, since concepts learned are nonlinear, this makes recall more challenging for students and harder to forget.
  • One formal group assessment per marking period. These are just too valuable to not include on a regular basis. The kids love them. Plus, real learning happens during an assessment! They include two-stage quizzes, group quizzes, and VNPS quizzes.
  • Assign problems that will be formally collected and graded. In addition to the daily problem sets that are worked on for homework and usually discussed the following day, I want to give one meaty problem that’s due every two weeks. I’ll expect integrity and independent solutions, but students are free to research how to solve them using whatever resources they want. This will hopefully promote deep thought and a formal write up of math on a complex problem. I would love to have students type up their responses. I foresee using the Art of Problem Solving texts to find these problems, at least to start.
  • Using DeltaMath as a learning resource, not just practice. I was surprised by how big of a role DeltaMath played in my students’ learning. Given the lingering Regents exam, my kids relied heavily on the ‘show example‘ feature of the site to explore and solidify key ideas brought out by problems that we discussed during class.
  • Check homework randomly, I think. Because I didn’t check homework at all, the majority of students didn’t do it. Since the homework consisted of problems that were the centerpiece of following day’s discussion, it was a necessary component of the class. I wanted students to internalize that if they didn’t do it, they would be lost the next day. It’s ok if they didn’t understand, but they had to try. Well, that didn’t happen. Most kids just tried the problems in class the next day and set us all back. A colleague gave me feedback that students will give priority to things that have incentives, like points. I get it, but refuse to accept giving a carrot for homework. To compromise, I may check the homework of a random set of 5-7 students each day. Any student is fair game and, by the end of the marking period, every student will have roughly the same number of homework checks. I had tested this out in May and I think it triggered some initiative amongst students to do homework. I also like the idea of possibly administering a homework quiz that’s based on the previous day’s homework. If they didn’t do the homework, they’ll struggle…and I’ll offer tutoring for them to make it up.
  • Deliberately teach problem-solving skills. I had a flawed expectation that students would somehow become better problem solvers by simply solving a bunch of problems and have discussions about them. While that happened for some, at the end of the year most of my students grew minimally when it comes to their actual problem-solving abilities. I’m still trying to figure out exactly how to get better with this, but I know purposeful reflection will play a big role. I will also need to help surface specific PBL skills for kids. I want to bring in the question formulation technique and problem posing. This is still up the in air…and I’m reading a lot about this right now.
  • Be uncomfortable. It’s a great thing. In past years, I unequivocally strived to have students that were comfortable and at ease with everything we did in the classroom. I hoped they would find what and how they learned as easy and unproblematic. If I’m frank, I did a pretty good job of that. This year, I landed on the cold realization that, in many ways, my students should be uncomfortable. How else will they grow? As this post showcases, I led by example.

That’s all I have for now.

A lingering thought. Years from now, I’ll probably look back at all this and realize that I was fighting a losing battle, that I was too idealistic, that my time with students could have been used more effectively. I’ll look back and see how foolish I was. Yes, foolish to think that I could somehow establish a subculture within my classroom of independent and interdependent problem solvers that relied more on themselves than on the teacher. A subculture that places little value of remembering a formula or procedure for a quick fix, but instead focused on the mathematical relationships, collaboration, productive struggle, and prior knowledge to own what and how they learned. I’ll laugh at myself and shrug it off as me being ignorant. I’ll recognize that my goals were too lofty and practically impossible in a day and age of teacher-driven learning, high-stakes exams, and point-hungry motivations.

With this in mind, I can’t help but quote Maya Angelou: “I did then what I knew how to do. Now that I know better, I do better.”

 

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