End of the 2017-18 school year

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Another school year in the books. As with each passing year, a lot happened in 2017-18. Bullet points seem appropriate.

  • First and foremost, my adventures with problem-based learning took up most of my mental real estate. That journey deserved its own post.
  • This was truly the year of the whiteboard. I had 12 of them wrapped around the edges of my classroom this year that we used every day. It was great.
  • I need to step my game when it comes to the cohesion and collective responsibility that my department shows for one another. Just like last year, I felt isolated this year. More than ever, this year I desperately needed support from colleagues that I didn’t receive. There are lots of reasons for this, but my own introverted nature certainly didn’t help matters any. Next year I hope I can be a better teammate and leader.
  • While PBL took off in room 227 this year, I’m very disappointed that my push to address racial inequities in my classroom stalled. I failed to build on many of the conversations that I started with my students last year. For example, my Mathematicians Beyond White Dudes initiative halted after Vivienne Malone-Mayes (No. 3). This was due primarily to my borderline obsession with implementing problem-based learning and all the struggles related to it. This issue is deeply personal and I’m very very dispirited that I let it trail off. Several of the kids even called me out on it near the end of the year. This only adds more fuel to the fire for next year. Specifically, with all this work on PBL and discussion-based learning, I’m now interested in exploring the intersection of those two strategies and the racially relevant pedagogy that I hope to espouse. I have a few books lined up this summer that I hope will help me think more about this.
  • I’ve begun toying with the idea of planning and organizing a ‘Math Night’ next year.  This is an exciting idea that I hope I can follow through with.
  • For the first time ever, I had my kids meaningfully write about the mathematics they were learning this year. It was a ‘metacognitve journal,’ a way of reflecting on their thinking about a particular problem that we solved. I only did one in late spring and it helped me realize that critical reflection like this journal must a component of my classroom moving forward, especially as I move to intentionally develop problem-solving skills in my students. I dramatically underestimated how long it would take me to grade them! Agh!
  • I checked no homework for credit this year. Sadly, this meant that the majority of kids didn’t do their homework. Am I ok with this? No. But I’m still not ok with checking it each day for points. #teacherproblems
  • This year I thought a lot about public and private school collaboration. I spent full days visiting both Phillips Exeter and Horace Mann schools. Both were worthwhile experiences. I hope to continue this work next year – especially with Horace Mann because of proximity.
  • In the spring, I was very close to having a parent observe my class. I was inspired by an NYCDOE survey that asked whether I’ve had any parent visit my class this year. Although it never happened, for the first time it made me seriously think about the inherent boundaries that exist between parents and the spaces in which their children learn. I may be opening a can with this one, but I would really like to have at least one parent in my room to observe instruction next year.
  • I got away from standards-based grading this year. As a result, I wasn’t able to help students identify and understand their strengths and weaknesses in any sort of accurate way. This should change next year.
  • Recently, a colleague of mine just spoke about getting kids to ask more questions in class and he mentioned the use of sentence starters. I’ve been exposed to them for years and never used them. I think they’re so inviting and accessible for students and can help elevate how they articulate themselves. I would love to try them next year.
  • I taught a math elective this year called ‘Explorations in Mathematics’ that started off strong but fizzled out after the first semester. Much of this had to do with programming.
  • One of the non-teaching highlights of the year was chaperoning a trip to Denmark in April. Along with 5 other teachers, guidance counselors, and administrators, we accompanied a wonderful group of 24 students on this unforgettable overseas adventure that included homestays with Danish families.
  • For the 2nd year in a row, I was nominated for a Big Apple Award. I don’t know why I was, but I am grateful and humble nonetheless.
  • I helped my school adopt the Math for America PLT model as part of our Monday PD cycle this year. This was a useful and engaging way to give teachers a direct say in the PD they experience. As far as I know, a first for school too.
  • I submitted the two remaining components of my National Board Certification. In December we’ll see what Pearson thinks of me.
  • Being the second year at my school, I found myself considerably less stressed about everyday happenings than last year. My sense of community grew.

 

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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.”

 

bp

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We have a lot to learn from skateboarders

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Last week I was sitting in the park watching a skateboarder. He was alone and clearly practicing his moves, trying to get better at a variety of different stunts. I must have watched him for 15 minutes and, I estimated that he nailed about 20% of his attempts, probably less.

As I watched him fail over and over again, I couldn’t but realize the rarity of his public display of failure. But in most other situations where we are around others, let alone perfect strangers, this is far from the norm. Rarely do we openly display our imperfections for everyone to see. If anything, we hide them to protect our image. Yes, in the public sphere, your weaknesses are yours and yours alone. We are only allowed to put our best foot forward. Otherwise, we’re uncomfortable and sometimes embarrassed.

Not skateboarders. In the skateboarding culture, public failure is not only commonplace but its desirable. Falling off your board is a necessary means of getting better, no matter if everyone in the park is there to witness it. You do it. You inherently admit weakness. Sure, getting better at maneuvering a skateboard requires lots of room and public spaces (like parks and empty parking lots) are the most convenient and accessible places to do so. Nonetheless, the willingness of skateboarders to outwardly showcase their shortcomings is fascinating to me.

My intrigue is heightened when I think about the culture of education in which I function. Students (and teachers) work in a system that often downplays struggle, placing lots of emphasis on correct responses. Case in point, its a regular occurrence for students in my class to erase their whiteboard work that hasn’t led them to a correct final answer. They refuse to be wrong publically — especially when all eyes are on them. This is certainly a reflection of my own inability to champion mistakes and struggle in my classroom, but its also representative of how formal schooling has made our kids feel and think about being wrong. If you don’t land on the correct answer, it’s not worth showing your process publically. No, you must keep that valuable part of learning all to yourself until you arrive at a “correct” answer when, only at that time, it is acceptable show your thinking.

There’s a lot we can learn from skateboarders.

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My NBCT journey…for now

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Four years ago I sensed myself reaching a professional climax. I finished my master’s degree a few years earlier and I started to level out. I had done a lot of little things as a teacher; I attended and facilitated lots of professional development, served as a model teacher for my school, led grade teams and the math department, interviewed teachers, mentored first-year teachers, ran after-school clubs. I’d been in the game for 10 years and I knew that I never wanted to leave. I find teaching students math to be a complex, unsolvable puzzle that is crazily addictive. So with this in mind, I began thinking about my next big challenge, my next big thing as a teacher. What would it be?

Whatever it was, I figured that it’d be something that could dramatically elevate my career. That meant it would probably be something that would require me to jump through some pretty big hoops to complete. I was still was very hungry to be a better teacher and I needed more than the in-school or out-of-school usual professional development to do the trick. I recognized the fact that I had a lot to learn, about the profession, my practice, and myself. I also wanted to reach the last for my salary step here at the NYCDOE and, because I see myself leaving NYC at some point down the road, achieve something that would be recognized by other states. After some deep reflection, I boiled my options down to two: an Ed.d or National Board Certification. I chose the latter in large part because the Albert Shanker grant paid for it all. Otherwise, it would have run me around $2000. Plus, I don’t know why but it just seemed natural for me to seek NBCT before an Ed.d.

I kicked things off two years ago with the content exam, which is component 1. It is essentially a college-level math exam, similar to the Praxis. Other than having to brush up on my calculus, I do remember having to learn the fundamentals of graph theory. As a math major, how was I never exposed to it in college?? Absurd. I’m pretty sure I got all those questions wrong on the exam. Plus, I left five answers blank because of my horrible time management. Despite my shortcomings, somehow I managed to earn a respectable score.

Thinking linearly, last year I submitted component 2. Its focus was differentiated instruction and the first where I actually had to write about my teaching. I had to showcase how well I could plan a unit, differentiate based on the needs of my students, and analyze student work in relation to the learning objectives I set and lessons/activities I planned. Out of the four components, this one was probably my favorite. Probably because it was the most cohesive. Sadly, I’m not sure I differentiated anything, but once again I earned a respectable score.

With some confidence, this year I pushed myself to submit the remaining two components. It was so much work that I still can’t believe that I finished them. Seriously. Component three required me to shoot video of two different lessons and analyze it. Four, by far the most confusing and stressful component, was clumsily duct-taped together by National Board to capture how I gather knowledge of my students, generate and use assessment, and how I develop professionally. In the end, I feel that I did ok, but just ok. Analyzing video from my class, while cumbersome, was far easier and engaging than anything that I was asked to do in component 4.

So it won’t be until December if I know I need to redo any of the components. But having completed all the requirements, I have been breathing much easier these last two weeks. And I remembered that I have a family! I’ve also been thinking about the extent to which the National Board application process has helped me grow.

I’m mixed. I think my expectations were too high. In many ways, completing the four components felt like merely formalizing the work I would do normally, so I found the NBCT application not as transformative as I hoped it would be. As of now, I don’t feel like I’m a vastly different teacher that I was when I started my journey to become NBCT. Assuming that I do get certified down the road, maybe that will change. I don’t know. But having now gone through the process, I know that many of my colleagues (both those in person and online) work much harder and smarter than I do and surely meet and/or exceed the NBCT standards. I just chose to complete all those damned forms and write 40+ pages of formalized commentary about my teaching — and spend a good chunk of three years doing so.

With all that being said, going through the NBCT process was undoubtedly worth it. The most valuable aspect of the NBCT application for me was how it served as a platform for structured reflection. It helped me be critical of my teaching in several big areas and hit me with prompts that forced me to rethink some of what I do every day and why I do it. I kind of do this now, but not nearly with the depth or rigor that NBCT requires. I like writing so I’m partial here, but maybe there was something to formalizing my reflections through those 40 pages. It did help tease out my ideas and compelled me to be more planned and meticulous with how I reach my kids. I don’t know, I think I need more time to more thoroughly put this beast in perspective.

But I can say that as I got closer to the NBCT standards, learned them, and began aligning my practice to them, I began to deliberately think about my teaching in ways that I never had. I was able to discover some weaknesses…like how little I leverage the unique perspectives and abilities of my students to further their learning or my abysmal efforts to work with the families of my students in any sort of meaningful way. As a result, I like to think that I developed some new strengths.

 

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Sidewalk Math

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Every time the weather gets turns favorable, I get inspired to grab some sidewalk chalk and do #sidewalkmath. It’s been a thing for me the last couple of years. It’s a great way to promote public displays of math (which we never see), get the general public thinking about math (which rarely happens informally), and work in some creativity in the process. I’ve been messing around with #sidewalkmath in the neighborhood where I live (here and here), and I’ve also had students take part the last couple of years.

With this in mind, last week I took the kiddos out to let them publicly showcase their mathematical prowess via the sidewalk. They were graphing trigonometric functions and the sidewalk was primed and ready to go. I numbered each slab in front of our school, paired them up, and gave them a trig function. I let them go. After they graphed their own equation, they had write the equation for another graph on the sidewalk.

 

 

I read somewhere that our school is located in the poorest congressional district in the U.S.  While the kids and I were out in front of our school sketching the functions, it hit me that the overwhelming majority of the people that walked by our math probably had clue what they were looking at. That’s disappointing for sure, but precisely why doing it was so important.

 

bp

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