Why we’re better together (crosspost)

*This post was originally published on the Teacher Voices blog at mathforamerica.org. It was co-authored by myself and the awesome Courtney Ginsberg.

Teaching is the most complex job in the world. We shape the future. We motivate students, deal with ever-changing expectations, and tackle mounds of paperwork. Through it all, we operate within a system that champions test scores over learning. This is a mere subset of the demands placed on us every day. If you’re a teacher reading this, you can no doubt think of many more.

Given this backdrop, no one would blame a teacher for focusing solely on their own classroom and their own students. Thoughtful teachers understand the urgency to serve the 30 smiling faces that walk into our classrooms each day. With that said, there is danger in not acknowledging the role we play in the larger context of teaching. When we fail to see our colleagues, both in our own school and out, as necessary partners in the work that we do with students, we become an island. Isolated, we create everything ourselves, work through problems alone, and have difficulty seeing beyond our classrooms. In this way, our potential, and our students’ success, is inherently limited.

As teachers of mathematics, the hallmark of improvement is the meaningful connections we make with other STEM teachers. These connections drive collaboration and inspire us to rethink what’s possible for our students, our classrooms, and our schools. Naturally, this is the setting where teachers become teacher leaders. We are empowered and unafraid to volunteer our time to lead professional learning courses or simply start a discussion on an interesting topic, like we do at MƒA. Occurring with little to no help from outsiders, these are the most meaningful types of professional development experiences.

This line of thinking contrasts the message that is often promoted from the top-down, which is for us to lean on “experts” to help us become better teachers. We are reminded to seek out these specialists and incorporate their models to better serve our students. This is a linear, straightforward approach to the challenge of teaching development. Go to the expert, learn from the expert, case closed.

While this sounds great and makes a lot of money for those in high places, knowledgeable teachers understand the reality: no matter how much success or experience you’ve had in (or out) of the classroom, no one is an expert at teaching. Many will claim otherwise, but becoming a better teacher isn’t linear – it’s more piecewise than anything. Different strategies are effective in different contexts with different kids. This is why teacher leadership doesn’t hang its hat on expertise. Instead, it relies on the collective knowledge and experiences of all teachers to push the community forward.

This type of collaboration amongst teachers happens every day. For example, several years ago, while co-facilitating an MƒA PLT with MƒA Master Teacher Mike Zitolo, Brian learned of their shared passion for classroom inter-visitations. Excited to learn from one another, they made unsupervised, grassroots plans to visit each other’s schools. The result was something that deeply impacted Brian. Mike’s methodical, know-why-this-is-important approach to physics was very different from the mathematics classrooms that Brian visited in the past (as well as his own). By immersing himself in Mike’s classroom, he not only gained a deeper appreciation for the STEM work that happens outside of mathematics, but learned how science can enhance how he teaches mathematics. The experience influenced Brian to publish a lesson that integrates a microcontroller into regression analysis.

A few years ago Courtney took former MƒA Master Teacher Phil Dituri’s workshop, “Making Group Work the Norm.” It sparked a real desire to collaborate more with her colleagues, so she spent time working through ways to incorporate them into her larger school community. She ended up designing PD for her STEM team to implement similar strategies. Shortly thereafter, Courtney heard MƒA Master Teacher Shannon Guglielmo speak at the annual MƒA MT2: Master Teachers on Teaching event. Courtney and Shannon attended graduate school together so this seemed like the perfect opportunity to reconnect. They talked and shared resources on her subway map theory, which led to collaboration around using statistics to solve community issues. This also allowed for deeper collaboration within their building as Courtney is working to set up inter-visitations for the 10+ MƒA teachers working at different schools within her larger building.

In both instances, teacher leadership wasn’t defined by the level of expertise of the people involved. It was developed through a genuine interest in learning from other teachers and a willingness to openly share knowledge amongst each other. This is the beauty and power of communities like MƒA. They are filled with teachers inspiring other teachers to be lifelong learners of STEM, who invariably work towards delivering the most meaningful and authentic instruction possible. In short, we lead each other.

To expand on the interdisciplinary STEM work that already has so many MƒA teachers engaged, many of us will come together next month for three days of growth. We will lead one another through a series of workshops that share our resources and best practices, all with the aim of leveraging big ideas in and out of the classroom. This teacher-designed, teacher-led conference, the Summer Think, will be the first of its kind at MƒA and will provide teachers a relaxing atmosphere to think in ways that is so hard to do during the school year. From exploring the social, economic, and ethical issues of climate change to infusing the design process into our classrooms, the conference will use mathematics and science as entry points to high levels of collaboration. With in-depth, multi-day workshops and a variety of support sessions all happening smack in the middle of the summer, this unique experience will embody teacher leadership.

Despite the resounding needs of our own students, our influence can and should extend beyond our classroom. Experiences like ours as well as those that will happen at the MƒA Summer Think demonstrate one simple fact: we’re better together.

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Day in the Life: Algebra 2 Regents Exam (Post #12)

I’ve decided to chronicle this school year through my blog. It’s part of Tina Cardone’s Day in the Life book project. This is the twelfth post in the series.

5:15am | Up and adam. I brew some coffee and head outside to sit and read for half an hour. The birds sing to me, which makes for a relaxing start to the day. Right now I’m in the middle of Why Don’t Kids Like School by Daniel T. Willingham. It’s pretty good.

I head back inside and put together some breakfast. I shower, grab the bike and make my way in.

7:15am | 13 minutes later I’m locking up my bike in the parking lot. This is still a little weird for me because for years I brought my bike up to my classroom.

On my way up to my classroom, I chat with a few teachers. Everyone is chill because we all know that today, June 16, 2017, is the fourth day of Regents exams. These are New York State high school exams. There is no more instruction for the year. New York City robustly organizes the grading of these exams in a pretty unique way, I think. Selected teachers from every high school in the city report to “grading sites” to mark the exams of students from schools other than their own. The organizational power that this requires is remarkable. For the most part, it runs pretty seamlessly every year. Unless you’re out scoring, you hang back at school to proctor the exams. If you’re not proctoring and have no other responsibilities, the time is yours to spend however you like. As for me, this morning I have to monitor a few seniors who are serving the remainder of their detention before commencement tomorrow, but other than that, there’s nothing that I have on tap.

What’s interesting about today is that my algebra 2 students are sitting for their Regents exam this afternoon. In total, there are about 75 students that will measure their understanding of algebra 2 against New York State’s ever-changing expectations. It’s a very anticlimactic end to their algebra 2 experiences.

7:30am | I make it up to my room, draft this post, and get lost in the abyss that is the internet. I’m hooked on brilliant.org, so of course I tackle a few their problems. I also continue working on my end-of-the-school-year draft that I began yesterday. The department chair comes in and tells me about this financial literacy course. Next year we will plan to have an alternative to Regents-bound algebra 2 and this course is one of the possibilities. It looks promising and it’s chock full of meaningful projects, which I like. We’ll see. Worst case, I incorporate certain features of the course and not others.

It’s crazy how two hours seemingly pass in the blink of an eye.

9:30am | I head down to the auditorium where there a bunch of seniors serving the last hours of their detention. While I fully expected it to be boring, I was pleasantly surprised at how enjoyable it was. It helped that I had several of the kids this year in class. We talked about future plans and they reflected on their past four years. One kid asked me about my feeling towards video games. I also made a bet with another about whether someone falls while walking on stage at commencement tomorrow. I said no, he said yes. The winner gets a Hershey’s.

Despite the fact that they were serving detention, the vibe I got was a communal one. Although I know it’s not true, it’s almost like they wanted to be there.

10:45am | On my way back to my classroom, I find a class set of tangrams in a closet. I’m thinking that I may use them next year in my discrete mathematics elective next year. I do a quick check-in with a girl doing makeup work to help her earn credit for the class. After, I go bunker down in my classroom and eat lunch.

Browsing Twitter, I read this tweet from Sara VanDerWerf. , I immediately place a hold on Blind Spot at the New York Public Library. Looks like a powerful read. It’s something I’ve been thinking a lot about over the last year.

11:45am | My classroom is being used for this afternoon tests, so I need to find another classroom to call my home for the next few hours. I do so and find that some of my students are hanging outside the building waiting to be let in for the exam. I head out there to greet them and remind them that they don’t need luck.

12:30pm | I pop into the various classrooms and give the kids a smile before they begin. No words, just a humble wave to accompany my grin. Other teachers this week have been bringing in candy and even bottles of water for the students. There’s something about this that doesn’t sit well with me. Maybe I’m overthinking things.

Anyhow, good feelings abound after my brief visit, but inside I can’t help but be disappointed that all of the work we’ve done this year has led to this moment. I leave them to work.

1:00pm | I walk up to the deli to grab a coffee. A colleague joins me. We talk about the upcoming “Field Day” that she’s planning for the last day of school. It’s an odd day because all of the grades are in and the exams are complete, but students technically still need to be here. She’s planning an entire at a local park full of all sorts of fun, outdoor activities.

1:15pm | I sit and continue my lazy day. I swear I’ve taken less than 1000 steps today.

I type up more of this post. I think about my students taking their exam. They’re great kids. I hope they’re doing well. I hope that their work is convincing to whoever grades their stuff. I could probably do something more productive with my time, but I decide to dive into more brilliant.org problems.

3:00pm | I decide that before I leave for the weekend that I should probably have a look at the algebra 2 exam, which all of my students are sweating through at this very moment. I get a copy from the test coordinator.

Look, historically speaking, my Regents results have never been something to call home about…and I know that there many other factors at play here. Nonetheless, despite it being a big part of my job description, I will openly admit that I’m not the greatest at preparing kids for these high-stakes exams. Last year, like 50 percent of my kids passed the algebra 2/trigonometry exam — and that was my highest percentage ever. So while I always hope and prepare for the best but, sadly, I don’t really have high expectations.

So back to today’s exam. As I comb through it, I’m shocked to realize how well my instruction aligned with the exam this year. My kids should do alright. But with my track record, I doubt it.

Let me stop. I’ll stay optimistic until the results starting coming in next week. (Secretly, I’m also banking on the ridiculously low passing score that NYS required.)

3:50pm | I leave school. It’s a nice Friday evening with the family. We go out for dinner.

9:20pm | Seemingly all I did today was solve brilliant.org problems, but somehow I’m tired. Go figure. Good night.


1. Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal?

I made a conscious decision at detention this morning to help repair a relationship that turned sour this year. The student that I made the Hershey’s bet with…um, let’s just say we had a rough year. He hated disliked my class. He struggled and I failed to reach him. Yeah, it wasn’t a great experience for either one of us. But I was really glad we connected on something lighthearted and fun at detention today. I also promised myself to email him next week to follow up on a modeling opportunity that he told me about.

2. Every person’s life is full of highs and lows. Share with us some of what that is like for a teacher. What are you looking forward to? What has been a challenge for you lately?

As the year has come to a close, I’ve struggled with feeling rooted in my school. I hoped that by this time, I would feel some sort of genuine connection to my new home, but that hasn’t really happened.

3. We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently.

Inspired by other bloggers, this week I invited a colleague to write a guest post for this here blog. What he produced was wonderful. He’s someone that has been talking about writing more for a long time…and I figured this might be a great opportunity for him. He not only seized the moment, but during the last couple of days, he’s been putting together his own website. His writing is taking off. He’s even thinking of writing a book this summer!

4. Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What is a goal you have for the year?

In preparation for the Regents exam, I needed to structure my tutoring in a way that met the needs of all my students and at the same time didn’t drive me crazy. What I ended up going with was assigning each student a minimum number of hours of tutoring that they needed to complete before the exam. The number of hours they were assigned was based on their performance during the school year. They had a tracking sheet that I stamped. Of course, every student didn’t complete all of their hours, but for the most part, it was successful.

5. What else happened this month that you would like to share?

Here’s something that I’ve never done before: I taught one of my classes how to solve a Rubik’s Cube. I use the word “taught” loosely. I borrowed 12 cubes (it’s a small class) from You Can Solve the Cube I attempted to show them the steps that I use to solve it. Not all of them ended learning how to solve it, but I think they enjoyed the change of pace. Next year I’m going to leave more time so we can get into mosaics.



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Why do you even teach, bro? (guest post)

Note: Last week, a Spanish teacher at my school and I were sitting around talking before freshman orientation. He’s super passionate about teaching. I learn something new every time he and I have the chance to talk. Anyways, while speaking with him on this particular day, I asked him if he’d fancy writing a guest post for my blog to share some of his thoughts. It was an open-ended invite and he was excited about the opportunity. In this post, he shares the relationship between his content area and his zeal for teaching.


I learned a long time ago that my love for Spanish had nothing to do with the art of teaching. You heard me right!

Your love for math, your love for English or literature even has nothing to do with your teaching. Some of us became teachers because we saw it as a stepping stone for that next big opportunity. Perhaps we were lured into the bear trap of education because of the time off. We reasoned that we could use that time off to write that best seller or design technology to revolutionize the way we live; perhaps we became music teachers to use the time to record that next big hit. Whatever may be the reasons, the fact is that some of us are in the wrong profession and we pay dearly for it, your students pay dearly, and the system pays dearly.

But a teacher that loves to teach can teach almost anything because their passion may actually hinge on the subject matter. Instead is all about the students they teach. When you love to help others succeed, teaching the subject matter that you love is the icing on the cake.

Because of their passion for helping students, these types of teachers celebrate the smallest milestone and push through the toughest days. Every day they renew their strength and faith and face each day’s challenges with optimism and a clean slate. They have the ability to forget about the wrong students may have done and focus on their future success.

So I conclude by asking you, why do you even teach bro?

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PD with Dan, modeling with mathematics

With the help of the NYCDOE, this past Wednesday was the third of three workshops that I’ve attended with Dan Meyer this school year. I’ve written about the first two, so why not cap off the trilogy? Read more here and here. In an effort to solidify my experience and have something to reflect upon at a later date, here’s a recap of the session.

The focus was on mathematical modeling. This is one of my weaknesses, so when I walked in and looked at the agenda, I was pretty happy. Teach me Dan! Things opened up with us sharing what we thought it meant for students to model with mathematics. The answers varied, but after feeling us out, Dan emphasized the difference between model the noun and model the verb. I had to catch myself here too as I hadn’t played close enough attention to this subtly. He used Desmos to collect our responses and our comfort level with mathematical modeling.

We then dove into the Penny Pyramid 3-Act. Dan worked his magic, as usual. During the debrief, he pulled from the CCSS and presented five actions that are necessary for students to be part of modeling experiences:

  • Identify variables
  • Formulate models
  • Perform operations
  • Interpret results
  • Validate conclusions

We talked about how the Penny Pyramid, while probably not ideal, works to get students to do all of these things. Our questions helped us to identify variables. Interestingly, Dan highlighted the vocabulary that we chose to represent the variables. This is important because, indirectly, he demanded precision and consistency from all of us when it came to describing key parts of the experience. Our tabular, algebraic, and physical representations of the pennies were the models, which we used to calculate the number of pennies in the pyramid. We spent time as a group discussing the meaning of our calculations and parts of our models – even those that weren’t correct. For example, one group landed on 22,140 pennies, which didn’t take into account that each stack was 13 pennies. Also: what does the 612 mean? The weakest part of our models was the validation. It’s not like we could actually count all the pennies. That said, we would compare outcomes of different models. There was also a newspaper article on the pyramid which helped with the actual count of pennies. Validation runs on a spectrum.

The afternoon was spent creating and improving some modeling tasks. We started with 25 billion apps and then went into a few graphing stories. We spent time thinking about how to structure modeling activities using these tasks. A great conversation occurred while exploring Distance from Camera. Someone brought up whether the graph should be piecewise linear or rounded periodic (like the solution). It was a great discussion, worthy of its own post. Dan remained vulnerable and eloquently showed us this ferris wheel Geogebra applet from the awesome John Golden. (Check out his full collection of Geogebra resources.)

We brainstormed how technology can help make our modeling dreams come true. The list was plentiful. Staying away from “textbook traps” topped the list. These include giving up numbers, tools, and other key information far too early in the modeling process. It’s also ironic that, because of technology, Dan was behind a desk for extended periods of time while we worked (he was typing our insights and using Desmos). Without technology, this teacher move is frowned upon.

The culminating task had us dig into several different versions of Barbie Bungee. Having never actually done this modeling activity, I learned not only about how to do, but also what not to do. Truth be told, if I would have looked at the activities before the workshop that day, I wouldn’t have suggested any changes. I would have been excited to implement them as is. But after purposefully rethinking modeling with mathematics with Dan for five hours, I felt very different.


  • The Penny Pyramid task would serve as a great introduction to summation notation.
  • Dan: “When there’s a great classroom experience, I ask myself: how could I have ruined this?
  • Not every aspect of modeling needs to every lesson. The goal is to feed students a healthy diet of modeling verbs.
  • Focus on broad questions. These will lead to more specific, granular questions. Avoid the reverse.
  • Seeing every teacher move I make as an investment into the lesson. Which moves are worth their investment? Which aren’t? This reflects the gravity that every decision we make. I need to be more deliberate.
  • Depending on what info we give kids, the level of modeling that they do could be very different. Don’t do the modeling for them! Give them procedural stuff.
  • It’s not if to give a handout, but when. This outcome was directly tied to Dan’s first session back in December, which helped things come full circle.
  • Once again, I was impressed with how Dan managed the audience. There were so many slick teaching moves (see notes).
  • I loved catching up with Sahar during lunch. We talked about her experiences visiting students homes with her school. She also gave me a tip about taking photos while students are working during the first couple of days of school to showcase how mathematical discussions should happen amongst students.
  • This wonderful periodic modeling Desmos activity.
  • If I ever do Barbie Bungee, I need to use Dan’s intro video.
  • Be mindful when moving between the real and math worlds. Don’t get lost on your travels.

Dan’s Google Doc for the session.


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Day in the Life: May 24, 2017 (Post #11)

I’ve decided to chronicle this school year through my blog. It’s part of Tina Cardone’s Day in the Life book project. This is the eleventh post in the series.

5:45am | I wake up. Boy, I’m tired. After staying up late to watch game 4 in Eastern Conference Finals between my hometown Cavs and Celtics, I certainly feel it. The early sunrise this morning helps pick up my mood.

I take an hour to eat, sip some coffee, draft this post, and shower. I’m on my way.

7:05am | I make it to school after a wet, soggy ride in. I make it up to my room and change into the clothes I keep in my closet for rainy days like today.

One of the Spanish teachers comes in to say hello and we chat. He’s no stranger, as we have periodically had some in-depth conversations about a variety of things this year. Today we talk at length about how our school years have gone and how they’re shaping up. We both have had disappointing moments and growing pains, but remain hopeful in the future. He’s a great guy. Our random talks have been a welcome respite his year.

I also spend a few minutes for an interview with a senior whose working on a project related to discrimination, racism, and stereotypes. Sharing my thoughts on camera with a student is a breath of fresh air. I don’t know her well, but I’m so happy that she’s dedicating time to researching these social issues. Our school needs it.

7:40am | Just like that, a half an hour passes. I throw on some music and begin mapping out the day for my students. Because the state tests are around the corner, we’re basically in Regents prep mode. At this time every year, I become a machine.

9:00am | First period comes to an end. The class is basically all seniors and today is prom. So yeah to say that they struggled to maintain focus is an understatement. I usually go to prom, but I’m sitting this one out. This is largely due to my lack of connection with the senior class…which is a consequence of this being my first year at my school. Next year.

I make it back to my room and remember that I need to run off a bunch of copies for my after-school Regents prep session after school today. I do that and come back to finish off plans for period 4 and 5.

10:35am | Fourth period begins. The focus is on solving a system of equations graphically. Specifically, we are using the graphing calculator to approximate the solutions to a given system of equations. I also give back their mock Regents that they took the previous Saturday. The results of which were promising. The lesson is ok, but nothing to call home about. The kids see a rational function for the first time and sort of freak out upon graphing it. Oops. We manage, but my poor pacing this year has caused all sorts of hiccups like this. I also manage to screw up one of the systems because the logarithm that I included in one of the functions doesn’t display properly on the graphing calculator because of a logarithm. This reminds me of Patrick Honner’s talk at MT^2 a few years back.

11:25am | Fifth period gets going. I head across the hall to the customary standing ovation. These kids are a blast. (Did I mention that I’ve started clapping for them when they walk out of the room?) The lesson is the exact same as period 4, but I make sure to develop the rational function a little better and skip the erroneous system.

12:15pm | I go heat up my lunch in the teacher’s lounge and run back to my room to scarf it down. I have some minor prep to do for period 8. While on my computer, I get a notice from UPS that my You Can Solve the Cube class set of Rubric’s Cubes arrived today. Excited, I pick them up from the main office. I recently learned how to solve a Rubric’s cube myself, so sharing this joy with my period 7 students (there’s no state test) is going to be great.

1:00pm | Speaking of period 7, they walk in. Because most are seniors, it’s a smaller group today (prom). I forewarn them that path to solving a Rubric’s Cube can get very frustrating. They nod, passively. I hand out the cubes and show them the first step in solving the cube. They practice this step over and over before the end of the period. They’re excited, I’m excited. It’s awesome.

1:50pm | My period 8 is officially starting “Regents Prep” today in class. A colleague made these fancy booklets containing all the Regents questions from like 2013 or something. We use those to review finding and using regression equations.

2:35pm | After school Regents prep starts for my algebra 2 students. I really like how I chose to set it up this year. Based on each student’s overall performance this year, I assigned them X amount of tutoring hours that they must get in before the Regents exam on June 16. They have a sheet to track all the hours that I stamp after every session they attend. It seems pretty efficient and holds every kid accountable.

4:35pm | The students staying for tutoring/Regents prep head home. I sit at my desk, reply to a few emails, and wait for the students completing their mock Regents to finish. At 5:05pm, I head home.

8:30pm | I’m still grading the mock Regents that the kids took, so I dedicate an hour to knocking out a good chunk of that.

9:50pm | Off to bed.

1. Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal?

While bogged down by the Regents and essentially turning myself into a test-prep machine during the last week or two, I’m pumped about getting the Rubric’s Cubes for the kids. It’s different, fascinating, and fun. In fact, that may just keep me afloat until the last full day of instruction on June 13.

2. Every person’s life is full of highs and lows. Share with us some of what that is like for a teacher. What are you looking forward to? What has been a challenge for you lately?

Hmm. Why am I drawing a blank? Too many highs and lows to describe? I’ll rain check this one. TBD.

3. We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently.

This month, I had a powerful moment this with a colleague about a t-shirt that she wore to school. To make a long story short, we connected on her decision to wear the shirt and, unfortunately, the disciplinary action that took place as a result. The entire situation was off-putting, but through it I learned so much about myself and my school about we address race and representation with colleagues and our students.

4. Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What is a goal you have for the year?

While not one of my classroom-specific goals, this school year was to make a whole-hearted attempt at National Board component 2. All year, I’ve had this thing in the back of my mind, but it wasn’t until February when I began to seriously think about the specifics of what I was going to do. After losing about two weeks worth of sleep, I managed to submit it this month. The focus was my mini-unit on complex numbers. I’m pretty sire that it won’t be the best that NBCT will read, but I was super proud of all the thought that I put into it. I learned a lot, too. Next year: components 3 and 4.

5. What else happened this month that you would like to share?

On an unrelated-to-teaching note, this month I’ve decided that I will be taking piano lessons during the summer. It’s always been something that I’ve wanted to do since I was young, a “lifelong goal” of sorts. I’m thrilled!


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