My two cents on letters of recommendation

For those of us that teach high school, we know this time of year well. ‘Tis the season for letters of recommendation! I’m feeling rather festive this year, and I have 7 of them patiently waiting for my attention as I type this sentence, so what am I going to do? Forget all about writing them, forget all about being productive. Instead, I’ll just ramble.

Where do I start? Well, when I think about writing a student a recommendation letter, it all begins with the request from the student. How a student asks is important to me. Other than the student being graceful and intentional, which is a given, I’m a stickler for facetime and eye contact. I don’t like it when I get requests by email. When I do get one like this, even if I don’t have them in class anymore, it’s almost always from a student that I see on the regular. In my head I’m thinking, just come ask me! (I’ve long believed that email is abused, especially when it comes to interpersonal relations, but I digress.) When I get a recommendation request by email, I always ask the student to see me in person, to make time to look me in the eye, even if I know that I plan on writing it.

Next comes the decision to actually committing to writing it, saying yes. In my experiences, it seems like some teachers feel obligated to write a letter of recommendation when a student requests it. It’s like, they have to ask and we have to say yes, but that’s just a formality. I get that we want to help students as they begin writing their next chapter, but when did helping out a student turn into me agreeing to camp out in front of our computer for hours and hours to compose dozens of recommendation letters?

When it comes down to it, I don’t mind saying no. If I don’t feel connected to the student, if I don’t feel like I’m the right person to tell their story, then I will simply tell them so. This might result in awkwardness, but I’d rather be upfront and encourage the student to find someone else that can better capture them through the letter. If I know that if I’m not thrilled to write it, to be able to go on and on about the student and share personal stories, then I’m not the right person for the job. Besides, if I did write it, I’d most likely be dragging myself through it and the letter itself would probably end up being mediocre at best. In addition, there’s another reason why I will tell a kid no: I must have taught them for at least a year. If this is not the case, then I won’t even consider writing it. It’s not personal. There are lots of highs and lows in a school year and observing a young person navigate those peaks and valleys is critical to me being able to endorse them without reservation.

While telling a kid no is not my favorite thing to do, I also go the other way and say yes without even being asked. In recent years I’ve requested, and lowkey demanded, that I write a kid’s letter of recommendation without them even thinking about it. I’m so proud that I take ownership of them and want badly to be their advocate. It’s an honor that I want to take on.

When it comes down to actually writing the letter itself, I used to have a canned letter that I would modify a little for each student. It was bad. That was a while ago, and I’m so not proud of myself for shortchanging those kids. They deserved way more than how I chose to represent them. I respect the process so much more now, in large part because of Sam Shah. Several years years ago I read his post on recommendation letters and totally stole the questionnaire that he asks his students to complete. I’ve modified it some, but this questionnaire is by and large one of the best resources I have when it comes to writing the letters. Once you read through it, you’ll know why. It lets them tell the story. Couple this with personal anecdotes and other written reflections from students, and the tone is set.

Through all this, I’ve even begun tinkering with the structure of each letter depending on the student and how I feel about them. For example, my letters these days often don’t start and end the same way. And playing around with these aspects of the letters makes them way more fun to write. Must they look and feel the same? How can I get the letter look and feel like the student that I’m writing it for? Rethinking these sorts of things makes writing it more of a creative act for me. Even if they never get to read it, it also helps me pay respect to the student and all that they are and hope to become. This jives well with my post last year about being selfish when it comes to writing.

Interestingly, my school recently brought in someone from a top university to give us tips on how to write an effective letter of recommendation. I couldn’t attend, but I really wish I could have.

Ok, ok, enough procrastinating.

 

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A five-minute conversation sparked so much sidewalk math

I’ve been really into sidewalk math for a while. It started with me laying it down with students at school to doing it at local parks in the Bronx, where I live. All of this ballooned into my sharing it last August at TMCNYC as a My Favorites.

After I shared it at TMCNYC, Michael Pershan came up and asked me whether or not I had thought about sharing sidewalk math with a larger audience. Other than Twitter, I hadn’t. He mentioned that maybe I should, that it might be well received by the larger teaching community — specifically those at math ed conferences, like NCTM.

Michael and I spoke for a mere 5 minutes, but our conversation inspired me to write a post where I rethought who benefits math ed conferences. Need it only be the attendees? Can we math teachers leave something to a local community to engage with both during and after we leave their space? Can we leave the host city better than we found it mathematically? Though there are many ways to do this, I was thinking of hosting a session at conferences, gathering teachers, taking to the streets, and doing sidewalk math. It’s not going to change the world, but it could help move the needle a tad bit towards spreading math and including more people in conversations about math.

Last winter and spring, I began pitching my idea. I wanted to do sidewalk math at conferences. I didn’t know any better and didn’t really want to spend buckets of dollars traveling halfway across the country, so I proposed my idea to five local conferences. All but one was in NYC.

I guess Michael was right, there was a thirst for public displays of math. All of the conferences let me host a sidewalk math session. Yay!

The odds are pretty good that I’ll never be asked to present anything this much ever again, so now that it’s over, I want to bottle up some of my experiences over these last couple of months.

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June 6, 2019: EdxEdNYCThis was the first one and by far the most nerve-racking. Having never have presented at a conference before, I was deathly scared about having an adequate amount of material for the time slot. Plus, because I built in time to actually going outside to do sidewalk math in the local neighborhood, if it rained, I didn’t know what the hell I was going to do. I was so paranoid that I literally checked the weather every few hours in the days leading up to the conference. In the end, it didn’t rain and the timing worked out really well. I had a couple of former colleagues in the session, so it was also great to able to share it with them. It’s a small detail, but I made an effort to stand outside the room and greet folks as they walked in. I was not only hoping to welcome everyone to the space, but also ease my nerves by connecting, however briefly, to each attendee individually. It really worked. I made a point to do this at all of the upcoming workshops, too.

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July 10, 2019: Math for America Summer Think | This one felt the homiest to me. Also, these teachers were probably the most eager and able to do sidewalk math. There were about 20 people in the session, which was about half of the EdxEdNYC group. And as someone who has been part of MfA for several years, I knew more than a handful of the folks in the audience. There was even a couple of science teachers there, who so eloquently created some sidewalk science. All in all, we fanned out and chalked up the Flatiron district pretty good. There were definitely some sidewalk math problems put down that I pocketed for future use. Interestingly, I learned that the park rangers at Bryant Park are not fans of sidewalk chalk. Boo! Anyways, I was 2 for 2 on avoiding the rain.

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August 5, 2019: Museum of Math MOVES Conference | Of the five sessions, this one was the most contingent on the weather. The session had no inside component. Thankfully, it didn’t rain! (Up to this point, I couldn’t believe the luck I was having. The rain gods were sparing me.) We met outside in front of the Museum of Math and went to town. The Museum of Math is across from Bryant Park, so I didn’t dare bring my chalk inside of the park for fear of a garden hose. I spent the good part of an hour mathing up the sidewalk around the park. I put down close to 20 pieces. Ironically, I talked about sidewalk math to more strangers than I did attendees. This was pretty cool in its own right. One of them even tweeted about one of the problems.

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August 14, 2019: TMCNYC | This was where it all started! Bringing my chalk to BMCC in lower Manhattan was like coming home. The organizers managed to allot the session a full hour, which meant that we could take to the streets. There was a threat of rain during the afternoon, so Michael Pershan and I went out early and scouted for covered areas. Thankfully, it didn’t rain until the end of the day. I was now 4 for 4 and I was convinced that fate was on my side. I brought so much chalk that the sidewalk math continued into the second and third days of the conference. I mean these people brought it! I swear one of the teachers even had a makeshift lesson going on in front of her sidewalk math. On my last day, I went all in and created some bulletin board math at a local restaurant.

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September 26, 2019: NCTM Regional Boston | This was the grand-daddy of them all. It was the last one of the sequence and by far the largest. I was uncertain about how many people would elect to come to the session, but there ended up being over 100 people jammed into a windowless room that was desperate for fresh air. On top of that, it was the last session of the day. Called a “Burst,” it was only 30 minutes, which was nice because I didn’t really have to worry about rain since we wouldn’t have time to go outside. This turned out to be great because right after the session, Boston was flooded with the heaviest rain I have ever seen in my life. I’m most proud of the fact that no one left the session while I was presenting. When it comes down to it, that’s all you can really ask for. I was also happy that I decided to give away several boxes of sidewalk chalk during the session that were used to create some sidewalk math in the days following my presentation. I wish I had thought of this for the earlier sessions I had during the summer. Who doesn’t like free stuff?

 

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Haiku #5

As an alternative means of capturing my thoughts and reflections, I’ve been writing Haiku about my teaching practice. This is the fifth post in the series.

As my teaching has slowed through the years, I’ve been paying more attention to the furious pace with which new teachers experience their students, their pedagogy, and their practice. My awareness of these early-career teachers has matured a lot lately. And maybe I’m just getting old and doing what old people do, but I am feeling more responsible for these teachers these days — even those of whom I don’t work with directly. I love listening to them.

I had a recent conversation with a first-year teacher that struck me for a lot of reasons. It inspired this Haiku.

Teaching, you’re new here

A place where a week feels like

A lost lonely year

 

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Thinking critically about the phrase “my students”

The other day I caught myself thinking about the phrase “my students.”

We say it all the time. I quizzed my students twice last week. My students and I are going on a field trip. A few of my students always seem to come late to class. It’s ordinary and plain. We don’t even think twice about it. But this time I did.

Spurred by seeing former students in the hallway and new classes of students, the possessive pronoun “my” stood out to me this time. They are mine. Not literally, of course. But these young people who were once strangers are no longer distinct from me. They are mine. Our paths have crossed. I am now responsible for them. In the spirit of knowledge and personal growth, they are bound to me. They always will be. They are my students.

Thinking critically about this possessiveness is empowering. For me, it represents an extension of myself through my students. Who I am as a teacher — and as a person — will be duly represented in what we build together. I can ignore, but I cannot escape the metaphysical ownership I have over this situation. How I plan, teach, and learn about them will be reflected in our shared successes and failures. To think about this gives me great pride. It also affects me when it comes to non-teaching matters like how I speak to them and think about them and work to relate to them. Yes, rethinking the word “my” when it comes to my students contributes to a greater, more attentive investment in my students and myself.

 

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The mess of non-thematic units and why they excite me

For the last two years, I’ve adopted a problem-based, discussed-based approach for algebra 2. The whole curriculum is interleaved, meaning that big ideas are parsed and revisited over long periods of time (weeks or months) to improve retention. At any given time, students are learning small parts of a few different units. This allows for extended exposure to the topics that my kids learn. This is not how a curriculum is commonly viewed because, with this model, there are no traditional units. By “traditional” I mean thematic (e.g. Unit 6: Logarithmic Functions). Instead, these thematic units are broken down and served piecemeal to students over long stretches — mainly through problems. The sequencing of this model is indiscrete and quite messy.

As evidenced by that bewildering opening paragraph, I find all this terribly hard to communicate with others. I made my best effort to describe it here. It is often referred to as spiraling. I think Henri Picciotto does a good job of articulating it.

Thematic units have the advantage of being simpler…and easier too, I think. They are a slow-moving mass of closely-related topics that stays for a little while and then leaves when the next one comes along. Everything in them is directly linked and, therefore, these units make it easier for students to draw connections between mathematical concepts. At the same time, they encourage the isolation of facts and skills. Because related ideas are all lumped together, these units offer an easier pathway to a deep understanding in a short amount of time. Or at least the illusion of deep understanding.

These units make everything easier for the teacher, too. Thematic units and their associated lessons are far easier to plan and execute. The whole process linear; the focus of each lesson is based on the previous. There’s no untidy looping in and out of concepts, no systematic revisiting of big ideas over time. The concepts march in a clean, single-file line.

This is my guess as to why textbooks and traditional forms of curriculum have adopted thematic units. Seen in this way, they make the most sense both for the student and teacher.

But easier doesn’t make it better, right? When learning is hard, when it places a higher cognitive demand on the learner, isn’t it more meaningful? By helping students learn something small, then forget it, and then recall it after a reasonable amount of time — and iterating this process again and again over the course of the school year — can’t we help ideas cement? By not blocking out content, and instead spacing out practice and frequently assessing on the same topics at greater depth, do we help students better retain it? There’s research that says yes. Make it Stick by Paul Brown really helped me understand this.

There’s no denying the challenge that this creates for teachers. Tracing how concepts mature over the course of weeks or months is not easy. Adjustments to the sequencing can be tricky, too, because concepts are so tightly intertwined. I’ve been personally building the lessons and sequencing for two years and its still not right. Granted, I only work on it during the school year — and pretty much on the fly. Nonetheless, at least compared to traditional units, I’ve found it far more demanding and unusual to plan. And I haven’t even mentioned the loneliness — I have met no teachers during this time who are doing similar work with their curriculum. Who knows, maybe one day I’ll be disciplined enough to sit down and formally document my sequencing for other teachers to understand — and to start a conversation — but, I’m not worried about that.

I begin another school year in two weeks. I have realized that coupled with the fact my students retaining more information than ever, the messiness of interleaving has awakened and excited me these last few years. (I could do without the loneliness, though.) After years of marching in a single-file line, interleaving has made my curriculum work more of a dance. It’s interesting and lively. It moves. It sways. Fortunately, I work under an assistant principal and principal that given me the autonomy to do this. They decided to accept the consequences of the risks that I inherently took on when I decided to throw my units out the window. They trusted me even though none of us fully knew what I was doing. I think that I was at the right place at the right time because I’m not sure many other schools or departments would be on board with such a break from the norm of traditional units. My students and I have learned so much.

 

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