I’m a hoarder of student work

I’m fascinated with the charm of student work. There’s something really inviting that my students’ feel about being asked to analyze and discuss someone else’s mathematical thinking. For whatever the reason, there’s a lure to it. If I project some anonymous kid’s work as they walk in the room, for example, it captivates them from the moment they glance at the board. It’s so bad that many won’t even put their bag down at their desk before they begin thinking about the work. Whether the work has errors or not, it almost never fails to pique their interest.

Other than generating student engagement and learning, the class discussion around the work often helps me better understand the student’s line of thinking, too. I regularly struggle to figure out my students’ thinking. By pitching the work back to them (anonymously, of course), they help me figure out what’s going on in the work in ways that I would not have been able to otherwise.

As a teacher, this is gold. But deep down I can’t help but wonder why they get so into it. Maybe it’s because I’m not asking them to actually do any computation? Maybe they’re trying to figure out if they did the problem correctly themselves? Maybe it’s the specific samples of student work that I’ve selected that are just nuanced enough? There has to be an interesting psychological aspect to this that I’m unaware of. I think the human element that comes with using a person’s written work to learn math may be at play here. It’s not neatly constructed on MathType or Latex or Google Docs. No, it’s human thought presented in one of it’s purest forms. Let me stop, I’m getting too deep. I’ll save that research for another post.

Because of all this, I’ve been hoarding student work. For the last two years, I’ve been collecting everything that I can get my hands on. Quizzes, exams, journals, you name it. I’ve been scanning, studying, and filing it all away.

But how? Scanning individual papers can take forever. Well, I’ve found student work to be so useful that it has forced me to rethink my assessments for the sole purpose of being able to scan them more easily. The idea is that I use scanned student work (and not just the overall results of the assessment) intentionally to further student learning. As long as it doesn’t take forever, or even more than 30 seconds for an entire class for that matter, why give an assessment if I can’t collect and leverage students’ written thoughts?

The most obvious example of how I’ve adjusted assessments to help me easily scan written work is exams. I never make them more than a single page (front and back). When I first started doing this a couple years ago, it had nothing to do with scanning student work and had everything to do with being lazy. I refused to take more than a day to get the exams back to the kids and knew that I wouldn’t be able to live up to this expectation if the exam was three pages of problems. I rarely give multiple choice problems and, if I do, I still require work.

Despite my laziness, over time I saw the real value in my one-page exams as being able to scan my kids exams quickly. Given the multifunction copier at my school, my exams serve an important purpose: they eliminate the need for stapling. Without a staple, each students’ thinking is contained in a single piece of paper — and this makes them dump-easy to scan. Before I mark the exams, I simply place them in the document feeder, hit scan, and they zip through one-by-one. Voilá, 15 seconds later, I have a PDF in my inbox of every students’ exam. Done. The same works for quizzes, too.

As I mark the exams, I take note of interesting examples of student thinking and grab a screenshot from the PDF. These samples usually become the focus of the opener for our post-exam reflections the following day, but also become features of future problems. I’ve framed the student work in different ways, mainly based on what I’ve seen other teachers do.

There’s the classic, What do you notice? What do you wonder?

There’s also the clever debate prompt, Who has a better error?

There’s even Algebra by Example tasks that use an example (often an incorrect one) to elicit a Why…? and extend student thinking.

Although I fail to ask Why? about any step of the example, here’s one of mine:

Another is the simple question, What do you think? Here’s one I projected last Thursday, the day following their exam.

Generally, restructuring exams so that all student thinking fits on one page is not trivial. It requires that I include less content on the exams and can affect how bunches of concepts, and big ideas, are taught and assessed. But this also means that, since I’m grading less per exam, I can test more frequently in smaller pieces. The exams arrive in smaller, bite-sized chunks rather than in all-encompassing behemoths. This is better for everyone. The kids like having less stuff on exams get more immediate feedback. I’m grading less per exam. And on top of the benefit of scanning and producing a goldmine of student work, I love it because I can be more precise and granular about which concepts I assess and how I assess them.


Dear E, (Student Letter #2)

To help me be more critical and mindful of the bonds I’m forging with individual students, I write anonymous letters to some of my current and former students. This is the 2nd post in the series.

Dear E,

I noticed early on what your passion was: art.

Boy-oh-boy, you were always drawing in class. While we were discussing geometric sequences, you were doodling another character. At first, I wanted to tap your desk immediately — and most times I did. I had to. You were struggling to grasp concepts and I was worried about you. I didn’t want you to fall too far behind.

But as the months passed, and the more frequently I observed you drawing, the more appreciative of you I became. After learning from another teacher of the pretty rad animated short film that you made, I realized that what I thought was doodling, was in fact so much more. It was — and still is — a definitive part of your identity.

Fascinated, I started picking your brain. I wondered how all this works for you. I tried to imitate your (famous) cat drawing. I thought it was pretty good. I even asked you to teach me how to draw.

Then, after winter break, you shared with me — and the entire class — that your New Year’s resolution was to improve at math. I was proud of that goal and how you made it public, but I’m prouder of the progress you’ve made in reaching it ever since. E, I see a change. I’m glad the notebook that I gave you is helping. You have deeper thoughts now, more to give. More to share. You’re more engaged now than you ever have — you were even giddy over an exponential modeling problem the other day. I’m impressed to see this side of you that I always knew was there.

It’s hard to admit that when I see you drawing in class nowadays, I don’t rush in to bring you back to math. I pause. You’re in your own world, doing what you do. Your appetite for a good drawing is hard to interrupt. I know, I know, there’s a place and time for that — and it’s not in math class. I guess I’m not a teacher’s teacher because there’s something about you being immersed in what you acutely love during class that doesn’t bother me as much as it probably should. I wait as long as possible before I tap your desk, bringing you back, stopping you from finishing a nose or eye or mouth.

When that happens, my bad. But can you show me the finished product after class?


Mr. P

P.S. By the way, I’m still waiting for my first lesson.

No Time Disease

Unexpectedly, I’ve noticed 3 things that my students are doing this year:

  • They are writing about math.
  • They are reading books.
  • They are using math to talk about social issues.

I mention these things not because I’m helping my students do any of them well. (Though we have been at it all year, a lot of kids still see no purpose in writing about math, for example. And I’m pretty sure that I haven’t helped their writing grow in any meaningful way.) No, instead, I bring these things up because they are symbolic of how to I’ve learned to deal with my No Time Disease.

Oh, sorry. What is No Time Disease? If you’re a teacher, you know exactly what I’m talking about. You have it. I have it. In fact, we all have it and there’s no cure, but some of us are better at coping with its symptoms than others. I know I’m learning. No Time Disease makes us sacrifice what we know to be important and worthwhile for our students because it conflicts with systemic and bureaucratic constraints. It makes us think we have no time for what really matters.

Take race, for instance. Integrating discussions about race in math class is practically forbidden. Bring up race at almost any math PD across the country and see what happens. You’ll hear crickets. And get stares. But assuming that the teacher gets the racial undertones of teaching math, which is an obstacle in itself (especially if you’re white), bringing conversations about race and math to our students often triggers thoughts such as:

  • I’m not sure how that will fit into my polynomial functions unit.
  • Our departmental goal is annotation…and that takes up so much of my energy.
  • Our school-wide goal is the lowest-third of students, so that’s my focus.
  • With all the standards that I need to cover, talking about race isn’t going to help them on the state exam.
  • I wish I could do it all. There’s just no time.

We’re great at coming up with lots of reasons that make us believe that we don’t have enough time to implement things that matter to us, helpful things that will help our students navigate the complexities of society. These excuses are symptoms of No Time Disease. They generate doubt. They force us to think that we can only do what the Common Core Standards or our school or our district says is best. They persuade us to think that we have no time for what we understand to be humane, relevant, and necessary.

I know this because my own values are changing. Looking back to just a few years ago, even if I had thought that writing, reading, and exploring social issues were valuable practices for teaching high school mathematics, my No Time Disease would have stopped me from doing anything about it. There would have been something that came up, something that would have justified my avoidance of what I knew to be important.

It’s not that we don’t have enough time for the stuff what we value, it’s that we instead make time for things that we don’t. Consciously or not, we prioritize. The decisions we make every day reveal what we believe is the best use of time. We teach in classrooms that reflect who we are and what we think matters. It may be annotation or a high passing rate on the state test or race. It may be all three. But this is why having my students write about math, read, and talk around social issues is so big for me. Those are teaching tools that actually represent me and what I’ve been passionate about for a while. I’ve never felt closer to my students than I have this year. I think this is a direct result of mindfully investing my own self into the learning process of my students, intentionally merging my passions with my instruction.

This requires a lot of tradeoffs. It means that I might get a lower teacher rating at the end of the school year because my kids did less test prep. It might also mean that my students may dislike me for part of the school year. I might catch heat from my admin. I’ll have to step out of my comfort zone. We may not even finish the curriculum. But I have to be able to accept these things and know that it’s worth it because my teaching will be more humanistic, more authentic, more wholesome.

It’s a tough pill to swallow, but a necessary one if I want to suppress the symptoms of No Time Disease.




Dear K, (Student Letter #1)

To help me be more critical and mindful of the bonds I’m forging with individual students, I’ve decided to write letters to some of my current and former students. This is the first post in the series.

Dear K,

“They have never done anything productive in my class.”

That’s what I overheard another teacher say about you recently. Knowing the teacher, he meant no harm. He really didn’t. He was in the moment and, like most teachers, stressed out about something. But intentions are beside the point. His comment struck me as bold and unbelievable. It was around this time when I realized just how misunderstood you are.

I’ll admit, I was hard on you when we first met. You knew what you wanted and you let everyone know what it was. You were intense and playful. I didn’t like this. I found your energy disruptive. I found it troubling that I didn’t know what to expect from you each day. Would you be cooperative and work hard? Would you put your head down the period? These are the questions that came to mind when you walked in.

Over time, for whatever the reason, maybe I was tired, I slowed down. I talked to you. I learned you. I stopped judging you. Our chats, which have happened right smack in the middle of class, have helped me discover our mutual love of reading, of books. I’ve told you about my writing. We came up with the idea of sharing our favorite books with one another. Because I read and write so much and talk about my reading and writing so much, one day you jokingly asked me, “Mister, why don’t you teach English?” I laughed.

So I have to thank you, K. By letting me into your world, you’ve reminded me to seek out my students’ passions. Whatever they are, I need to find them. There’s so much that teachers can learn from students if they just ask. Meaningful teaching and learning don’t always have to be connected to an Aim and Do Now. You’re proof of this.

I think you’ll remain unpredictable to me. I like that. In fact, I’ve told you that I think you’re unpredictable, and you’ve said, “I need to change,” as if you being unpredictable is a bad thing. If no one else tells you, at least I will: don’t change! The world needs your freshness. People don’t see the world like you do; you refuse to conform and speak out when something’s on your mind. Don’t let others, even your teachers, make you feel that you need to leave your true self at the classroom door, either. Bring it every day. Yes, I hope more teachers learn to appreciate your joyful, yet fiery, presence. They’re really missing out.

I look forward to reading your favorite book. Do you think we can talk about it after class instead of when we should be learning how to factor polynomials? Just a thought.


Mr. P

P.S. By the way, I don’t teach English because I don’t want to. I don’t want to read Shakespeare or Chaucer. I want to teach math. I love math. I also love to think about teaching math. And as William Zinsser said, “Writing is not a special language owned by the English teacher. Writing is thinking on paper.” Reading and writing help my passion for math, learning math, and teaching math come alive. Also, reading takes me to far away places — sometimes through math, sometimes not. And I like being in faraway places.