Math Haiku

Last year, after chatting with some of my students about their poetry, I decided to attend a free poetry workshop at my local branch of the New York Public Library. The focus was haiku, a form of poetry that, despite not writing many, I’ve always found appealing ever since I was asked to write one in second grade.

Haiku is a succinct art form that forces you to be strategic in your decision-making. With 17 syllables to work with, there’s little wiggle room in a haiku. Because its syllabic nature is numerical (5-7-5), like math, it demands logic and efficiency. Carefully chosen words and phrases are the expectation, yet ideas must be surfaced and communicated with precision. Beautiful math is often considered elegant, and haiku mirrors this in its simplicity. Even then, because of its brevity, most haiku are open to multiple perspectives. It’s kind of hard to establish a context with 17 syllables.

After the workshop, with newly-discovered energy to unearth my inner-poet, I started writing my own haiku. It’s been quite fun. To have more of an appreciation for its Japenese roots, I’m reading about the history of haiku in On Haiku by Hiroaki Sato.

At any rate, around the same time as the workshop, I came across Patrick Honner’s post about math haiku. Wanting to enrich the writing that I’m doing in my students, all the while bring my budding interest of haiku to them, I followed up with Patrick about his post earlier this year. He didn’t disappoint. About two weeks ago, I asked my kids to write two math-themed haiku. Teenagers’ creativity never ceases to blow me away. Here is some of their haiku:

 

to find the inverse
we must flip the y and x
then we solve the rest

 

life, like factoring
grouping ourselves to fit in
to find we’re alone

 

one plus one is two
two times two plus one is five
five, my favorite

 

if you need some help
ask the mathematician
who’s that? look within

 

the missing value
was fading in confusion
after being solved

 

squares have sharp edges
but they have 90 degrees
it is like summer

 

it is an odd plot
for the positive function
to graph negative

 

between the sequence
lies a common ratio
use the equation

 

allow math inside
a stream of numbers and facts
filling the silence

 

math is made for whites
that is the common stigma
that idea should change

 

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Was I Going to Be Arrested? (crosspost)

This post was originally published in the Tiny Teaching Stories feature of Education Week. Special thanks to Catherine Gewertz for the opportunity.

As I ushered students out of my 5th period class, a police officer was waiting for me outside the door. My heartrate spiked. I sheepishly approached him. Was this really happening? Was I going to be arrested in front of my kids? What did I do? My career is over.

We locked eyes. He said, “Is the answer 13?” Startled, I paused. Huh?

Suddenly, relief fell over me. My anxiety lifted. I confidently replied, “No, there’s more. Keep at it.”

He was just checking his answer to the Sidewalk Math problem I created in front of the school. Whew.

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Burn 5 minutes

I think early and often about relationships, classroom culture, and how both affect learning — and learning math in particular. Last year I wrote about how I try to resist the expectation that content must supersede humanness. I’m getting better, but I’m still prone to neglecting the social fabric of my classroom in favor of shoving content down the throats of students. I have seen and felt this from other teachers, too. But this content-vs-humanness predicament not entirely on us. The pressures from our district, our administration, and parents are real and seem to be getting worse. As more and more demands and expectations are placed on us, we’re faced with few alternatives other than to place a firm emphasis on content and move on.

On top of all that, learning is hard. It’s devilishly tricky to fuse new knowledge with old.  And there’s a ton of hidden baggage that our kids carry, too. About math, about learning, about what kind of student they’ve been told they are. This only adds to the complexity of the work.

But neuroscience tells us that our brains need strong social connections in order to flourish. To help someone learn, to help them consolidate what they now know with what our curriculum says is important, requires a relationship. It calls for an honest, unconditional exchange of self on behalf of the student and teacher. Surely this involves sharing an understanding of math, but for me, our relationship must exist outside of math and outside of the curriculum. I work with my students to acknowledge the gravity of this and why I’m so serious about the bond we share. Our relationship is an intimate one and does its best work when deep, trusting bonds can be created and nurtured between teacher and student. That’s what I believe, at least.

Knowing this doesn’t make it any easier, though. My ambivalent struggle to balance the weightiness of content with authentic relationships is ongoing. In my wonderings, the opening of class has been a focal point. I view it as a critical time for my students, a moment of their physical, psychological, and emotional arrival. As such, I see value in engaging them as humans before I engage them as emerging mathematicians. It’s an opportunity to plug into one another again. The past 24 hours have chewed us up and spit us out and now we’re back here, together, hoping to be better than we were yesterday. Before our energies shift and get tangled in math, I’ve come to savor this magical reunion that I have with my students each day.

I show this by moving our opening conversation away from math. After the Bell Ringer, no matter what’s on the agenda, I deliberately pause, find eyes, and ask how everyone is feeling. We popcorn out about our lack of sleep or celebrate how someone caught the bus this morning by the narrowest of margins. We then fill the next few minutes with informal dialogue. House talk. It could be about a thought-provoking book, a funny moment from the hallway or cafeteria, or how someone’s new baby sister is doing. I will often ask students to share something kind they did for another person that day. Or something that has made them think. It’s can be a lot of things, but no matter what, it captures what we’re thinking or feeling at the moment. It’s a casual check-in with nothing on the line.

Unscripted, it lasts all of five minutes. Then we’re on to discussing homework or whatever else is on tap. I know some of my colleagues call for every second of every period of every day to be a one way street to math or whatever else is being taught. This is fair. But in a content-driven school system that, despite lionizing social-emotional well-being of students, still manages to exclude it from its bottom line, this is my push back.

Last year, I read Matthew R. Kay’s Not Light, But Fire, a book on a mission to help teachers bring meaningful race conversations into the classroom. One of his prerequisites is building conversational safe spaces with our students. Like me, he also uses the start of class to “Burn Five Minutes,” as he calls it, to reorient students to the space and connect with them as humans. His rationale is far more eloquent and polished than what I’ve done with this post, so I’ll close with an excerpt from chapter one:

[When I burn five minutes, I] acknowledge students are thinking people who hold opinions independent of my curriculum…I show them that I find them worthy enough to warrant five minutes speaking as equals. (At the beginning of class, no less. Consider the difference between an athlete being asked to start a game and being invited to play in “garbage time” at the end when the outcome is obvious. That’s the difference between starting class with informal conversation and mopping up extra minutes with it.)

This time commitment is minimal, until one steps back and considers that five minutes a day becomes nearly two hours of informal chatter over the course of a month. This banking of conversational democracy buttresses all other classroom dialogue — students can take more risks, and our classroom culture can survive more mistakes, because students are less likely to consider our respect for their opinions either disingenuous or capricious. We build with them every day, and not just about things that they will eventually be graded on.

 

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What if teachers were encouraged to be students?

Last year, my school did intervisitations. It was nice, we visited each other’s classrooms and met afterward to debrief. I mainly visited English and AP Environmental Science, and having spent months sprinkling myself into these classes, there were plenty of takeaways. One of the biggest, though, had nothing to do with taking low-inference notes, thinking about questioning, or any other activity that usually finds its way into a typical intervisitation.

I wanted to learn what was being taught. Being haphazardly obsessed with learning, I couldn’t resist myself as I started to see my colleagues’ classes as avenues to knowledge. It was expertise served hot, fresh, and free each day. Best of all, it was right down the hallway — not at a local university or behind a URL. It was accessible. All I had to do was walk in and sponge it up. (Thankfully, I work with folks who are open to this.)

So as I journeyed through my colleagues’ lessons, picking apart assessment strategies, my student-like curiosity began to overthrow the teacher in me. I started to wonder. The more classes I visited, the more questions I had. In world history, why was the Roman aqueduct an engineering marvel? In science, how do the eating habits of certain animals evolve? In English, how do you write an effective profile?

As my school’s ocean of knowledge revealed itself, I dove in headfirst. I audited one unit of grade 10 English near the end of last year. This year, I’m taking physics for more than a semester. I’ve cashed in one of my two free periods to become an unofficial student.

It has been fun. I attend class every day, scribble down notes, do homework, sweat over exams. I’m sitting on tables thinking about the inclined plane with students who I teach in algebra 2. Instead of being tethered to my computer for 45 minutes, I now use 8th period to wrestle with ideas, lose myself in unfamiliar problems, mess up, and fill my time with ah-ha moments. It’s thrilling.

This renewal of thought that comes from being a student again makes me think. What if teachers were required, as part of their teaching load, to take a class at their school?What if teachers were encouraged to be students? What if we sat alongside some of our own kids in a class and learned with them?

The initial reaction, mainly from rank and file folks like myself, is probably, we have so many things to do already, how could we have time for this?

While that sounds a lot like a symptom of No Time Disease, I get it. I’m voluntarily giving up my prep period to take a class. It’s a tradeoff that I find worth it, but which can’t be expected from the average joe. But what if taking a class was built into our schedule? What if we taught one less class so that we could then enroll in one?

In addition to having a more intelligent teaching corps who is more capable of making connections between disciplines, this may also serve us well with how students perceive us. If we were in their classes learning with them as equals, and they are literally able to see us first not as teachers, but as learners — as humans grappling with new knowledge as a means to better understand ourselves and the world — then maybe they will be more apt to do the same. Maybe.

 

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