Dear Teacher,

Abigail Kirchman is a Math for America Master Teacher in New York City. She teaches at a transfer high school, The James Baldwin School, which is affiliated with the New York Performance Standards Consortium and NYC Outward Bound. In addition to the course Misleading Statistics, Abigail enjoys teaching classes such as Probability and the Lottery and Islamic Art and Geometry. Contact her with questions and ideas at @abbykirchman.

What will you do when a student asks you for a pencil? This question was first posed to me at the 2010 Minnesota Spring Mathematics Conference in Duluth, Minnesota. “Really?” I thought, “We drove three hours and gave up our weekends to learn about this?” I wanted to have real teacher debates about the philosophy of learning. I wanted new activities I could use in the classroom tomorrow. But as the conversation began, I saw there was plenty to think about.

You could ask the student for collateral … a shoe, for instance! Buy boxes of golf pencils—cheap—and guarantee a return. Refuse to give pencils—teach natural consequences. Require students to ask a friend—build collaboration. All these options for what is ultimately a split-second decision that, without a plan, can happen in every hour of every school day.

We all spend hours planning every week and make hundreds of in-the-moment decisions (in front of classrooms full of teenagers, no less). I sometimes find myself thinking, “What should I focus on? What matters? What decisions are the most effective? Most sustainable? Most important?” Answers vary.

Additionally, many of us teach in schools driven by test scores, where we are evaluated on our students’ ability to correctly bubble in an answer sheet. When this is your context, it is difficult to remember that successful teaching is not defined by high test scores. So, what, then, do we focus on to create a space where, as Socrates encouraged, students can examine their own lives? What takes precedence in our long list of conflicting priorities?

Connection—between students, colleagues, and with the content we teach—must come first.

We must connect with our students. Our students thrive on real relationships. Notice a student in a genuine way and you have a connection; do this three times and you will have a relationship. It’s a formula, and formulas only go so far. Being in the mindset of noticing, however, allows us to think about relationships and remember the humanity of the students we teach.

I used to think knowing my students meant learning their names and something about their math ability. A solid seating chart and a good diagnostic will do the trick. But my students taught me otherwise. We have to take the time to see when someone is not feeling well or is tired from work the night before. It’s our job to listen to the anxiety our students experience in a math classroom and to process the feelings of frustration during problem solving to support them in learning.

To set the tone, my first assignment is for students to write a letter that describes their math story, hopes, goals, and the information they think is important for me to know about them. It may seem counterintuitive. We have so much content to teach; how can we take this time away from the math? However, connecting with students is a necessary investment in their learning; before anyone can learn, they need to trust the people around them and feel safe.

We must create opportunities for students to connect with each other. Too often, students at the end of a semester in my class don’t even know each other’s names. I’m working on it, and it’s important to work on because a class is a community of learners.

This doesn’t mean we have to throw out individual think time or force groupwork. Rather, we have to continue to think about ways to build relationships between students. It’s so human. I’m much more likely to go to a professional development [opportunity] where I know someone versus one where I am alone; I’d prefer to be at a party with my friends than with all new faces.

In the classroom, I am trying to use seminar structures that require students to use each other’s names and recognize each other’s ideas. I also use and create tasks with roles in which students must depend on each other to be successful. Additionally, think-pair-share and other discussion protocols support student conversation in a nonthreatening manner.

When we give students structures within which to work, we enable them to interact with safe social expectations and avoid awkwardness. People feel comfortable and are able to focus on learning and inevitably build community. It’s our job to create this environment, where all students are accepted and can take the risks necessary to learn.

We must connect with our colleagues. Being a good teacher requires connecting with our colleagues in addition to connecting with our students and supporting spaces for them to connect with each other. Just like our students, we need support and community to empower our students.

The traditional image portrayed of our career is that of the individual teacher alone in the classroom. But lone teachers cannot fully support a classroom of diverse learners. Today, we have the benefit of various learning experts in the form of special education teachers, English as a new language teachers, social workers, and paraprofessionals. Each of these educators can lend a different viewpoint to our students and our work.

By listening to other’s perspectives, I have learned how to shift my classroom structures to be more accessible, equitable, and inclusive. My colleague called to my attention my grading system, which penalized students doubly for not understanding concepts. He helped me develop a new system focused on content mastery. Students began to talk about their growth in terms of learning targets, rather than meaningless percentages. In the new system, students can attempt to show mastery on learning targets multiple times and in a variety of ways. Now, their grade is linked to the learning. A small shift in my thinking, in collaboration with a colleague, made a substantial difference in the communication between my students and me and their confidence in their ability to learn.

Connecting with our math departments provides another invaluable space to improve our practice. In my math department meetings, we spend time analyzing and revising tasks, building and trying structures, and visiting each other’s classrooms. Together, we can diagnose and address misconceptions and concerns related to the mathematical understandings of our students. When we noticed students were struggling to verbalize their thinking, we modified a double-entry math journal to help them record reasoning during and after problem solving. The tool supported students in communicating their ideas.

One student in particular comes to mind. This student had presented her final paper to a panel of three evaluators and failed. We knew she understood the concepts, but her explanations were incomplete. To prepare her for the revisions, we gave her the double-entry math journal to organize her thinking. The difference between her initial communication of ideas and her revisions using the tool was phenomenal! She shared that she felt finally able to express her mathematical thought.

Our departments enable us to mathematically support our students in a way that is specific to our own settings. Without these teacher-to-teacher connections, we miss out on opportunities to improve the learning and success of our students.

Beyond department meetings, we often work together across grade teams and content areas to meet the goals of the school. When participating in interdisciplinary planning, colleagues from other content areas will often suggest statistics: “Can’t you relate some stats to that? You could teach the stats around …” Our colleagues are right! Statistics is inherently connected to a wide range of content, specifically with regard to issues relating to our students’ lives. Unlike algebraic fractions or asymptotes, statistics lives in a context, and students should never have to ask how our class relates to their lives.

With our current access to data, connecting students with content is easier than it has ever been. In my Misleading Statistics course, students receive data from their own city. They consider what may be related—perhaps average death age and smoking rates in neighborhoods in the Bronx? Or percentage of population with a high-school degree and average salary across Brooklyn? Students select data for real questions they have. Does high school really have an impact? How bad is smoking? As they work through their statistical analysis, students are engaged in their own questions and their own data. Through this work, they are truly statisticians. I don’t know the answers any more than they do, which sometimes feels uncomfortable as the “teacher,” but, together, we learn about the world through the perspective of statistics.

Of course, being in New York City has its advantages; we are inundated with data about our everyday lives. (My favorites are Infoshare Online, which has a variety of New York City and state data, and City Digits, created by Brooklyn College and MIT’s Civic Data Design Lab.)

In our post-NCLB [No Child Left Behind] era, there is also no shortage of data within our schools. My students’ final statistics project was to analyze data within their community by studying attendance and grades in various classes. In our transfer school setting, many of our students struggle with attending class due to health issues, family concerns, and, sometimes, motivation.

We asked, “What is the relationship between being in school and achieving academically as measured by grades?” Students worked in teams to study different class periods throughout the day. Using anonymous student data and Desmos—a free online calculator—students modeled the data, represented it graphically and algebraically, and analyzed the correlation. As many students had correctly predicted, they found attendance to be highly correlated with grades.

After revisions and edits, students presented their findings to our attendance team—a group of administrators, social workers, and support staff—which developed a dialogue between students and faculty. This gave students voice and ownership in a conversation that otherwise can feel artificial and imposed. Unlike previously, we weren’t talking about students in a closed-door room; rather, we included them in the conversation as part of the community. Students felt proud to do meaningful, relevant work.

Connecting All Around

In my efforts to connect, I often fail. Sometimes, I make wrong assumptions about contexts that will relate and topics that will motivate. I’m normally about two years behind the trends (I finally learned about Snapchat!), and my contextual references can fall flat.

Finding what truly connects to students requires careful and constant listening. Only by connecting to our students can we find the math that connects to their lives. To that end, it’s not just okay—but necessary—for us to ask our students questions about what is relevant and interesting to them, especially in our ever-shifting culture. (Myspace is over, by the way.) We should build in time to understand what students are thinking about and bring it into our classrooms.

Teaching is a privilege; it is also extremely difficult. The first years, in particular, present an exhausting amount of social and emotional thinking, as well as the challenge of creating learning spaces for many learners at the same time. Sometimes, it seems impossible and we lose our own sense of humanity in bathroom-less days and late nights.

Teacher dropout rate is a real concern, and so we also should consider what keeps us well and in the classroom. As we work to connect with students and content, we naturally connect to the work. Among the many decisions—from pencils to grading systems to content—it is convenient that, by prioritizing the connection with students and content, we are sustained and motivated to continue. By connecting, we too remain connected.

With the beginning of a new school year comes a fresh start. Don’t stop at the seating chart and textbook. Get to know your students and find content that connects to them.

Best of luck,

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