As the Spring term ends, I thought I’d share with readers two vignettes from my teaching career. The intention is for us to remember how much of teaching is the emotional connection between student and teacher. For me, this is the reality of the experience, and is what makes possible the communication of mathematical ideas.
- Completing the Square
This first story started when I got a terse note from the high school guidance office about James:
“James has a difficult situation at home. Any leeway you can grant him about deadlines, tests, or quizzes would be greatly appreciated.”
Well: my classroom was run with very few deadlines. Students could re-take quizzes and tests whenever they learned the material, except that I had to report to their parents quarterly about their progress, at which time they got a grade.
So it was easy for me to meet James’ needs.
What was the ‘difficult situation’? I didn’t know, and it didn’t really matter. From the cryptic note, I assumed it was a divorce, and that the family was not anxious for everyone to know. But it could have just as well been a marriage: a new step-parent or step-sibling can take some getting used to. Or it could have been the birth of a new, much younger sibling. Any one of dozens of such circumstances looms large in an adolescent’s life. It didn’t matter to me–James needed to be cut some slack, so I cut it.
James was surly, a sure sign of instability in his life. He made little irritating comments, usually addressed to me–within the bounds of adolescent propriety, but on the rebellious side. Something’s going on, I thought. Of course, it wasn’t really me he was angry at. I was an authority figure and he needed a target. I was willing to play that role for him. I have found that the most constructive way to deal with this situation is to ignore the barbs and engage whenever the student shows a more positive side.
So I found ways to dodge his anger and get at the person it was hiding.
James had a habit of wearing bright orange gym shorts. I took to teasing him about them. “You’ve got to get rid of those shorts!” I would say, in various ways. James loved the attention and developed a variety of snappy comebacks. Eventually, he mellowed, promising me a pair of orange shorts as a gift at the end of the year.
James often asked to leave class during the lesson. I knew full well that he didn’t have to use the rest room and was hanging out with friends in the hall. I went a step further, asking myself why he was not engaged in school, and what he might need in his life in order to continue attending school. I knew there was an answer, thanks to the note from guidance. But I didn’t know what it was.
James was getting a straight C in the class. He wasn’t closing doors to mathematics, but couldn’t find the resources in his life to take the next step. I waited to see what I might do.
In April, his father called, angry. Why is James getting a C? He has to go to a good college. I went to Harvard business school. A C is simply not acceptable. Why wasn’t I notified earlier that James was doing so poorly?
In fact he was notified, quarterly, of James’ progress, but didn’t respond. It turned out that he had a lot on his plate. During the conversation I found out what the matter was. His wife, James’ mother, was dying. She had been in and out of the hospital for treatment, and was getting ready to leave her family, and this world, forever. Now I understood fully James’ anger, and his father’s anger.
We all feel helpless in these situations. There’s not much you can do or say. I told James’ father what a wonderful son he had, how James was doing a great job keeping his life together during this crisis, how he might not get the greatest grade, but that he would eventually be able to recoup his academic losses. In this most difficult yet of James’ years on earth, I said, it is amazing that he is able to keep up a C average in a difficult subject. These comments dulled the father’s hostility. I was part of the solution, not part of the problem.
After this call, things got better between me and James. He knew that I was aware of his problems, and sympathetic to them. He looked me in the eye when he asked to leave the room and made arrangements to retake quizzes he had done poorly on. Luckily, James learned mathematics easily, and a few sentences from me set him back on the right path when the work got tough.
I was moving from one classroom to another the next year, and part of my daily routine was searching the school building for useable cartons to pack away a 30-year accumulation of books and materials. One day, I found two empty cartons in the delivery room, and was carrying them down the hall when I passed James.
He was stretched out on a bench in the hall. “Do you need any help with those, Dr. Saul?”
I really didn’t, but he clearly wanted to engage me. I decided to accept the invitation. “I’d love some help, James. Would you like to help me pack some books?”
We went down to my classroom. James and I talked about the books we were packing, how heavy they were, who had written them, who had given them to me–and eventually how it feels to be living in a house with a dying parent.
Then he said, “My mom is going into the hospital again, for a week.”
I gave James what I could–mostly the same words I had for his father, and especially how a C average is not so bad, given what he had to handle outside of school. He couldn’t stay too much longer, because he had an appointment with the dean at 3:00. I told him I was glad for whatever help he could give me, and not to be late for his appointment.
Later I met him in the hall, where he told me that he his appointment was actually with a ‘cute girl’. I told him that I knew what that was like, and that we all shared certain feelings in life. And that we are not alone in handling them. He looked at me and smiled. He knew that I wasn’t just talking about cute girls.
The next day, I met James in the hall again. He had come to math class, but left in the middle, and hadn’t returned. We were working on completing the square, a challenge for this group, but a challenge they must meet if they are going to attach any meaning at all to the quadratic formula.
After an exchange of pleasantries, I asked James, “Do you know how to complete the square?”
“Yeah, it’s not that hard, except when you get fractions.” It was clear, from the way he answered, that he knew how to do it, and had practiced it enough to know where the difficulties lay.
“So come and take a quiz when you’re ready,” I said.
“Okay.” James looked down. Then he looked up at me. “Dr. Saul,” he said, “Give me a hug.” I quickly obliged.
Sometimes it is as important to complete a circle as to complete a square.
- The Chain Still Holding
“That building–that’s what scares me.” It was Ivan who said this, pointing to the Hancock tower in Boston, across the river. I was sitting with him on the MIT campus, talking about his problems adjusting to America. A brilliant mathematics student, he had come from Bulgaria for six weeks of study with equally gifted American high school students at a summer program I ran here. He was 17 years old, and the year was 1993.
I had noticed that Ivan was too much in his room, not playing enough Frisbee, not bonding with other students. My job was to draw him out. So we were sitting, late one night by the banks of the Charles River, and talking heart-to-heart.
“That building scares me,” he repeated. “America goes too fast, too far. The people move quickly. The cars goes fast. The food tastes like…nothing.”
We took our meals in a student cafeteria.
“But don’t you have trouble getting food back home?” I queried. The American experience was overwhelming him, and I hoped to turn him towards its positive aspects.
“Yes. It is difficult. Prices have risen and salaries have not kept up.” He paused before taking the bitter medicine: “I think, wherever Communism has come, it leaves garbage behind.” His face got hard, and he was silent for a bit.
Then, “I dream each night of having breakfast at home.” Home was Dobrich, a town in an agricultural area of Bulgaria which Ivan considered “not too small.”
His monologue was strangely compelling. There was some reason why I had to listen, had to respond, to the expression of bewilderment, of events running away with him, and of his own country and his own upbringing, betraying him.
For a while I didn’t understand my own reaction. And then, slowly and quietly, understanding came over me. I suddenly felt like a link in a chain, a stitch in a fabric.
There are moments when the meaning of life overwhelms you, forces itself into your consciousness, and thrusts still deeper, into your unconscious mind. Suddenly, Ivan’s confusion and awe, and even the tears he was clearly holding back, were mine as well. It wasn’t a tall building that scared him. It something greater.
In 1913, my grandfather Froim arrived in America from a small town in east Europe. Mother Russia had become more of a warden than a guardian to her Jewish children, who were leaving in droves to build America. Stories of his confusion have become family legends. When someone showed him the subway to the Bronx, he thought he was going down into a root-cellar. His cousin, who had arrived two years earlier, had to teach him how to drink liquids through a straw. Seeing the Woolworth building from afar, he tried to walk over for a closer look. But he didn’t realize how big it was, and how far away, and spent his whole lunch hour getting nowhere.
I grew up with these stories. But why did I react to them so strongly? Why did my soul vibrate, hearing them? Could it have been because I knew I would be having this conversation in Boston? Was it for this moment that my grandfather repeated them to me, these stories that took place in 1913, and were told me in 1963? Are these messages sent across the years, from one struggling immigrant to another, with myself as the medium?
It was more, though, than giving back to Ivan what my grandfather had given to me. More: I was Ivan, I was Froim, and I was at the same time a father and grandfather to both. They say this happens, that the roles reverse as one grows older, and you begin to care for your parents as once they cared for you. But I didn’t expect these feelings at forty-something, with both my parents in good health. I wasn’t ready.
“The child is father to the man,” says the poet. I hadn’t felt the feeling to these words so strongly before, and was overwhelmed.
And I wasn’t ready for the brush with eternity that these feelings would bring, of a contact with events that happen over and over again, and so occur outside of time. It’s not just the experience of the immigrant, or the foreigner. It’s the experience of the child and the parent. Somehow, in this conversation, with a youth I hardly knew on the banks of a dark river, I felt a contact with the future as well as the past. My own children, and their children, will feel these feelings, will go through these experiences. And my adventures will become their legends. The chain is still holding, the fabric unrent.