And what about the other direction? Drop down six from the perfect eighteen bodies and we have the Last Supper. And that’s the problem. Twelve is small enough to fit around the holiday dinner table—too intimate for many high schoolers to protect their autonomy on the days they need to, and too easily dominated by the bombast or bully, either of whom could be the teacher herself. By the time we shrink to six bodies, there is no place to hide at all, and not enough diversity in thought and experience to add the richness that can come from numbers.
The small class is, in other words, potentially as difficult for a teacher to manage as the very large class. In one case, the problem is the number of potential interactions to manage. In the other case, it is the intensity of the potential interactions. As another teacher memorably put it, when a class gets too small, the students start acting “like siblings in the backseat of a car. There is simply no way for the cantankerous kids to get away from one another.”
Here’s another comment from a high school teacher. He had recently had a class of thirty-two and hated it. “When I face a class that large, the first thought that I have is ‘Damn it, every time I collect something to mark, I am going to spend hours of time here at the school when I could be with my own kids.’” But he didn’t want to teach a class of fewer than twenty either:
The life source of any class is discussion, and that tends to need a certain critical mass to get going. I teach classes right now with students who simply don’t discuss anything, and it is brutal at times. If the numbers get too low, discussion suffers. That seems counterintuitive because I would think that the quiet kids who would hesitate to speak in a class of thirty-two would do so more readily in a class of sixteen. But that hasn’t really been my experience. The quiet ones tend to be quiet regardless. And if the class is too small, among the speakers, you don’t have enough breadth of opinion perhaps to get things really going. There is also something hard to pin down about energy level. A very small group tends to lack the sort of energy that comes from the friction between people.
And a really, really small class? Beware.
I had a class of nine students in grade-twelve Academic French. Sounds like a dream, doesn’t it? It was a nightmare! You can’t get any kind of conversation or discussion going in the target language. It’s difficult to play games to reinforce vocabulary, grammar skills, et cetera. The momentum just isn’t there.
The economist Jesse Levin has done some fascinating work along these same lines, looking at Dutch schoolchildren. He counted how many peers children had in their class—that is, students at a similar level of academic ability—and found that the number of peers had a surprising correlation with academic performance, particularly for struggling students.5 In other words, if you are a student—particularly a poor student—what you need is to have people around you asking the same questions, wrestling with the same issues, and worrying about the same things as you are, so that you feel a little less isolated and a little more normal.
This is the problem with really small classes, Levin argues. When there are too few students in a room, the chances that children are surrounded by a critical mass of other people like them start to get really low. Taken too far, Levin says, class-size reduction “steals away the peers that struggling students learn from.”
Can you see why Teresa DeBrito was so worried about Shepaug Valley? She is the principal of a middle school, teaching children at precisely the age when they begin to make the difficult transition to adolescence. They are awkward and self-conscious and anxious about seeming too smart. Getting them to engage, to move beyond simple question-and-answer sessions with their teacher, she said, can be “like pulling teeth.” She wanted lots of interesting and diverse voices in her classrooms, and the kind of excitement that comes from a critical mass of students grappling with the same problem. How do you do that in a half-empty room? “The more students you have,” she continued, “the more variety you can have in those discussions. If it’s too small with kids this age, it’s like they have a muzzle on.” She didn’t say it, but you could imagine her thinking that if someone went and built a massive subdivision on the gently rolling meadow next to the school, she wouldn’t be that unhappy.
“I started in Meriden as a middle-school math teacher,” DeBrito went on. Meriden is a middle- and lower-income city in another part of the state. “My largest class was twenty-nine kids.” She talked about how hard that was, how much work it took to follow and know and respond to that many students. “You’ve got to be able to have eyes in the back of your head. You’ve got to be able to hear what’s happening when you’re working with a particular group. You have to really be on top of your game when you have that many kids in a classroom so that over there in a corner, they’re not just talking about something that has nothing to do with what they’re supposed to be working on.”
But then she made a confession. She liked teaching that class. It was one of the best years of her career. The great struggle for someone teaching math to twelve- and thirteen-year-olds is to make it seem exciting—and twenty-nine kids was exciting. “There were so many more peers to interact with,” she said. “They weren’t always relating with just this one group. There was more opportunity to vary your experiences. And that’s the real issue—what can be done to enliven, enrich, and engage the child, so they aren’t just being passive.”
Did she want twenty-nine children in every classroom at Shepaug? Of course not. DeBrito knew that she was a bit unusual and that the ideal number for most teachers was lower than that. Her point was simply that on the question of class size, we have become obsessed with what is good about small classrooms and oblivious of what can also be good about large classes. It is a strange thing, isn’t it, to have an educational philosophy that thinks of the other students in the classroom with your child as competitors for the attention of the teacher and not allies in the adventure of learning? When she thought back to that year in Meriden, DeBrito got a faraway look in her eyes. “I like the noise. I like to hear them interact. Oh, it was fun.”
6.
A half-hour drive up the road from Shepaug Valley, in the town of Lakeville, Connecticut, is a school called Hotchkiss. It is considered one of the premier private boarding schools in the United States. Tuition is almost $50,000 a year. The school has two lakes, two hockey rinks, four telescopes, a golf course, and twelve pianos. And not just any pianos, but, as the school takes pains to point out, Steinway pianos, the most prestigious piano money can buy.6 Hotchkiss is the kind of place that spares no expense in the education of its students. The school’s average class size? Twelve students. The same condition that Teresa DeBrito dreads, Hotchkiss—just up the road—advertises as its greatest asset. “[Our] learning environment,” the school proudly declares, “is intimate, interactive, and inclusive.”
Why does a school like Hotchkiss do something that so plainly makes its students worse off? One answer is that the school isn’t thinking of its students. It is thinking of the parents of its students, who see things like golf courses and Steinway pianos and small classes as evidence that their $50,000 is well spent. But the better answer is that Hotchkiss has simply fallen into the trap that wealthy people and wealthy institutions and wealthy countries—all Goliaths—too often fall into: the school assumes that the kinds of things that wealth can buy always translate into real-world advantages. They don’t, of course. That’s the lesson of the inverted-U curve. It is good to be bigger and stronger than your opponent. It is not so good to be so big and strong that you are a sitting duck for a rock fired at 150 miles per hour. Goliath didn’t get what he wanted, because he was too big. The man from Hollywood was not the parent he wanted to be, because he was too rich. Hotchkiss is not the school it wants to be, because its classes are too small. We all assume that being bigger and stronger and richer is always in our best interest. Vivek Ranadivé, a shepherd boy named David, and the principal of Shepaug Valley Middle School will tell you that it isn’t.
1 The
definitive analysis of the many hundreds of class-size studies was done by the educational economist Eric Hanushek, The Evidence on Class Size. Hanushek says, “Probably no aspect of schools has been studied as much as class size. This work has been going on for years, and there is no reason to believe that there is any consistent relationship with achievement.”
2 The psychologists Barry Schwartz and Adam Grant argue, in a brilliant paper, that, in fact, nearly everything of consequence follows the inverted U: “Across many domains of psychology, one finds that X increases Y to a point, and then it decreases Y.…There is no such thing as an unmitigated good. All positive traits, states, and experiences have costs that at high levels may begin to outweigh their benefits.”
3 My father, a mathematician and stickler on these matters, begs to differ. I am oversimplifying things, he points out. Inverted-U curves actually have four parts. Stage one, where the curve is linear. Stage two, where “the initial linear relation has flagged.” This is the area of diminishing marginal returns. Stage three, where extra resources have no effect on the outcome. And stage four, in which more resources are counterproductive. He writes: “We take a term in house construction—footing—to label the first stage, and then use the mnemonic ‘footing, flagging, flat, and falling.’”
4 A classic inverted-U curve can be seen in the relationship between alcohol consumption and health. If you go from not drinking at all to drinking one glass of wine a week, you’ll live longer. And if you drink two glasses a week, you’ll live a little bit longer, and three glasses a little bit longer still—all the way up to about seven glasses a week. (These numbers are for men, not women.) That’s the upslope: the more, the merrier. Then there’s the stretch from, say, seven to fourteen glasses of wine a week. You’re not helping yourself by drinking more in that range. But you’re not particularly hurting yourself either. That’s the middle part of the curve. Finally, there’s the right side of the curve: the downslope. That’s when you get past fourteen glasses of wine a week and drinking more starts to leave you with a shorter life. Alcohol is not inherently good or bad or neutral. It starts out good, becomes neutral, and ends up bad.
5 The clear exception: children with serious behavioral or learning disabilities. For special-needs students, the inverted-U curve is shifted far to the right.
6 Although the Hotchkiss website claims to have twelve Steinway pianos, the school’s music director has said elsewhere that they actually have twenty—plus a Fazioli, which is the Rolls-Royce of performance grand pianos. That’s more than a million dollars’ worth of pianos. If you are playing “Chopsticks” in a Hotchkiss practice room, it’s going to sound really good.
Chapter Three
Caroline Sacks
“If I’d gone to the University of Maryland, I’d still be in science.”
1.
One hundred and fifty years ago, when Paris was at the center of the art world, a group of painters used to gather every evening at Café Guerbois, in the neighborhood of Batignolles. The ringleader of the group was Édouard Manet. He was one of the oldest and most established members of the group, a handsome and gregarious man in his early thirties who dressed in the height of fashion and charmed all those around him with his energy and humor. Manet’s great friend was Edgar Degas. He was among the few who could match wits with Manet; the two shared a fiery spirit and a sharp tongue and would sometimes descend into bitter argument. Paul Cézanne, tall and gruff, would come and sit moodily in the corner, his trousers held up with string. “I am not offering you my hand,” Cézanne said to Manet once before slumping down by himself. “I haven’t washed for eight days.” Claude Monet, self-absorbed and strong willed, was a grocer’s son who lacked the education of some of the others. His best friend was the “easygoing urchin” Pierre-Auguste Renoir, who, over the course of their friendship, would paint eleven portraits of Monet. The moral compass of the group was Camille Pissarro: fiercely political, loyal, and principled. Even Cézanne—the most ornery and alienated of men—loved Pissarro. Years later, he would identify himself as “Cézanne, pupil of Pissarro.”
Together this group of remarkable painters would go on to invent modern art with the movement known as Impressionism. They painted one another and painted next to one another and supported one another emotionally and financially, and today their paintings hang in every major art museum in the world. But in the 1860s, they were struggling. Monet was broke. Renoir once had to bring him bread so that he wouldn’t starve. Not that Renoir was in any better shape. He didn’t have enough money to buy stamps for his letters. There were virtually no dealers interested in their paintings. When the art critics mentioned the Impressionists—and there was a small army of art critics in Paris in the 1860s—it was usually to belittle them. Manet and his friends sat in the dark-paneled Café Guerbois with its marble-topped tables and flimsy metal chairs and drank and ate and argued about politics and literature and art and most specifically about their careers—because the Impressionists all wrestled with one crucial question: What should they do about the Salon?
Art played an enormous role in the cultural life of France in the nineteenth century. Painting was regulated by a government department called the Ministry of the Imperial House and the Fine Arts, and it was considered a profession in the same way that medicine or the law is a profession today. A promising painter would start at the École Nationale Supérieure des Beaux-Arts in Paris, where he would receive a rigorous and formal education, progressing from the copying of drawings to the painting of live models. At each stage of his education, there would be competitions. Those who did poorly would be weeded out. Those who did well would win awards and prestigious fellowships, and at the pinnacle of the profession was the Salon, the most important art exhibition in all of Europe.
Every year each of the painters of France submitted two or three of his finest canvases to a jury of experts. The deadline was the first of April. Artists from around the world pushed handcarts loaded with canvases through Paris’s cobblestoned streets, bringing their work to the Palais de l’Industrie, an exhibition hall built for the Paris World Fair between the Champs-Élysées and the Seine. Throughout the next few weeks, the jury would vote on each painting in turn. Those deemed unacceptable would be stamped with the red letter “R” for rejected. Those accepted would be hung on the walls of the Palais, and over the course of six weeks beginning in early May, as many as a million people would throng the exhibition, jostling for position in front of the biggest and best-known artists’ works and jeering at the works they did not like. The best paintings were given medals. The winners were celebrated and saw the value of their paintings soar. The losers limped home and went back to work.
“There are in Paris scarcely fifteen art-lovers capable of liking a painting without Salon approval,” Renoir once said. “There are 80,000 who won’t buy so much as a nose from a painter who is not hung at the Salon.” The Salon made Renoir so anxious that one year he went down to the Palais during jury deliberations and waited outside, hoping to find out early whether he got in or not. But then becoming shy, he introduced himself as a friend of Renoir’s. Another of the Guerbois regulars, Frédéric Bazille, once confessed, “I have an appalling fear of getting rejected.” When the artist Jules Holtzapffel didn’t make it into the Salon of 1866, he shot himself in the head. “The members of the jury have rejected me. Therefore I have no talent,” read his suicide note. “I must die.” For a painter in nineteenth-century France, the Salon was everything, and the reason that the Salon was such an issue for the group of Impressionists was that time and again, the Salon jury turned them down.
The Salon’s attitude was traditional. “Works were expected to be microscopically accurate, properly ‘finished’ and formally framed, with proper perspective and all the familiar artistic conventions,” the art historian Sue Roe writes. “Light denoted high drama, darkness suggested gravitas. In narrative painting, the scene should not only be ‘accurate,’ but should also set a morally acceptable
tone. An afternoon at the Salon was like a night at the Paris Opéra: audiences expected to be uplifted and entertained. For the most part, they knew what they liked, and expected to see what they knew.” The kinds of paintings that won medals, Roe says, were huge, meticulously painted canvases showing scenes from French history or mythology, with horses and armies or beautiful women, with titles like Soldier’s Departure, Young Woman Weeping over a Letter, and Abandoned Innocence.
The Impressionists had an entirely different idea about what constituted art. They painted everyday life. Their brushstrokes were visible. Their figures were indistinct. To the Salon jury and the crowds thronging the Palais, their work looked amateurish, even shocking. In 1865, the Salon, surprisingly, accepted a painting by Manet of a prostitute, called Olympia, and the painting sent all of Paris into an uproar. Guards had to be placed around the painting to keep the crowds of spectators at bay. “An atmosphere of hysteria and even fear predominated,” the historian Ross King writes. “Some spectators collapsed in ‘epidemics of crazed laughter’ while others, mainly women, turned their heads from the picture in fright.” In 1868, Renoir, Bazille, and Monet managed to get paintings accepted by the Salon. But halfway through the Salon’s six-week run, their works were removed from the main exhibition space and exiled to the dépotoir—the rubbish dump—a small, dark room in the back of the building, where paintings considered to be failures were relocated. It was almost as bad as not being accepted at all.
David and Goliath: The Triumph of the Underdog Page 5