After Django Reinhardt lit the nightclub music scene on fire, classically trained musicians began trying to transition to jazz. According to Michael Dregni, who wrote multiple books on that period, improvisation was “a concept that went against conservatory training. . . . After years of rigorous conservatory training, it was an impossible transition for some.” Leon Fleisher, regarded as one of the great classical pianists of the twentieth century, told the coauthor of his 2010 memoir that his “greatest wish” was to be able to improvise. But despite a lifetime of masterful interpretation of notes on the page, he said, “I can’t improvise at all.”
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Cecchini’s analogy to language learning is hardly unique. Even the Suzuki Method of music instruction, synonymous in the public consciousness with early drilling, was designed by Shinichi Suzuki to mimic natural language acquisition. Suzuki grew up around his father’s violin factory, but considered the instrument nothing more than a toy. When he fought with his siblings, they beat one another with violins. He did not attempt to play the instrument until he was seventeen, moved by a recording of Ave Maria. He brought a violin home from the factory and tried to imitate a classical recording by ear. “My complete self-taught technique was more a scraping than anything else,” he said of that initial foray, “but somehow I finally got so I could play the piece.” Only later did he seek out technical lessons and become a performer and then an educator. According to the Suzuki Association of the Americas, “Children do not practice exercises to learn to talk. . . . Children learn to read after their ability to talk has been well established.”
In totality, the picture is in line with a classic research finding that is not specific to music: breadth of training predicts breadth of transfer. That is, the more contexts in which something is learned, the more the learner creates abstract models, and the less they rely on any particular example. Learners become better at applying their knowledge to a situation they’ve never seen before, which is the essence of creativity.
Compared to the Tiger Mother’s tome, a parenting manual oriented toward creative achievement would have to open with a much shorter list of rules. In offering advice to parents, psychologist Adam Grant noted that creativity may be difficult to nurture, but it is easy to thwart. He pointed to a study that found an average of six household rules for typical children, compared to one in households with extremely creative children. The parents with creative children made their opinions known after their kids did something they didn’t like, they just did not proscribe it beforehand. Their households were low on prior restraint.
“It’s strange,” Cecchini told me at the end of one of our hours-long discussions, “that some of the greatest musicians were self-taught or never learned to read music. I’m not saying one way is the best, but now I get a lot of students from schools that are teaching jazz, and they all sound the same. They don’t seem to find their own voice. I think when you’re self-taught you experiment more, trying to find the same sound in different places, you learn how to solve problems.”
Cecchini stopped speaking for a moment, reclined in his chair, and stared at the ceiling. A few moments passed. “I could show somebody in two minutes what would take them years of screwing around on the fingerboard like I did to find it. You don’t know what’s right or what’s wrong. You don’t have that in your head. You’re just trying to find a solution to problems, and after fifty lifetimes, it starts to come together for you. It’s slow,” he told me, “but at the same time, there’s something to learning that way.”
CHAPTER 4
Learning, Fast and Slow
“OKAY? YOU’RE GOING to an Eagles game,” the charismatic math teacher tells her eighth-grade class. She takes care to frame problems using situations that motivate students. “They’re selling hot dogs,” she continues. “They’re very good, by the way, in Philadelphia.” Students giggle. One interjects, “So are the cheesesteaks.”
The teacher brings them back to today’s lesson, simple algebraic expressions: “The hot dogs at [the] stadium where the Eagles play sell for three dollars. I want you to give me a variable expression for [the cost of] N hot dogs.” The students need to learn what it means for a letter to represent an undetermined number. It is an abstraction they must grasp in order to progress in math, but not a particularly easy one to explain.
Marcus volunteers: “N over three dollars.”
“Not over,” the teacher responds, “because that means divided.” She gives the correct expression: “Three N. Three N means however many I buy I have to pay three dollars for [each], right?” Another student is confused. “Where do you get the N from?” he asks.
“That’s the N number of hot dogs,” the teacher explains. “That’s what I’m using as my variable.” A student named Jen asks if that means you should multiply. “That’s right. So if I got two hot dogs, how much money am I spending?”
Six dollars, Jen answers correctly.
“Three times two. Good, Jen.” Another hand shoots up. “Yes?”
“Can it be any letter?” Michelle wants to know. Yes, it can.
“But isn’t it confusing?” Brandon asks.
It can be any letter at all, the teacher explains. On to part two of today’s lesson: evaluating expressions.
“What I just did with the three dollars for a hot dog was ‘evaluating an expression,’” the teacher explains. She points to “7H” on the board and asks, if you make seven dollars an hour and work two hours this week, how much would you earn? Fourteen, Ryan answers correctly. What about if you worked ten hours? Seventy, Josh says. The teacher can see they’re getting it. Soon, though, it will become clear that they never actually understood the expression, they just figured out to multiply whatever two numbers the teacher said aloud.
“What we just did was we took the number of hours and did what? Michelle?” Multiplied it by seven, Michelle answers. Right, but really what we did, the teacher explains, was put it into the expression where H is. “That’s what evaluating means,” she adds, “substituting a number for a variable.”
But now another girl is confused. “So for the hot-dog thing, would the N be two?” she asks. “Yes. We substituted two for the N,” the teacher replies. “We evaluated that example.” Why, then, the girl wants to know, can’t you just write however many dollars a hot dog costs times two? If N is just two, what sense does it make to write “N” instead of “2”?
The students ask more questions that slowly make clear they have failed to connect the abstraction of a variable to more than a single particular number for any given example. When she tries to move back to a realistic context—“social studies class is three times as long as math”—they are totally lost. “I thought fifth period was the longest?” one chimes in. When the students are asked to turn phrases into variable expressions, they have to start guessing.