The Math of Khan
Not just a YouTube phenomenon, but a model for educational transformation
Michael Macor/San Francisco Chronicle/Corbis
Watching videos online usually means goofing off. But over the past few years, millions of decidedly enterprising people have turned on their computers to watch, of all things, math and science lectures. At KhanAcademy.org, Salman Khan, a former hedge-fund analyst, narrates more than 2,700 free lessons, each about ten minutes long, on everything from polynomials to valence electrons. In video after video, Khans disembodied voice explains concepts as his pen swiftly draws illustrations on a digital board. Students can also work math problem sets, proceeding through a sequence that stretches from arithmetic to calculus.
Khan began making these videos around 2004. Seven years later, they and his problem sets have become a pedagogical phenomenon, attracting fame, controversy, and, beginning last year, funding from Microsoft founder and philanthropist Bill Gates. What makes Khans videos so appealing? Has he invented a teaching tool that works? And what do his discoveries mean for the broader goal of improving education?
The quest to deploy computer technology in classrooms has been going on almost since the genesis of personal computers themselves. By the early 1980s, Apple computers had infiltrated many schools, and a whole generation of Americans in their thirties can recall rainy days spent playing Oregon Trail or MathBlaster—ways to turn kids love of watching stuff on screens into real learning. With the rise of the Internet, many educational institutions entered the online-learning market, hoping to broaden their reach, and for-profit companies began offering software for schools as well.
So when Khan charged down the Oregon Trail of online learning, he wasnt discovering new territory. As he describes it, he was just trying to help a seventh-grade cousin—and later, other young relatives—with math. He lived in Boston and they lived in New Orleans, so hed coach them over the phone. To supplement the calls, he filmed explanations and posted them on YouTube. He soon learned, as hes joked in speeches, that they preferred me on YouTube. Khans cousins could watch the videos whenever they wanted, rather than waiting until he got off work. They could rewind if something was confusing, instead of having to ask him to explain a second time. The videos enabled truly individual pacing.
Khan didnt make the files private, and soon he started hearing from fans. For good reason: hes a born teacher. He uses simple, straightforward language. He illustrates complicated concepts in visually elegant ways. His voice is smooth, he doesnt try to tackle too much in any one lecture, and his energy is infectious. In one video, he explains one of maths most beautiful equations: eπi + 1 = 0. If this does not blow your mind, then you have no emotion, he enthuses.
After hearing how much his videos were helping students, Khan posted them at KhanAcademy.org. He also wrote software that would test student comprehension of math topics. The exercises we give students . . . give much better feedback than every other answer in the back of the book, says Khan. Get ten problems in a row right, and you move on to a more advanced level, scoring various badges and energy points along the way. Ten consecutive correct answers shows mastery: Why is it wrong to expect to get perfection? Khan asks. A coach function quickly lets a teacher or parent using the software know if a student is stumbling. Its the same feedback that a quiz would give, but in real time and without the laborious grading.
The sheer comprehensiveness of Khans site, along with his teaching skills, led to even greater attention. In particular, Bill Gates began mentioning in talks that his own three children were watching the videos. Soon, Gates was lending his presence to Khans crusade, appearing with him at one of the TED organizations well-known TED Talks in early 2011. That generated coverage from Wired to The Economist to O. The Bill & Melinda Gates Foundation, along with other philanthropists, has also granted money to Khan Academy to translate the videos into other languages, deploy them in classrooms, and expand their scope beyond math and science.
One of Khans most significant achievements is that he has enormously expanded the worlds access to a master teacher. Even if you arent one of the lucky 30 students to land a spot in a great teachers classroom, you can still learn from the best. Because the lectures and problem sets invite individual pacing, it doesnt matter whether youre a quick study or not.
The model could work all over the world, even in places where lousy schools and bad infrastructure would otherwise prevent kids from learning. Translate Khans lessons into Berber, send children in rural Morocco to a town library staffed by a Peace Corps volunteer, and the kids could learn calculus just as privileged children in suburban America would. Picture this scenario in Delhi slums or in Rio favelas, and you can see why Gates is excited. For that matter, Khan Academy is a great resource for Americans who have turned to home schooling. I understand their math, but sometimes I cant convey my understanding to the boys, says Annie Peters, a mom who home-schools her three sons. Rather than risk confusing and frustrating them, I turn to Khan. Its like having a private math tutor that I can pull out on a whim.
But an even more innovative aspect of Khans approach is what he calls flipping the classroom, an attempt to change the way mainstream American education works. At the moment, of course, most students learn new ideas in the classroom and then practice at home. Khan envisions a world in which that process is reversed: students would acquire knowledge by watching his videos at home and then spend their classroom time practicing. Instead of lecturing and introducing new concepts, teachers—who would get constant feedback on each students performance through Khans software—would become tutors, helping struggling students through their difficulties. Teaching would become less about presenting material and more about one-on-one instruction.
Thats roughly what Harsh Patel, a Teach for America instructor at PFC Omar E. Torres Charter School in Chicago, has done in his classroom. The school is on the citys southwest side; its students are almost exclusively the children of poor Mexican immigrants, many of whom dont speak English. In late 2010, during his first semester of teaching, Patel struggled to explain math concepts to his fifth-graders. He knew about Khan Academy—I used it myself in high school and college, he says—and after winter break, he decided to flip his own classroom. Because I only had two computers in my classroom, one of which wasnt working, he scrounged up more from friends, eventually getting enough to create a computer station that his students could rotate through. To watch Khans lessons, some of his students would stay after school to use these computers; many, however, could see the videos at home. (Surprisingly, 80 percent of my students had Internet access at home, usually through their parents smartphones.) For Patels 90-minute math class, half of the students would work on Khan problem sets during the first 45 minutes (with Patel answering questions as they came up) while the other students worked in groups on projects that Patel produced. Then theyd switch.
Patel charted how quickly students could plow through to mastery and posted their successes prominently. They just loved the tracking aspect, Patel reports—earning energy points and badges, achieving mastery on math skills, and seeing friends achieve mastery, too. I noticed it started being a cool thing, he says. Towards the end of the year, not 100 percent, but all but three to four students were really motivated. The Khan Academy curriculum helped free up time, too: Patel could work with struggling students without feeling guilty about neglecting faster learners, because he knew that they were still doing something really productive. Thats particularly important in the era of No Child Left Behind, when, as the National Association of Gifted Children has found, progress among the top 10 percent of students has stalled as schools have focused on helping low achievers meet certain benchmarks (see The Excellence Gap, Autumn 2011).
Erin Green, the principal of Covington Elementary School in Los Altos, California, mentions the same advantage. Back when she was a teacher instructing disadvantaged students, she remembers, she could see that outlier students needed challenge and was disturbed about neglecting them. But last year, Covington and a few other Los Altos schools participated in a Khan Academy pilot program, using Khans videos and exercises to complement their math classes. Suddenly, advanced students could work ahead without the teachers having to plan individual lessons and instruction, while students who were behind could get help privately, so they dont have to ask a question and have everybody hear, says Green. Since the problem sets required mastery to move on, teachers could be sure that students were understanding the material. Its a great resource, Green says. It makes me want to be a teacher again.
Khan himself agrees about the importance of individual pacing. While he doesnt dispute the fact that gifted kids can get bored in class, I think this problem—the one-pace-fits-all lecture or curriculum—is even more damaging for remedial classes. Peoples gaps are all over the place. With an advanced class, youre more confident the foundation material is in place, so the question is how fast you move on current material. Khans approach helps ensure that struggling students fill those gaps. Some seventh-grade remedial students, for example, may simply never have mastered a few skills in third-grade math. If you dont fill those gaps, theyre never going to be able to do well, Khan maintains.
Flipping the classroom has another advantage. A commonly heard rationale for smaller classes is that its difficult to teach children at various levels of preparation within a single classroom. But Khans system does away with that worry, allowing a single teacher to handle a large, diverse class. The best teacher in the world cannot differentiate instruction the way an online system can, points out Gisèle Huff, the executive director of the Hume Foundation, which has focused its educational philanthropy on digital learning. Some of the blended learning models incorporating Khan Academy can have 40 children in a class. The whole configuration of the way learning happens changes. Needless to say, a world of fewer (and, one hopes, better) teachers clashes with the model envisioned by the teachers unions. But its perfect for teachers who thrive on guiding individual aha moments. It makes them the people they thought they would be when they went into teaching, Huff says.
Of course, its too early to declare the success of the classroom-flipping revolution. There is no robust evidence from the Los Altos pilot program yet. Khan does have data from the pilot showing that the proportion of students scoring below basic achievement fell while the proportion scoring advanced rose; on the other hand, the teachers piloting the program were exceptional and knew that their work would be closely watched. Green notes, too, that her school is already high-scoring by California state standards. Patel likewise reports that while I really tried to get as many metrics as I could to quantify it, I couldnt narrow out Khan Academy for being the reason that his students showed improvement. Still, the qualitative data showed me obviously it was. The students loved it, and I could see them learning more materials. They learned concepts they wouldnt have learned until seventh or eighth grade and were able to apply them and teach them to each other.
Theres another reason that Khan Academy will disturb the education establishment. For all Khans reliance on technology, his pedagogical approach—lectures and problem sets that drill kids on skills—is a very traditional one. But this approach has fallen out of favor in the pedagogical debate on how children learn. The fashionable theory in todays schools of education—constructivism—maintains that students construct their own knowledge from their experiences; lectures and drills are therefore frowned upon. And so, as Gatess money and star power enable Khan to scale up his program so that more schools can use it, opposition is mounting. Sylvia Martinez, the president of a nonprofit called Generation YES and a critic of Khans approach, worries that just because you can speed up an assembly line doesnt prove youre doing it better. Children learn best when they are engaged in things that are important to them.
Readers of City Journal are familiar with the arguments against the constructivist approach. Its possible, of course, that in the hands of a master, it can work. One of the most relentless critics of Khan Academy is Frank Noschese, an award-winning physics teacher at John Jay High School in New York and a part-time blogger. In Noscheses physics classes, students learn principles through experimentation—for instance, using little battery-powered buggies, rulers, and stopwatches to answer those traditional questions about when two trains leaving distant stations would meet. In a good classroom, Noschese says, theres a lot going on that I dont think I can get from a video like Khans.
The problem is that few teachers are as good as Noschese. Discovery-based learning can be a disaster in the hands of mediocre teachers, with well-meaning people encouraging creativity but never ensuring that students have actually learned anything. Constructivism has been ascendant for years, after all, but educational achievement among American children has been abysmal. In an imperfect world full of imperfect teachers, Khans approach could be enormously useful.
The clearest parallel is with Kumon, an after-school math and reading enrichment program that has provoked antagonism for similar reasons. Developed in the 1950s by Toru Kumon, a mathematics teacher in Japan, the Kumon approach also focuses on individually paced learning and on achieving mastery. Students of preschool age and older work through a sequence of lessons on math and reading—usually at Kumon centers and at home, though some schools have implemented the curriculum, too. Then they take timed tests to show that they understand each concept. Kumons tutors answer questions and quickly grade tests. Students usually need a perfect score on a concept to move ahead.
There is some evidence that Kumon promotes competence. One high-poverty Alabama school that implemented the Kumon curriculum for many years saw student test scores match the state average, while comparable students in other high-poverty schools lagged far behind. A study in Oklahoma found that students who received Kumon instruction far outscored non-Kumon students the following year on standardized tests. Unsurprisingly, Kumon curricula have sometimes proved deeply controversial. Researchers who tried to bring Kumon to the Pontiac, Michigan, school district wrote that the fiercest resistance to their project came from university-level K12 education academicians. Indeed, we were shocked at the antagonism our efforts encountered.
Gatess funding is also allowing Khan to confer with humanities teachers and expand his model to their subjects. How could problem sets work in the humanities? It would be the type of stuff youd find on the SAT or AP exams, Khan says. He admits that that first pass wont let you have a deep, rich, conversation (though he hopes that one day, Khan students all over the world could participate in online discussions). Clearly, the problem sets wont be as sequential as they are in math. Yet even in the humanities, there is factual knowledge that people tackling the subject should learn. If you picture something like art history, theres some aspect of just knowing the scaffold of material, he says. If you have the scaffold, then youre ready to go deep and have a rich discussion. Likewise, while writing is an art, the rules of grammar let writers express themselves in ways that other people understand. You can do problem sets on grammar, even if theres more to composition than that.
Theres some reason to think, as Khan continues honing his program, that his science lectures could use some improvement. Derek Muller did his dissertation at the University of Sydney on using videos to teach physics concepts. Hed give students a test on a certain concept, like gravity, and measure their understanding. Generally, they did poorly. Then hed show them a video similar to Khans, explaining the concept in a straightforward fashion, and then test them again. The students rated the videos as clear and compelling, and they were more confident that they understood the concepts, but their actual comprehension barely budged. The problem with physics, Muller explains, is that we live in the physical world, where we see things and develop our own—often incorrect—explanations. If you throw a ball up into the air, for instance, it travels up for a while, which would make the average person guess that some upward force is acting on the ball while its in the air. Muller discovered that what really improved peoples scores was to confront them with common misconceptions and explain why they were wrong. He developed a video series called Veritasium that takes that approach. Students dont rate these videos as clear. But after they watch them, their comprehension scores nearly double.
Muller still thinks that Khans videos are helpful for reviewing concepts; even as exposition, he says, theyre better than what many students have now. My experience with the literature is that telling—that is, lecturing—is a lot more effective than it is currently fashionable to say. As for Khan himself, Hes an excellent speaker and is good at what he does. In fact, Khan sometimes intuitively confronts peoples misconceptions, Muller-style. He remembers that this was tough for me, I can imagine why this is tricky and then explains why people tend to make a certain mistake, Muller says.
Over time, as Khan Academy discovers that some videos work better than others, the videos will get better. And as they do, theyll help even more people. Needless to say, theyll never solve all educational problems. But individually paced, sequential learning works for so many students that Khan Academy may deserve the hype its getting.