The Boy Who Could Change the World (34 page)

How is one supposed to develop anything? We understand the world by making models, generalizing from the patterns we experience
and testing those generalizations against the real world. We learn because something puzzles us—we want to understand what it is or how it works, and we set off on the trail of adventure to figure it out. But there's no time for this in school. We're supposed to sit in class, not explore the world. Indeed, we don't get to explore at all—the real world is kept carefully at bay.

Instead we're spoon-fed an endless stream of predigested facts: definitions, names, dates, places, equations—all disconnected from reality and from each other. Instead of learning about the world, we learn random facts and rules. But even those you're not allowed to care about. When the fifty minutes are up and the bell rings, you have to stop being interested in this and switch over to being interested in that. But curiosity cannot be ordered around via remote control, the channel changed at fifty-minute intervals. The only way to survive is by giving up on curiosity altogether, not caring about the subjects you're supposed to be learning, just letting it all become a blur.

And that's fine, because it
is
all a blur. A class in physics isn't much different from one in biology or grammar. All education becomes memorization. The only difference between the subjects is the kind of stuff you need to memorize—is it animal names or parts of speech? Instead of trying to understand something, you just try desperately to remember it—at least long enough to repeat it back on the test.

It's a wonder anyone learns anything.

Perhaps they don't. That was the thought that haunted Eric Mazur.

Now, all the signs said that Eric Mazur was a good teacher—a great one, in fact. He taught at Harvard—the most prestigious school in the country, if not the world. I've talked to plenty of Harvard professors and believe me, just that is enough to make most of them feel pretty good about themselves. But even at Harvard, he stood out.

Take the teacher evaluations the students had to fill out at the end of the course, “the dreaded end-of-semester questionnaire.” Mazur taught introductory physics, and physics was not exactly a popular course with most students. “Most of my colleagues, when they
taught this introductory pre-med class, would come close to suicide when they saw the results . . . because these pre-meds were not too kind to their physics instructors. But not so for me—I got 4.5, 4.7 on a 5-point scale.”

Was Mazur getting good ratings by just making things too easy? For that he looked at the exams. “I could give these students questions that I considered quite complicated—questions that I wasn't even sure
I
could do flawlessly under the pressure of an exam. I mean, a stick is lying on a frictionless surface, a puck hits it, the two stick together and start to rotate, now calculate the angle and rotational position as function of time. No problem for most of these pre-meds.”

There were some warning signs. “For example, some students would write, at the bottom of their end-of-semester evaluation, ‘Physics is boring.' Even though they gave me [a] high rating, they would write that down. Or, ‘Physics sucks.' I could never make any sense of it and, therefore, preferred to concentrate on the positive signs and ignore the negative ones.

“You know, my dentist once told me—and I couldn't even speak back because I had the thing in my mouth—‘Oh, you're a physicist. I got an A for physics in college but I really didn't understand anything.' It always bothers me when I hear these things and I never know how to react. I never understood what the cause was.”

Then, in 1990, after six years of teaching, he saw an odd little article in an old copy of the
American Journal of Physics
. Ibrahim Halloun and David Hestenes, two physicists at Arizona State, had given their students a physics exam, but a very strange one. Most physics exams ask fairly complicated questions requiring a bunch of math to solve, like the one with the stick and the puck. But instead of making their physics exam harder, Halloun and Hestenes decided to make it easier. It involved no jargon or advanced math; indeed, it didn't require any calculation at all. The questions were so simple and understandable you could even give the test to someone who had never taken physics.

For physics students, they should be trivial. They didn't require much more than understanding Newton's laws. “The first week we describe motion—velocity, acceleration, and so on. The second
week you talk about Newtonian mechanics—Newton's three laws. And then . . . things start to build on top of that.”

Now, we've probably all heard Newton's laws. Take number three: “For every action, there is an equal and opposite reaction.” Even English majors are fond of quoting that. Now, maybe we don't know exactly what it means, but surely physics students should—especially those doing pretty advanced physics at Harvard.

Well, in their test, Halloun and Hestenes asked students a fairly simple question about Newton's third law. It's question number two—and it ended up being the hardest question on the test:

            
2.
  
Imagine a head-on collision between a large truck and a small compact car. During the collision,

                 
(a)
  
the truck exerts a greater amount of force on the car than the car exerts on the truck.

                 
(b)
  
the car exerts a greater amount of force on the truck than the truck exerts on the car.

                 
(c)
  
neither exerts a force on the other, the car gets smashed simply because it gets in the way of the truck.

                 
(d)
  
the truck exerts a force on the car but the car doesn't exert a force on the truck.

                 
(e)
  
the truck exerts the same amount of force on the car as the car exerts on the truck.

Now, by Newton's third law, the answer has to be (e). The reason the car gets smashed and the truck doesn't is because an equal force translates into much greater acceleration in the smaller, stationary car. But, of course, most people don't understand that. (You may not even understand it after my one-sentence explanation.) Like most people, 70–80% of physics students say (a).

This wouldn't be such a big problem, except that, for a physics student, this question is incredibly basic. “The whole rest of the semester—another nine weeks or so—builds on top of Newton's laws. In other words, if you don't understand Newton's laws, you can't really make much sense of anything else in the entire semester.” And yet, in question after question like this, it became clear: the students didn't understand Newton's laws.

“When I read that, it didn't really register,” Mazur said. “After all, this is high school stuff”—how could university students flunk it? Especially Harvard University students, most of whom had aced AP Physics.

Knowing that most people wouldn't believe them, Halloun and Hestenes had repeated the study in all sorts of schools with all sorts of teachers. They tested a physicist who emphasized basic concepts, one who used lots of exciting lecture demonstrations (and won multiple awards), one who teaches problem solving by example, and a new teacher who was unsure of himself and just read straight from the textbook. They couldn't detect any difference—not even between the award-winning teacher and one who read from the textbook. Measured by a simple test like this, all were equally bad. It didn't make a difference what the teachers did; the students still didn't learn anything.

“Well, I felt challenged,” Mazur recalls. “My reaction, you can probably already predict this: ‘Not
my
students!' After all, I was at Harvard—maybe this was some problem that was in the Southwest of the United States, right? . . . I wanted to show that my students could ace this test. . . . At that time we were dealing with rotational dynamics, and the students had to calculate triple integrals of complicated bodies with different moments of inertia. You know, we were so
way
beyond Newtonian mechanics there was no comparison between [this test] and what we were actually doing in class.

“But I was so desperate to get this data, I walked into class and told my students I was going to give them this quiz. I called it a quiz because I didn't want to scare them—you know how pre-meds are. . . . But I had to give them some incentive to take this test seriously, so I told them, ‘Look, if you take this test seriously, you can use your score to help you study for the upcoming midterm examination.' Now, I told you, the midterm examination dealt with far more complicated materials, and I realized as soon as I said that, it was actually a huge lie. And I was worried that as soon as I said that my students would be offended by the simplicity of this test as soon as they started on it.

“Oh, boy, were my worries quickly dispelled. Hardly had the first
group of students taken their seats in the classroom when one student raised her hand and she said, ‘Professor Mazur, how should I answer these questions? According to what you taught me, or according to the way I usually think about these things?'” How was he supposed to answer that?

Sure enough, the results came back and Mazur's class wasn't very different from any of the others. “When I saw how poorly my students had done, my first reaction was ‘Well, maybe you're not such a great teacher after all.' But that could obviously not be true, right? So I didn't think about that too long. Well, what's another reason the score could be low? Dumb students. But that's pretty hard to say at [Harvard]; we have a very selective group of students. So I thought about it a little bit more and then, my mind, my twisted mind came up with the perfect excuse: . . . the test! There had to be something wrong with the test!

“Take this question about the heavy truck and the light car, right? You don't need to have taken physics to know you're much better off in the heavy truck than the light car. So maybe students were confusing damage or acceleration with force—maybe it's just a matter of semantics!

“So I decided to do some testing of my own. I decided to pair, on an exam, two questions of different types on the same subject. One was a typical question out of the textbook, on which I knew students would do well, and another was a word-based question a little bit like the one with the heavy truck and the light car. And I decided to stay away from Newtonian mechanics, because we all have some intuitive notions of Newtonian mechanics before taking physics. I decided to do some testing in DC circuits, direct current circuits. I think very few people have any intuitive notions about circuits.”

All right, so here's the standard question (don't worry if you don't understand it):

            
5.
  
For the circuit shown, calculate (a) the current in the 2-resistor and (b) the potential difference between points P and Q.

To you, this question may seem impenetrable. But for the physics students, this was the standard sort of problem they were used to answering. “This is straight out of the textbook. It's not a particularly hard problem, it's about 2/3 of a page of cranking numbers—but it's not a completely trivial question either.”

Now, for comparison, here's the conceptual question:

            
1.
  
A series circuit consists of three identical lightbulbs connected to a battery as shown here. When the switch

                 
S is closed, do the following increase, decrease, or stay the same?

                 
(a)
  
The intensities of bulbs A and B