The interviewer handed the students a battery, a wire and a light bulb and asked them if they could make the bulb light. They could not. This might not be alarming if the students were fourth graders, but they were not. The students were clothed in caps and gowns as they prepared to graduate from Harvard and MIT. A student graduation speaker declared of MIT that "We are the premier science and technology institution in the world" (it is not clear if this is a statement of total identification with the university or simply poor grammar).

Thus begins "Minds of Our Own," a three-part videotape series on our misconceptions about how the world works. The bulb-and-battery problem is followed by the mirror problem. If you want to see more of yourself in a mirror, should you move closer or farther away? Most get it wrong, one way or another. It doesn’t matter—the mirror shows the same amount of you no matter which way you move.

From the aces at MIT, the camera cuts to middle-schoolers who are asked if they will be able to see an apple in a totally dark room. They say yes. "Eyes will always adjust," one of them says. "You can’t make a room you can’t see in," says another. So they are put in such a room and even after a total failure to "adjust", they are still convinced that ultimately they would have.

We then skip to Jennifer, identified as one of the best science students in a class taught by a veteran and, by conventional accounting, successful science teacher. Confronted with the battery-and-bulb problem, Jennifer cannot make the bulb light up. The teacher then explains the rudiments of electrical circuitry using batteries and bulbs. One month later, Jennifer makes the same mistakes as before the lessons. Given the bulb to explore, she observes that one internal wire is attached to the side of the bulb, another to the bottom. She now understands that her placement of both external wires on the bottom wouldn’t work—one needs to be on the side. But she still doesn’t think that she can make the bulb light up because she has only the battery, bulb and wires, not the socket that was used to support the bulb and make the connections convenient when the lessons were taught.

A final example (for this column, not for the tapes) is Conor, identified by his parents as a boy who asks lots of questions. The tape reveals that Conor is indeed inquisitive and has a keen interest in science. Asked how we see, Conor formulates a notion of objects sending messages to your head. We emit light from our eyes—Conor says it’s like a bat’s radar—that bounce off the objects. This misconception apparently comes from watching "educational" animated science programs on television. It showed light being emitted by a flashlight (but not by the eyes).

This last example is especially salient because in the Sixth Bracey Report I described the science curriculum reform efforts of an affluent elementary school system in which some of the teachers held Conor’s theory.

The point of these tapes, produced by the Annenberg/CPB Math and Science Collection is not that American teachers are lousy. The point is that children bring to the classroom profoundly held ideas of how the world works and that these ideas are incredibly resistant to change. But they are also wrong and therefore in need of change. The point is also that our pedagogy does not equip teachers to teach for understanding and to then detect misunderstandings through assessment. By the usual means of observation, and certainly with any paper-and-pencil test, we would conclude that Jennifer got it. But she didn’t.

You would think we would be further along in teaching and testing for understanding. That we aren’t only reveals that we have profoundly held ideas of how children learn and that these ideas are incredibly resistant to change. And wrong. Piaget has passed through this country twice, once in the 1930’s again in the 1960s and 1970s. Even if the specifics of his theory are wrong, his work should have called our attention to the power of pre-existing ideas more than it has. Our pedagogy is still overwhelmed by our British Empiricist legacy which sees children as passive vessels, and sees a child’s mind as a tabula rasa—a blank slate. If kids don’t learn, it’s a failure to "absorb" the material. "I taught it but they didn’t learn it."

In a somewhat more mundane fashion, thirty years ago, Neil Postman and Charles Weingartner wrote that "Educational Discourse, especially among the educated, is so laden with preconceptions that it is practically impossible to introduce an idea that does not fit into traditional categories."

Postman and Weingartner went on to lay out an "inquiry method" of education. Unfortunately, they unnecessarily wrapped themselves around Marshall McLuhan and this probably doomed them to not be taken seriously, even though the book attained some currency. The principles of inquiry, and the consequences of didactic teaching, as described by Postman and Weingartner are remarkably similar to those depicted in "Minds of Our Own." They lack only the dramatic and powerful taped examples of students and teachers who haven’t experienced inquiry. The tapes also show teachers and kids who, in some instances, try it and who are changed by the experience.

Postman and Weingartner’s principles, laid out didactically as they must be in print are these:

The teacher rarely tells students what he thinks they ought to know.

His basic mode of discourse with students is questioning.

Generally, he does not accept a single statement as an answer to a question.

He encourages student-student interaction as opposed to student-teacher interaction. And generally, he avoids acting as a mediator or judge of the quality of ideas expressed.

He rarely summarizes the positions taken by students on the learnings that occur.

His lessons develop from the responses of students and not from a previously determined "logical" structure.

Generally, each of his lessons poses a problem for students.

He measures his success in terms of behavioral changes in students.

The major problem with these principles is that, spread over only a few pages, they make the process of inquiry learning look easy. It is not. At one point in the tapes, Jennifer’s successful, veteran science teacher describes how hard it was to give up thirty years of "explaining" concepts and how insecure he felt when he tried the act on the principles of inquiry.

At another point in the tapes, we see high school students exploring the battery-bulb problem a little further. The students sometimes work as a whole class, sometimes in groups. They build their own logic and understanding. For example, after figuring out the circuitry needed to make the bulb light, they go on to ask what is it about electricity that makes the light light in the first place. One conjectures that the electricity stops in the filament, causing it to glow. Another says that can’t be because there were two bulbs and they both lit up. If the electricity stopped in the first bulb, the second would stay dark. This is progress.

The teacher of this inquiry class expresses satisfaction with their progress but expresses some anxiety over the political incorrectness of his approach "You spent four class periods to figure out a light bulb? Sheesh, you oughta be able to do that in 15 minutes.

I have often spoken of "The Tyranny of Scope and Sequence." Linda Darling Hammond speaks of a "Curriculum of Coverage." Such a curriculum guarantees that teaching will be shallow and that misconceptions will abound. Is there some school system that has managed to avoid this? It appears from some of the TIMSS data, that Japan has either overcome or bypassed such a curriculum. The curriculum analyses found Japanese texts much thinner than our. They found as well that Japanese teachers attempt to teach far fewer topics per year. Maybe they can take four periods to figure out a light bulb.

TIMSS also videotaped a random sample of eighth grade teachers teaching mathematics in Germany, Japan and the United States. The videos are revealing.

In one, an American teacher is dealing with complementary and supplementary angles. He repeatedly gives the students the number of degrees in one angle and asks how many degrees the complement or supplement has. The "hard" question he gives as seatwork asks the students to figure out how many degrees each angle has if the two angles are both supplementary and equal. He announces that he wants to finish the "unit" before spring break and that, therefore, the unit test will be next Thursday since some of them are likely leaving for break early. This approach to teaching has sometimes been called "the vaccination method" of education; once you’ve "had" complementary angles, you’re inoculated and don’t need to have them again.

In another lesson, a teacher explains how you can know how many degrees there are in a figure no matter how many sides there are: you use a formula (n-2(180)). She also says that "A lot of mathematics is just reading the directions carefully."

The American and German teachers are interested in procedures and algorithms: they want their students to know how to get to the answer. To the answer. A commentator on the Annenberg tapes comments that if kids think that this is learning, learning then tested with multiple-choice tests, then the kids surely will lose interest in learning.

And such an approach to learning does not serve anyone well. In his chapter on "Promoting Student Understanding" in Educative Assessment: Assessment to Inform and Improve Student Performance, Grant Wiggins stands our testing system on its head. "We have perhaps gotten the whole matter backwards in testing: any hope of having an educative assessment system may well depend upon our ability to ferret out, discover, and target the misunderstandings that lurk behind many, if not most correct answers" (p. 72).

When we look at Japanese teachers, we see pedagogues more in the mold of Postman and Weingartner’s inquirers. The teachers begin class by linking the students’ work for today to what happened yesterday. Using animations on a compute screen, he reminds them that the area of a triangle whose base is on one of two parallel lines remains the same even if the apex moves along the other parallel line.

He poses a problem: two adjoining properties have a bent border (see figure). The landowners wish to straighten the border without either property gaining or losing area. How can the students’ knowledge about triangles and parallel lines be brought to bear to solve this problem? It might be good to recall here that these are eighth graders. The students initially work alone. Then those who think they’ve got it work with those who don’t. Some work in pairs, others in small groups.






Finally, the teacher calls on those students who think they’ve solved the problem to come to the blackboard and explain it. Two students do; they use different but equally correct methods. We should mention that from the tape it is not clear how many of the rest of the class have now "got it." We do know that Japanese 8th-graders were third among 41 nations in TIMSS.

Another Japanese teacher poses this problem to the students: You have 2100 yen. There are 10 people in your family and you want to buy each of them a small cake. There are cakes that cost 230 yen and they taste better than those that cost 200 yen. How many of the more expensive cakes can you buy, stay within the 2100 yen limit and still assure that each person gets a cake?

First he questions the class to make sure they understand the question. The class then works on the problem. After a while the teacher explains one way of solving it, a method that involves counting. Afterwards he asks for student solutions. One involves setting up inequality equations. Unlike a Postman-Weingartner inquirer, this teacher does judge the quality of the student’s answer. He tells the class that her way works better than his. His is OK when you’ve only got ten things to consider, but becomes cumbersome and time consuming if you have, say, hundreds, because so many items would have to be counted. The student’s solution involves equations that work equally well and equally fast no matter how many items are involved.

One can have a successful life carrying around a lot of misunderstandings. My wife agreed with Jennifer and made it through the day. I had to look at myself walking away and towards a full-length mirror. If someone had asked us where the great mass of majestic redwoods come from (as is asked on the tapes), neither of us would have said "the air." It is also true that our understanding of understanding is limited and the literature of transfer suggest it is always contextual to some extent. But misunderstanding can lead to errors, as with my friend who doesn’t like to boil water in microwaves because the water is never hot enough (for her, boiling equals bubbles rising, not a set temperature). It can even lead to irrational behavior and major misdeeds—e.g., those arising out of caricatures and stereotypes. There are 800,000 Tutsis who could tell you all about it if they had not been deemed so inferior that other Rwandans, Hutus, saw it as their duty to kill them (see Philip Gourevitch, We Wish To Inform You That Tomorrow We Will Be Killed With Our Families).