Excerpts from an interview with Lee Shulman, President of the Carnegie Foundation for the Advancement of Teaching

Recorded July, 2002

Discussion of transfer

The problem with transfer and the problem with structure are very closely related to one another. There's a very simple fact that we all have to learn to deal with, and that is we never have enough time to learn everything we will ever need to know in order to live our lives successfully and fruitfully. So it doesn't matter how long you would make medical school, for example. No physician could ever learn enough in medical school to anticipate every possible patient that will ever walk in her door. And therefore, the challenge of education is always to ask, "What's the least amount of material we can teach really well that will, in turn, make it possible for those whom we teach to use that knowledge in the widest possible range of situations – including not only situations that we can anticipate but also situations that no one can anticipate." And that's abstractly the problem with transfer. How can you learn less, and make much more of it?

And basically there are two kinds of transfer that you can think about. One is the transfer that occurs between learning the parts of a task and then using those parts to do something much more complicated. So, for example, when you were in first or second grade, you learned addition, and you learned subtraction, and you learned multiplication. At some point you had to learn long division. Now, that required transfer, because you had to take what you already learned about adding, and subtracting, and multiplying, and apply all three of those processes to learning a new kind of skill called division. And you can call that vertical transfer – it's taking small pieces and putting them together into a larger more complex skill. If you're learning a performance of some kind – football players learn very specific small skills, and then they learn to put them together into a new play that they learn to run. And that's a very, very important part of transfer. And so as educators, we often ask ourselves, "What are those simpler skills that, again and again turn out to be useful in more complex, later things, we want students to learn. Let's make sure we teach those simpler skills very, very well so that when they confront the more complex skills, they can put together what they already know." Now it turns out that very often, you already have some simpler skills or simple kinds of knowledge, but when you confront the new task, you don't realize you already know what it is you need to do that task. And that's why problem solving, and transfer, and metacognition are so important, because they involve being wise enough to know that you already know something, and to use it when it's necessary. Anyway, that's one kind of transfer, from simple to complex.

A second kind of transfer occurs when you have to take what you've learned in one situation and apply it to a new situation at roughly the same level of complexity. And so, for example, if I have learned about the, notion of a revolution in studying the history of the United States, and then I study the history of France, can I apply the notion of revolution, can I transfer what I know about revolution, from the American context to the French context, and subsequently, to the Russian context, if I then study the Russian revolution? These are examples of a more horizontal kind of transfer, where I can take an idea from one situation and move it to another. And, you can do that within a subject matter area, so, for example, you can do it from the concept of revolution for the United States and for France, (I'm doing that from within history), or you can do it across subject matter areas. So, for example, when the teacher was teaching bridge building to the students, he used concepts like balance, and form, and function to help remind them what they needed to keep in mind as they built their bridge. Well, where have they learned those concepts before? They might've learned them in looking at a piece of art, and looking at a lovely painting, and a teacher might say, "Well, notice what makes this beautiful is the way in which the painter balances various elements and the connections between the formÉ" But now if they've learned those in art, if they've learned them well, then the teacher can draw upon those ideas in a totally different area, such as bridge building, or frankly, biology, and so there are concepts that can be used across, and that would be an example of this second kind of transfer.

It's important for teachers to understand the concept of transfer, because it's absolutely necessary to protect them against what is probably the worst sin of teaching, which is trying to cover all of the material with equal attention across all the things you anticipate a kid might have to know. First of all, that's impossible. Second, it is deadly boring. And third, it's bad psychology. The reason teachers have to understand the notion of transfer is whenever they teach, they have to ask themselves, "What is it about what I'm teaching now that will be of value, of use, a source of understanding, or of pleasure to my students at some point in the future, when they're in a situation that is not identical to the one they're in now?" And that has got to be a mantra for the teacher, always asking, not just "Where am I?" and "Where are they now?" but "Where might this be going?" and if they can keep on thinking of that question as they teach, which is the question of transfer, then it can transform the kind of teaching they do.

The ways a teacher can facilitate transfer – that's a very interesting challenge. Probably the most obvious way, and a way that teachers often think that they shouldn't do – because they almost think it's cheating – is explicitly to point out to students the variety of situations to which what they're learning today might be useful or transferable in the future, and give them a chance to not only talk about, but even take the time to have them DO some of those transfer kinds of tasks themselves. So for example, when teachers want students to understand that some of the very basic skills they're learning now are going to be really important, because, at a later date, they're going to have to put those together in some more complex processes, one way to do that is to actually to give the students first, the complex task, or process that they're going to need the separate skills for. That gives them a kind of vision of the more complex whole that they're aiming toward. Then, when they learn the individual processes, they can anticipate the later transfer. We do that in all kinds of situations. We can do it in arithmetic, but we also do it in something like medicine, where we teach medical students all kinds of basic ideas, and they have no idea why they're learning these things.

Well, what we now do is, early in medical school we give them much more complex cases to deal with, and they realize they don't know what they need to know in order to solve those more complex problems. And then we say to them, "Okay, we're going to move back to much more basic ideas and skills that are going to be the way in which you will eventually be able to solve this kind of problem." We do it with engineering students as well – give them a complicated design problem. And then when they realize how complicated, how many different components there are to the design problem, they are then ready to go back to the more basic processes and understand that these have transfer value to what it is they're going to need later. So, one of the most important strategies is to actually give students the chance to encounter the variety of transfer situations, for which what they're learning now can be very useful. And I think that's not done very often, and it's probably one of the most frequently missed opportunities that we as educators don't take advantage of.

Another thing that can facilitate transfer is – as you teach the basic ideas – to have students practice talking about them with each other, and writing about themselves what these skills entail, and what these ideas mean to them, because one of the most difficult things about transfer is that you have the knowledge you need, and you don't know you have it, or you don't recognize that it's useful in this new situation. People know far more than they realize they know, and they'll give up on a more complicated task. So teaching the initial material in ways that increase the awareness of the students of what they know, how they know it, and a variety of ways of trying to represent the idea in their own head – just multiple connections – makes it more likely that when they do encounter a situation in the future where that knowledge is useful, they've got it packaged or organized in ways that'll make it more available.

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Discussion of learning skills in context

Learning skills in context both can increase the transfer of skills and knowledge, but it also can decrease it, if it's not used well, and let me explain what I mean. If you use a context, if you use a particular problem, or a simulation, or if you say, "We're going to use this for bridge building, or we're going to do it for another, very interesting real life task," it increases the students' engagement with the ideas – it makes them work with the ideas much more actively and flexibly. It's very likely they'll do it collaboratively and talk to one another about it, which raises awareness. It has all of those virtues which makes the ideas become more alive and salient for them, and all of those things – as I said before – make it more likely that the ideas will be transferable.

The danger one has to worry about when one puts learning in context is the students somehow learn that what it is they're doing only applies in this situation. The context takes over, and they fail to recognize the value of what they're learning when they're not building bridges with toothpicks, when they're not rubbing balloons on their heads, when they're not writing a particular essay on a particular topic that was assigned. And so the teacher is always doing this really challenging balancing act of – on one hand taking full pedagogical advantage of the richness that a context can contribute to the learning process; at the same time, constantly reminding the students, in a variety of ways that what they're learning has value beyond the context as well – making comparisons, making analogies. So that the kids don't think that what this is really about is toothpicks, because it's not.

Another important way to think about transfer is to remind ourselves that classrooms are very special artificial environments that we create in order to educate. Students live most of their lives outside the classroom, and when they live their lives outside the classroom, they are living in rich environments in which a lot of learning is taking place, and so there are two kinds of transfer we have to keep very, very much in mind. One is – how can we as teachers use the rich variety of experiences that students have outside the classroom, and bring it to bear inside the classroom, so that you ask students to think about something they already know how to do outside and apply what they know inside? And of course, we also have to get the inside out – have to keep on reminding students that what they're learning is not only valuable inside the classroom, but to get them to think about the ways that transfer can occur outside.

Let's try to think of a few examples of that. Carol Lee, at Northwestern University, has been working on the question of how do you help students from African-American, urban communities, use the knowledge they already have about using words, rhymes, and sentences – that come out of the way in which they already use rap and things like this in their lives outside the classroom – to the interpretation, and analysis and then creation of written material inside the classroom. And she's done stunning studies that show that when you can begin with students becoming much more conscious of the ways they're already using language outside the classroom and then show them how they can apply those usages in the analysis of production of literature inside the classroom, you get amazing increases in learning. And so there's an example where culture and cultural artifacts and practices outside the classroom get transferred into the classroom and facilitate learning. So that would be an example of outside-in.

We all know that almost every little boy that says he can't learn to do division can probably do baseball batting averages in his head when he's outside the classroom. Here's just an example that there are all kinds of varieties of intuitive uses of mathematics that kids engage in without thinking of them in formal terms outside the classroom. And if teachers can identify those, and help the students bring what they already know and do outside the classroom into the learning of the mathematics and doings inside the classroom, there will be much more rapid learning of the mathematics.

The notion here is for the teacher to be enormously cognizant of how smart kids are outside the classroom in a variety of ways, and to have them make that connection inside. Probably the most frequent strategy that gets used to do that – and we see that on a number of the tapes – is where the teacher begins by asking the students, in one way or the other, what they already know. And as the students begin to express things they already know, the teacher begins to identify the hooks from their outside experience that she'll then use to facilitate the learning inside the classroom.

Now the inside to outside is the one we probably do more frequently, and that is where we have kids study a particular problem or task – or set of processes in the classroom – and then we assign a project or an assignment of some other kind that calls upon the students to take what they've learned inside and apply it outside. And again, we see this in all kinds of things, we see it in kids taking the mathematics they learn in the classroom of calculation and graphing and other kinds of representation, and going to the nearest busy intersection outside the school, and beginning to do a traffic flow study to try to decide whether they need an extra stop sign or an extra stoplight. You see it when kids take things they're learning in biology, and they get a chance to get out and study a local body of water to check for pollution levels, or to check for what kinds of wildlife live out there. And these are just examples of teachers saying, "Hey, this is a set of ideas that doesn't stop being useful in the classroom. Let's go out and use it in a variety of settings and see how much transfer there is that way." So the transfer goes both ways.

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Discussion of the structure of subject matter

When we say that a subject matter has a structure, what we mean is that the ideas, the facts, the principles, the theories, the skills of a subject matter are not just some sort of long list of names that can be arrayed in any order, and you simply have to sit down and memorize them, and that's what it means to know the subject. Anything worth knowing usually has some sort of organization. And that doesn't mean there's only one organization for the subject, but it means if you understand the organization, you have much more likelihood of gaining some mastery over the subject, of moving around in the subject, and of using it. Let me take a trivial example. You send me to a supermarket to buy a long, long list of groceries, and the list starts with avocadoes and ends with zwieback crackers – something like that for the baby. (Do they still have zwieback for babies? I don't know.) And I don't know anything about the way that supermarkets are organized – I just think they're random – it will take me forever to buy that stuff, because I'll go down the list, and I'll go one at a time, and I'll be wandering all over the place. I won't know where to look for things, and I won't know how to organize my actions inside the supermarket. But most of us understand the structure of a supermarket. We understand that different kinds of things you might want to buy. Groceries tend to be grouped together in certain categories, but not only that, categories tend to be organized in certain ways, and sometimes we know that structure even though we haven't explicitly thought about it. We know, for example, where to look for produce. The likelihood is that the produce is going to be along the walls of the supermarket, and for some reason, when you walk into the supermarket they're either along the right-hand wall, or the left-hand wall. Why? I don't know, but I know that they're organized that way. I know that the meat and the fish counters are also likely to be along walls. Now does it have to do with the availability of water and electricity? Maybe, but I don't know. And the canned goods are likely to be in the middle and they're going to be organized in certain ways, right? If I know that organization, if I know that structure, then I can move through and do what I need to do and even remember what's on that list much better than if I don't know the structure at all. In fact, what I tend to do when I get a list of things to go to the supermarket and buy – on those rare occasions when I'm trusted alone in the supermarket; men are not very trustworthy, we are impulse buyers – I reorganize the list. And I rewrite the list, so I put all the fruits and vegetables together, and all the milk and dairy products together, because I am trying to change the task so it fits my knowledge of the structure.

We do that in other places. If I'm a physician, and I'm doing an examination of you, I don't just randomly say, "Let me just look at your nose, how's your toe?" I have a structure – it's the structure of the human body and its organ systems – so I will systematically check the gastro-intestinal track. I will check the respiratory system, the cardiovascular system, the neurological, right? Because, not only does that give me a structure for moving through the examination, it also structures my memory for any signs and symptoms that I encounter, that may be relevant in diagnosing what you have. So, every time we call something a subject matter, I would say, we call it that because it has some principle of organization that connects the ideas with one another that gives them some kind of order, some sort of meaningfulness, and it's like a code. If you were to be a teacher and you taught students about supermarkets, and you never taught them the code, you never said, "You've got to understand, there's a structure here – there is a predictable way in which these things are organized." You wouldn't be teaching the students well, because if you understand the structure, then you could go to a supermarket in Buenos Aires, you could go to a supermarket in Tel Aviv, and you could find your away around.

Well that's true of teaching kids mathematics; it's true of teaching kids history; it's true of teaching them biology; it's true of teaching them literature. You've got to look for the ways in which meaning is created through organization – through the way things are connected and ordered – and if you can help students get access to that, you can give them so much more power than if you just give them long lists of things.

When we say that subject matters have structures, what we're saying is that they have ways in which the core ideas in the subject are connected with one another so that the students can acquire meanings that would be hard to acquire otherwise. It means students beginning to detect patterns and regularities.

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Discussion of looking for the structures of subject matter

Looking for structures in subject matters is really a great deal of fun, because it's what makes the subject matters the exciting kinds of domains they are. And the way you do that is to make students much more aware of how certain ideas keep on coming up again and again in the subject area, and to make them aware of the patterns and regularities in the subject. So, for example, as you begin teaching kids arithmetic and they learn that two plus three is exactly the same as three plus two and that two times three is exactly the same as three times two, that's a wonderful structure. We call it commutativity. It means that the order in which you do things doesn't matter. In this case it's the same going backwards and forwards. And then you say to them, "Well, does that mean that three minus two is the same as two minus three, or that three divided by two is the same as two divided by three?" And as they begin to realize that isn't the case, you begin to afford them access to one of the structures of mathematics – which is that some kinds of processes do have this commutative property and others don't. And what are the implications of that? Where can you go from there? And this is again a question of transfer. We talked about that earlier, because as you begin to get access to those structures you're getting ideas that you can apply again, and again, and again in new situations.

And so the notion of structure in mathematics is probably one of the most obvious ones. Mathematics is a field where most people who teach mathematics will readily understand the notion that there are certain kinds of structures. There's a notion of balance. There's a notion of equilibrium. There are notions of ratio and proportion that just keep on coming up again, and again, and again, and whether you're doing primary arithmetic or you're doing algebra, those notions return, repeat themselves – and you get a sense of how these organizations really make sense of the subject. In the case of a field like literature, the structures tend to be somewhat more elusive. They aren't as obvious. They don't stare you in the face the way they do in mathematics. But they're there, nevertheless, so that you find that teachers of literature will often ask students to think about notions of theme. What's the theme of this story? And students will say, "Well, I'm not sure, what is a theme?" And so you begin to get examples and try to show them. Well, what about character? What about plot, and how is plot like or different from theme? These are aspects of the structure of literature in some sense. And, we have centuries in which people are trying to identify these structures and to use them to help people learn these ideas and appreciate these ideas. When you're studying Shakespeare, what's the difference between the structure of a tragedy and the structure of a comedy, and how do you know when you're reading or watching or experiencing each one? Those are aspects of the structures of literature. So you can go field by field and get examples of structures.

Many scientists will argue that in modern biology the theory of evolution is the central structure of all of biology. And it's got core concepts, like adaptation, like organisms and environments, like the notion of chance, and what's the role of chance in how well organisms adapt to environments – and how does that relate to notions of evolution? I mean, these are core ideas and they keep on coming up again, and again, and again. And to teach biology without introducing students to those core ideas would be like teaching people supermarket without giving them any sense of the organization. So in just about every field of study you get a kind of grammar, a kind of syntax, a kind of structure of the field which is the code that students have to be given access to so they don't think all their learning is a long list.

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Discussion of pedagogical content knowledge

Pedagogical content knowledge is an idea that we developed to try to explain a really interesting anomaly – and the anomaly is that many people who know a subject very, very well, find it nearly impossible to teach what they know to somebody else. It's a really intriguing problem. The world is filled with people who know how to read, but they can't teach reading to somebody else. The world is filled with people who can write, but then their own child comes with an essay they have to write, and they ask for help, and they don't know where to begin. There are people who are great historians and have enormous difficulty explaining the histories that they themselves know to someone else. And we certainly know that the world is filled with mathematicians who seem to find it very difficult to teach mathematics to others. So the notion of pedagogical content knowledge grows out of the question: how is it possible for someone who already knows something to teach it to someone else who doesn't? How do you create a bridge between what you know and what somebody else does not yet know, but needs to know? And, like building any kind of bridge, it requires a different kind of understanding, a different kind of process. It requires understanding both what you know and what is already inside the students' heads, so that you can create powerful, and flexible, and rich connections between those two.

What do those connections look like? Well, first of all, pedagogical content knowledge often takes the form of understanding what kinds of examples and analogies, metaphors, stories, drawings that you might put up – visual representatives, experiences the students have outside the classroom already – that will create some of these meaningful connections between what the students already know and what it is we want to help them know. And that's not a trivial task. It's an extraordinarily difficult, complex task that takes years, and years, and years to learn. And, in fact, having taught now for nearly 40 years, I'm still learning, developing pedagogical content knowledge with respect to things I know. As I get more and more insight into how to explain them to others.

So, for example, in the teaching of mathematics – this very abstract, powerful, symbolic system – how do you teach mathematics to members of the species that are young and concrete and very much caught up in their own personal experiences? That requires pedagogical content knowledge. It requires understanding what kinds of experiences, what kinds of objects to manipulate, what kind of examples you can use to help students acquire an understanding of very, very complex ideas. And the important insight of pedagogical content knowledge was really at two levels. One was that someone who understands a subject matter deeply still doesn't know what he needs to know in order to teach it to someone else; that subject matter knowledge is not sufficient for teaching, although it's increasingly clear that it is necessary. So, teaching something well to someone and only having pedagogical knowledge of it, but not content knowledge as well, is also probably impossible. So there are two kinds of understanding and a very substantial part of pedagogical content knowledge is not only the understanding of the subject so you can figure out the variety of hooks that you can help create in the subject, but it's having profound understanding of who the students are, so you understand where the hooks are in them, as well.

And that's where questions of culture, and of language, and of the developmental status of the students become absolutely essential parts of pedagogical content knowledge. You cannot build a bridge from one side of the Golden Gate to the other if all you know about is your side of the Golden Gate, because how are you ever going to know how to anchor it at the other end unless you understand that terrain very, very fully. That's why pedagogical content knowledge is equally concerned with a profound understanding of the subject matter at one end and of the student's intellectual and motivational developmental and cultural standing at the other. It's a very complex idea, but I think it captures the essential challenge of becoming an extraordinarily good teacher.

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Discussion of finding the core ideas in a subject area

How do you identify the central ideas in a subject area? That is the million dollar question, really, because it is the question that the scholars in that area wrestle with constantly. I mean it's not one of these simple questions where the answers are in the back of the book. And so it is a process of careful analysis. For example, one of the things I've done in preparing teachers is I've asked them, "Imagine now that there's a class you're teaching, and you've got 20 weeks to teach this class. Now, think about all the things you might want to teach in those 20 weeks. What if you then learned that you only had ten weeks for teaching it. What would you leave out? Would you simply lop off the last ten weeks? Or would you try to reorganize it in some fashion to make sure that certain ideas or stories or principles or concepts or facts were in it? Well, what if you learned that there are only five weeks to teach the class?" And I keep on pushing it back. And then I'll say, well what if you had one day? And somehow in one day you had to somehow help students get access to what really counted? Now, at that point some of the students will just throw up their hands and say it's not fair. But the very exercise of asking that kind of question forces us to rethink, and rethink, and rethink what does it mean to understand this subject well?

So if I were to say to you, "If you were an English teacher, what if you could only teach one story, one novel, or one play and that had to be in some fashion, the window to the world of literature for your students. Which play would you choose? Why? And what would you ask students to do with the play? Would it be ÔKing Lear'? Would it be ÔRomeo and Juliet'? Would it be one of Arthur Miller's plays? Would it be a Faulkner short story? Would it be Tolstoy's War and Peace? And why?" I mean, that's the kind of question that pushes you to begin to wrestle with, what's the big idea here. And what's interesting is that there may not be a single big idea.

For example, in elementary arithmetic, Dr. Lee Ping Ma has studied what she called the profound understanding of fundamental mathematics, and she discovered that in elementary arithmetic knowledge is organized into what she called knowledge packages – just clusters of ideas that are connected internally to one another, and then those ideas in turn, those packages, are connected to one another. And what she discovered was that in China the teachers and the kids understand those packages and teach them, whereas in the United States we tend not to. We tend to teach arithmetic as if it's just a set of computational processes. And Lee Ping Ma maintains that's the reason why consistently in international comparisons the Chinese kids dramatically outperform American kids, because we don't stop and ask what those basic core ideas are.

Similarly, with a field like history. What are some of the core ideas about human power, about the clash of cultures, about the way in which societies organize themselves to engage in certain kinds of activities, internally and externally? And how is it that if you understand those, then you could look at different societies, different nations, over time in different places and be able to see the patterns and the regularities? But you've got to be able to understand those patterns and regularities yourself as a teacher before you can do that. And then you notice that some of the ideas we've been talking about earlier, ideas of transfer, ideas of structure, apply here as well. We're talking about the transfer of knowledge. If you can get access to those key, core structures of a subject matter you can transfer that learning.

I mean, think of the example of learning a foreign language. If you try to learn how to conjugate every single verb in a language, one at a time, as if each verb had its own unique character, you'd spend a lifetime learning the language and every time you encountered a new verb, you would think you have to learn its conjugation from scratch. But would we learn? We learned a new language. Isn't there a certain limited number of kinds of conjugation? And if you say, "What's the word for to bungee jump," and the person says, "Oh, it's such and such." And you think, "Ah, that's a such and such kind of word." You're thinking about kinds of conjugation. They say, "Yup, that's right." You immediately know how to conjugate it because you understand a core principle that transfers, that applies over and over again. And they might say, "Well, it's almost like that. There are a couple of little exceptions." That's fine, too, because you're still doing variations on a theme. And we know about this musically as well. I mean, there's certain kinds of musical performance with certain kinds of structures, and you learn to anticipate them. So, it's different for each area. You've got to know it in each area. You can't simply know it in one and say, "Well, I understand the structures that work in history, I guess I now don't have to worry about mathematics, biology, physics, etc." You have to know them for each subject and then begin to elaborate and work with them in your teaching the student.

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Discussion of structures in science and history

Science and history make an interesting contrast if you begin to think about how notions of understanding are the same or different in those two fields, and therefore, how their teaching might differ. Let's take a vivid example. When we first introduce science to kids, one of the first ideas they learn is the idea of an experiment. What do scientists do? They do experiments. And, you know, you put on your white coat. And as they learn about scientific method they learn about experimental groups and control groups. And they learn the great stories of scientific experiments. They learn the store of Pasteur and they learn the stories of Jonas Salk and they learn – I mean the notion of an experiment is very much at the center of what it means to do science, to generate evidence, to make inferences and come up with theories in science. Now, let me set aside for a moment the undeniable fact that there are fields of science where it's very hard to do experiments – like astronomy. But let's just take it for a given that experiment is a great idea in science. And now we start learning history. Well, how do you do an experiment in history? Well, you suddenly realize that that's not the way you do history. We don't have, we can't put one historical period in an experimental group and another one in a control group and see what the difference is. But we're still doing comparisons. We're still trying to create evidence. I mean there are certain ideas that do cut across – notions of description, of analysis, careful, careful observation, notions of what is the evidence for your claim, notions of theory. But the fundamental process of experimentation which is at the heart of work in science, has no real analogy in history – if what you mean by experiment is that the scientist is controlling conditions and studying what happens under conditions that she herself has controlled.

So what does a historian have to do? The historian in some sense has to look for comparisons where, if you will, nature has made experiments, not scientists. So you ask, well, why was it that the American Revolution had these properties and proceeded this way, but the Russian Revolution, which we also call a revolution, had different properties and worked out a totally different way? Why is it that the American Revolution yielded a democratic form of government that remained stable for 200 plus years and the Russian Revolution yielded a more autocratic kind of government that had other kinds of properties. Well, you can say that's almost like an experiment. So you're still trying to generate evidence through comparison and contrast, careful observation and analysis. But you don't have what the scientist in the experimental discipline has, which is control over the variables that you're using for your work. And so what's really important as teachers teach different disciplines to students, is for the students to appreciate that there are certain kinds of ideas like description, like analysis, like careful observation, like evidence, inference and theory, if you will, that are useful across disciplines. But there are other ways in which very important methods of work in one discipline just don't show up in another discipline. And I think history and science make a lovely contrast here.

History and literature also make a lovely contrast. Because when a student study history, one of the first questions they always have to learn to ask is did it really happen that way? And that, that's, you know, if somebody says that beings from outer space came down to the North American continent in 1775 in the middle of the night, they wrote the Declaration of Independence, slipped it under Thomas Jefferson's pillow and then went back up into outer space. Well, you know, that's a perfectly interesting narrative and the question is, but what's your evidence that it really happened that way? Did it really happen? Now, if I write a novel and it's a novel about beings from outer space coming down and slipping the Declaration of Independence under Thomas Jefferson's pillow and somebody says, "That's a perfectly awful novel Ôcause it didn't really happen that way." My response is, "You don't get it. This is literature, this is a novel. It has different purposes. There are different canons that we use for determining whether it's a good novel or a bad novel, and they're not the same as the ones we use for determining whether something is good history or bad history – unless we're going to use the novel for teaching people history." And so here again, understanding the differences in what counts as evidence and what counts as knowing a subject between subjects becomes terribly important for teachers to understand, and in turn for students to understand.

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Discussion of metacognition

Metacognition is thinking about your own thinking. Sometimes we use the phrase "going meta" instead of metacognition, and what we mean by that is being able to step back and, see yourself and what your doing, as if you were someone else observing it. It's becoming an audience for your own performance. And in this case it's your own, intellectual performance. We know that this is extraordinarily useful when we think about learning physical skills. So that when someone is learning to play golf, we know that seeing video tape of their own swing is enormously helpful for beginning to understand what they're doing well, and what they're doing poorly, because, so typically, we don't even know what we're doing when we do it. And therefore, it's very hard to improve a process that you're engaged in if you don't have any idea of what you're doing when you engage in it. I mean it's no accident that ballet studios have mirrors in the walls. Because even someone as exquisitely skilled as a ballet dancer, does not really understand what she looks like and what she's doing just from trying to experience it in her body. She has to be able to see it as others might see it before she can begin to improve it, and modulate it, and notice now that physical skills are so much easier then intellectual ones, because physical skills are at the end of the day, visible. They're there. You can see them.

Cognitive work, intellectual work, thinking and feeling is invisible, it can't be directly observed, so the question for us is, what's the equivalent of the mirror on the dance studio wall, of the videotape of the golf swing? We're saying, "How do you become thoughtful about your own thinking as you're doing mathematics and history – as you're doing the teaching of biology, the teaching of composition." And, that's a great challenge. Helping people learn how to go meta on their own thought processes, which are themselves not directly visible. And yet, if you can't do that, it becomes very difficult to improve them – to get better at them – because how can you improve on those things you can't see or feel, and therefore you can't understand. And that's the great challenge, not only of cognition, but when we talk about cognitive apprenticeships for example. It's so much more difficult to model, and to shape, and to guide processes that aren't directly visible. It's not like learning to become a blacksmith, or to be a shoemaker, or even to be a midwife. When learning to be a mathematical problem solver, or someone who can creatively think up narratives in writing, you need to be able to go meta on your thinking, and not only on your observable performance. So that's what megacognition is.

I think it's, important for teachers to give students chances to reflect on their learning, because the students are the last ones to realize, very often, what they're doing when they're successful and when they fail. Here again, if I'm hitting a golf ball, and I see when I finish my stroke the ball has gone two feet to the left of the tee, I've got pretty good evidence that there must've been something I've done wrong with my swing, because it just didn't get anywhere. But still, I need, some way of analyzing and looking at my swing, or I have no chance to learn to hit the ball so that it's going to go 200 yards and straight down the middle. Well, if I'm learning to write an essay, and let's say I write two essays, and I get an A from you on one of them and a C on the other, and the teacher says "See, you CAN write a good essay, do more of what you did on the A essay, than what you did on the C essay." And I say, "But I don't know what I did on the A essay that was different then the C essay, I just have no idea." That's where it becomes terribly important for the teacher to assist the student in reflecting on their own learning, because otherwise, how do I become better, how do I move my learning from the kind of thing I did in the C situation to the kind of thing I did in the A situation, if I don't have access to the kind of understanding of my own performance that I need to improve it.

And I think that's the essence of it, and it's true in field after field. It's so true in mathematics, where kids get confronted by things like more complex contextualized word problems, and they get some right and some wrong, and they just don't understand what it is they did when they got it right – they just don't have that meta understanding, "What was I doing when was doing it well as against what am I doing when I'm doing it badly." And that may be at the end of the day, the most important thing we can teach students, and what's tragic is that very often – because of the press of time – that's the thing we sacrifice. So for example, think about hands-on science. We design these wonderful laboratory experiences for the students, and they go, and they roll balls down inclined planes – remember that from one of the tapes. Or we have them construct their bridges out of toothpicks, and we expend so much time doing, having the experience – doing the experiment – that we don't take the necessary time the next day, or at the end of the hour to say, "Okay, stop doing what you're doing. What was really happening there? What were you learning? Why was it that you concluded the ball did this – it was doing this – and when the ball did that, something else was happening? Think about your own thinking here. How were you using the evidence, how were you, on what basis were you making those inferences." And the students should then be discussing it, arguing about it, trying to make these things clear.

Very often we do these lab experiments, and we run out of time, and so at the end of the day they've done the experiment, they've had the cognition, but they have not been able to go meta, and in the absence of going meta, the cognition is almost a waste of time, because they don't know what they know. And therefore, the likelihood that they will be able to transfer that to another situation is dramatically reduced. Metacognition is one of those processes that helps take what we learn in one situation and transforms it into a level of understanding that is much more likely to transfer to another situation. And that's the kind of connection there is between metacognition and learning and transfer. It's at the heart of the process of taking what you've learned, and making it useable in transfer situations.

It's important for teachers to give their students MANY opportunities to reflect on their learning, because the learning itself is rarely sufficient to create understandings of a sort that can be transferred readily to other situations, and because the absence of opportunities of reflection on one's learning is part of why some kinds of learning are simply barren and infertile, if you will, and other kinds of learning turn out to be highly productive and useable again and again. And I think the heart of it is creating opportunities to step back and analyze, and reflect on your own practice. I mean, it's no accident that when we prepare people to do very complex and important kinds of skills, we create opportunities for reflection.

I spent years teaching medical students how to take medical histories from patients. And we didn't just teach them to do the histories. We had them practice it and then look at a videotape of their own performance, so they could begin to see things they were doing that were and were not productive of getting good information from their patients. Without looking at their own practice they found it very, very difficult to improve that practice. When students learn to write we often have review groups, where students review each other's essays, and critique and give feedback. Well, that's a way of going meta, because if you can step back and say, "Suzanne, did you notice that when you used this word, it had much more power than when you used that word? Why do you think that was so? And how can we get you to use more words of the first kind than of the second kind?" And you say, "I didn't even realize I was using those words. I mean, it just, it just came to me naturally." And you say, "Well then, if you're just doing it naturally, then you're not going to get control over using it purposefully." And that requires going meta. Then, maybe helping you reflect that way, I get some insights into my own performance as well. So these are just several examples of how it is that going meta, becomes the lever for ratcheting learning from a low level to a much higher and transferable level.