the opening interchanges of the dialogue
Bob: American society has been undergoing major transformations from the electronic revolution, from nuclear family fragmentation, from the disappearance of minority role models in the education system, and even from changes in social perceptions of the value and necessity of labor. It is very clear that America’s public education system is in trouble. I have committed a large part of my life to work in the area, and I wonder whether the educational technology community can develop innovations of real value as opposed to projects whose primary outcome is career advancement. What are the problems?
Oliver: There’s no clear answer. We need to ask fundamental questions about issues relevant to education. We need to ask what learning consists of in kids and in grownups. Is teaching a foreign language different from teaching arithmetic? I think it probably is, in all the important details. Is there anything at all conceivably general about instruction ? I think not, but if somebody wants to look at that, let him look. What kinds of games canwe play which will make it attractive for kids or grownups to learn something? How do we understand and measure motivations? How do we put together a vocabulary that will permit us to talk consistently about motivations and motivation structures?
Finally, we have to ask organizational questions. How do we fit all those questions together in a way that can be thought about and that can be a base for research? Without a generally accepted base, we won’t get any kind of durable change. You’ve mentioned a lack of role models. Well, teachers need them too, and they need to see research being done by great people. Even if it doesn’t apply directly, such research will surely make teaching easier and more effective.
Didactic and Constructive Views
Bob: Educators generally view knowledge as something to be transmitted from one person to another. My sense is quite different, that self-construction by the student of his own knowledge is central. We need to develop constructive alternatives to students "getting taught." Years ago in a BYTE magazine article, I claimed that "the central question of education is how one can instruct while respecting the self-constructive character of mind." I still think that’s true, but I need to develop some more explicit and better articulated description of my answer. There are of course many proponents of this viewpoint.
Oliver: None of us has a competent expression of what education’s about. And if we had, it still wouldn’t face up to problems of others’ views because it won’t face up to their values, depending on whom you’re talking to. Education is not like a problem in physics with something to be solved. It’s about how to make things better. It’s a control process that we’re worrying about. Being precise is difficult because we’re aiming at the high level issues,like respect for learning and the applicability of learning outside the schools.
Just to take issue with what you said, an important question is the extent to which knowledge is stuff that is transmittable by a teacher at all. Clearly some is, some isn’t, and some can go either way. Telling someone, however accurately, how to ride a bicycle is no help; a teacher, or better yet a parent, can help a child learn, but not by transmitting knowledge. That Sofia is the capital of Bulgaria is most easily transmitted from a teacher or, equivalently, a book or an atlas; and there is no way that a child can derive it just by thinking about it, the way he can discover arithmetic facts. I think that probably educators know all this too. But your point is well taken.
Bob: Let me raise one possible kind of education problem with an example.As a child my son seemed to have some natural talent for singing–which could have been developed for his own lifelong satisfaction. In such a situation,what would be the right thing to do?
Oliver: That’s a ‘should’ question. It has to do with what is worthwhile.
Bob: For me, that’s a reasonable question: what are the worthwhile things?
Oliver: Well, in some sense it isn’t a reasonable question, in that there isn’t an answer. I mean it’s not a question that can be argued about; it’s an expression of your own values, a different kind of question. Is it worthwhile to make money? Surely, for many reasons. Is it worthwhile that making money is the over-riding justification for everything? Not for me, and, I am sure, not for you. MY primary should is different: to find out the truth about the world. Here’s another example of how not to think about education.
Education is not Physics
Oliver: At a conference recently someone said we need "a physics of software." Such a program is not feasible, because in software there aren’t any physical truths with which you can get as accurate as you want by trying hard enough; and not only accurate but precise, with physical laws which are real laws instead of tendencies. I’m sure education is very much more like software than physics, even if there is some precision to be had. With respect to any vision of educational innovation, we must realize that the physical sciences are very special and limited, and thus provide generally a poor archetype. In physics, things work because you can narrow down consequences and bound them, and look down into detail. The accidents of context do not have much affect on the outcome of lawful relations.
In education, we can’t do that; to discuss a vision of education means we have to look upwards to purposes and values at least as much as downward to detail. We must ask what kind of society do we want and do other people want, and even what will other people want after they’ve been well educated. To present a dream about education is to ask what culture is about; and to ask what cultures will be about or be wanting; and to ask what the distribution of human goals is going to be. This isn’t to say such questions are not answerable. It’s essential to ask such questions, but the process of creating answers is going to be rather difficult and quite different from doing a hard science.
Bob: Your friend Von Foerster said it very well, "The hard sciences appear hard because they tackle soft problems. The soft sciences face the harder problems."
Is a Common Curriculum Possible?
Oliver: And because of the difficulty of education research, too often the content falls by the wayside. I recently met a fellow who studies instruction. Not instruction with respect to any domain. Not instruction with respect to any age or pupil set. He doesn’t want to instruct anything particularly, just instruct in general. My own conviction is that nothing much will come of this.
Bob: I share his interest. There’s a profound question, in fact, of how much domain independence there can be in education. Is it possible to imagine creating a general curriculum for a wide diversity of people; one focused less on specific context than ideas of proven power? Consider it as a thought experiment designing education for colonies in space. For those strange new artificial worlds, which have to be completely designed, what sorts of minds and educations should people have in such an environment?
Oliver: We don’t need the space station as context to discuss the issue. Let’s look at the question directly. What have you in mind?
Bob: If then we think about the content fields of knowledge, we need to ask what are they? How stable are they? Are they independent of what we want to do? What is the nature of knowledge? And how can we imagine a way of people relating to one another in respect of the different fields of knowledge which will focus on the most important ideas, and how can we think about what people should know, what their minds should contain?
Oliver: You used ‘should’ several times. Exactly where does that should come from?
Bob: Right at the heart of education is the question of freedom and individual choice; how do the goals of a teacher relate to those of a student ? As we look at our own children, do we want our children to grow up to be the kinds of people we are– and the answer may very well be yes– or to be people who will most effectively adapt to the circumstances they find themselves in ? Or do we want them to grow up to be people who have visions of their own to which they will try to make the world adapt? There probably is no single answer to any one of those.
Oliver: There can’t be, of course. I’d say that any vision of ours has tobe with respect to those values and just those. At some level those values and decisions aren’t right or wrong, at some level those are the way we are. It’s not education to enforce values–because values will change with knowledge–it’s education to support them. It is not just a farcical idea to teach values, but it can also be extraordinarily destructive– look atHitler. I always say a pox on ideologies, but I have an ideology of my own which is very like yours, with your notions about freedom and so forth. Maybe we’ve spent enough time talking about this level of generality, but I think it always should be borne in mind that values are held with respect to a society and a culture, and, for me at least, without regard to any binary notion of good and evil.
Bob: Let’s get specific then. Suppose we made a catalog of terrific ideas. My common curriculum would be such a collection, whether in music or athletics, or in language or mathematics. The issues are what should such a catalog contain and how do the contents relate to what a person knows. Let me give you an example. I think that Cantor’s proof–
Oliver: His Diagonal Theorem–
Bob: If you will, his proof of the non-countability of the reals is one of the simplest and most elegant arguments I know. I would like students to run into that, see it with the same intensity I have to its power and beauty. So I would propose that proof as one straight forward enough to be accessible and exotic enough to be engaging, as an example of what might go into a common constructive curriculum. (See Box.)
Oliver: I am not arguing that Cantor’s proof is not beautiful and compelling.Indeed, the intensity of feeling that a mathematical fact may offer is as great as any. On viewing for the first time certain infinite series of Ramanujan,
G. N. Watson says:
"[I felt] a thrill which is indistinguishable from the thrill whichI feel when I enter the Sagrestia Nuovo of the Capella Medici and see before the austere beauty of the four statues… which Michelangelo has set over the tomb of Giuliano de’Medici and Lorenzo de’Medici.”
from “The final problem: an account of the mock theta functions,”
J. London Math. Soc., 11 (1936) 55-80.
But there could never be more than one citizen in a thousand who could appreciate that. I don’t know that there are any ideas that should be part of everybody’s education. I don’t know whether that’s a should, or a should not, or a nevermind. Let’s face it, Bobby Fischer, as a world-class chess master, probably related most of his life to playing chess. That’s where his beauty was. He wouldn’t give a damn about infinite sets–why should he ? But I do think most kids are a little broader than that.
Bob: That’s the question I’m raising: can one in principle imagine the existence of such a thing as a student-centered curriculum? … or do we have to look at education as a process of individual and personal negotiation between individuals who know each other? Can there be in principle such a thing as a common student centered curriculum?
Are the real numbers countable ? We start by assuming the opposite: that the real numbers, both rational and irrational, can be all put in one to one correspondence with the natural numbers, and are thereby countable.Let us consider only those numbers between zero and one, each one represented symbolically as a decimal. Write them in an array; by assumption, this array contains all the real number between 0 and 1. If there is inevitably some decimal number not in this collection, then the numbers between zero and one are not countable. Here is an example of the array:
. 2 6 0 1 1 …
. 6 3 4 2 5 …
. 1 9 7 0 3 …
. 1 4 4 8 6 …
. 7 9 5 5 4 …
Let us construct the decimal number represented by the diagonal, that is, by the bold-faced digits, .23784 … . Now let us construct another number that differs from that one in every digit; it might be .12673… . This new number will be different from every number in the collection in at least one digit and is therefore not in it. Consequently, the real numbers between zero and one are not countable.