LC0cO3 Microtheories in Microworlds

The Role of Microtheories in Microworlds

Practical matters are often in advance of the theoretical questions that
are of greater interest to some of us. And indeed, if you look around at any
education conference, you will see marvels of modern technology available —
but one of the questions we should always ask is “What does this mean ? What
does this all amount to ? What is really profound in this body of work?” The
touchstone that I use, the guide that I follow in trying to answer this
question, in respect to educational issues, comes from some questions put
forward by Jean Piaget in a book he wrote for UNESCO titled The Science of
Education and the Psychology of the Child
.[1] Piaget said that we can not claim to really
understand what we are doing as educators unless we can answer three questions:
What is in the child’s mind ? How do our actions change what is in the child’s
mind ? And why do some changes persist for a long time while others do not ?
Of course, you know the notions of constructivism, and the notions of
constructionism as formulated here try to provide some sorts of answers to that
question. My own research tries to look in exquisite detail at questions of
what’s in the mind and how it changes over time. But I would like to say
something else about that. I think I have a contribution to make here. I
would like to talk a little bit about the way these word worlds relate to a
child’s language knowledge. And how microworlds relate to what children do.

Let me take the following starting point. Monday we heard Seymour Papert joking
about grammar. “Should we teach children grammar so they can speak better ?
That’s perfectly silly.” Of course it is. If you ‘can spell all the words you
use and your grammar’s as good as your neighbors,’ [2] what more do you need ?
What is it one learns
from playing with a BEACH microworld ? The child learns that there are two
classes of words in the world. There are object-names, such as SUN or CAR or
TRUCK. Then there are action words, the words that change things. What are we
really teaching the child ? If you are only dealing with one word at a time,
it’s hard to say that you are dealing with parts of speech. But let’s look a little closer.

Apple Sprite Logo State Variables
State Variables and State Changers
POSITION FORWARD :number; BACK :number
HEADING RIGHT :number; LEFT :number

We have here a short description of the set of state variables that completely
describe everything there is to say about a Sprite Logo Object. It has a
number, it has a shape, a color, location, and heading. What we are doing in a
sprite Logo Word World is segregating words of the computer language and the
natural language into names for objects and state variable changers. Does that
take us very far ? Perhaps not very far, but it moves us in an interesting

The CITY microworld

The CITY word world, with Logo sentences.

Some of you may recognize this as a very early sketch of Tech Square, home of
the Artificial Intelligence laboratory. I think you can see in the top line of
the slide a typical statement in the language I used to control this
microworld. The word NEW determines that a new object will be created. If
you want to have more than one object of a specific type in your word world,
you have to be able to distinguish between them. That’s what adjectives do for
nouns. The word BLUE modifies the following word GIRL; together they specify
the shape and color for a single object. When you can use adjectives, you can
have a red girl and a blue girl, and others as well. What I am suggesting to
you is that it is possible — even easy in Logo word worlds — to justify for a
child greater complexity than is possible in microworlds controllable by one
word at a time. Years ago I could not get very far with the TI-99 because
there was precious little memory in the computer. But Logo sprite systems and
LogoWriter systems have much more memory available now. Let me show you how
one might go ahead to actually parse something such as this phrase:

Suppose we have a phrase “the red girl walks fast.” What would we like the
sentence to do ? First, to specify the active object and then to change it’s
state. By writing procedures for the specific words, anyone can make that
happen. Consider this example. What does the word “the” do ? Does anybody
know ? Well, surely a five year child will not know. So it has my
favorite procedure “TO THE” — which does absolutely nothing: it outputs
whatever is input to it; it passes the buck. We can distinguish between sprite
objects of the same shape by color differences. The word RED defines the value
of a global variable which makes it possible to use that for testing against a
two part data structure which contains a sprite number and a color. Thus we
can tell at any point whether we are talking to a red girl, a blue girl or
yellow girl or a green girl. We can do this with elementary Logo procedures.
In the same spirit of radical simplicity, you need not distinguish between WALK
and WALKS unless you want the difference to make a difference. You have
here a very simple set of procedures, which is all you need to parse sentence
level statements in this Logo word world.

Are we teaching the child grammar ? The person who makes such procedures learns
grammar of a sort. What sort of grammar is it ? And how does it relate to the
“real thing” that grown up serious people study. Here I think we get to the
key issue of my talk. I suggest that as the child proceeds to build things like
this, sets of procedures, the child is beginning to construct in her mind a
microtheory of the domain — a microtheory to go with the microworld.
And what is that microtheory about ? It specifies what are the objects of the
microworld, what are the relations between the objects in the world and how
each specific one relate to each relevant other.

About Different Kinds of Theories

Let’s talk a little more about the notion of a microtheory. We hear a
lot about microworlds. But what about theories. In my recently published
book, volume two of Artificial Intelligence and Education, the ideas I’m
describing right now appear in the first chapter, titled “Shared Models: the
cognitive equivalent of a lingua franca.” It begins with a discussion of what
you might call a common sense theory of what theories are all about. It has
four components; four types of theories are dealt with: perspectives, common
sense theories (or minimal models), technical theories (such can be as
elaborate as quantum electrodynamics), and presentational theories, the kinds
of simplified stories we tell to lay-people or to children give them a flavor
of what a technical theory is all about.

Let’s start with an example of a perspective. The world, for the longest time,
was something we thought of as the center of the universe. And, of course,
many of us still do. Once people got off the surface of the planet, it became
very hard not to see that what was most important about the world was not that
it was so big or capacious but that in fact that served as a container for the
biosphere in which all of us live. Though it’s kind of a peculiar observation
to think about it this way, the earth is kind of a jar — but with the contents
on the outside. Strange characteristics for a container; but with implications
relating to the fragility and stability of the environment and the possibility
of evolution. A simple observation, such as that one, embodies a perspective.

Sarkhar’s Theory of Social Cycles

Let me give you an example of a common sense model, a specific one
which — if we are going to talk about changes — is not inappropriate. For
the past couple years there has been a fad of predicting financial ruin.
There is a fairly popular book lately called “The Coming Great Depression of
the 1990’s.” In that particular book, the author advanced a theory, a cyclical
theory, of the development of society. He says that when you have a time of
trouble, you get a revolution, and what happens in a revolution is that the
Army takes over. Rule by the military is eventually replaced — because
military people are often not so flexible as others — is replaced by
intellectuals taking over and getting power; they dominate the country or
region. But of course intellectuals are too much caught up in ideas and pay
too little attention to details. Those people who pay attention to the small
details, the bankers and administrators eventually dominate the world. And
what do they do ? To amass all the fortunes and power of their region of the
world, they grind down everybody else. They drive soldiers and intellectuals
down into the lower classes, so that once again society has trouble and
revolution. This is what I would consider a minimal model. It is essentially
a common sense theory for thinking about phenomena that are too important to
let pass, but for which we can have no better theory than the kind of thing
represented here.

About technical theories: I suppose you already know what those are about, so I
won’t say much about them. These are all the theories of modern science.

Presentational theories — what are those ? They are simplifications used to
introduce and explain technical and common sense theories.

How MicroTheories Work in MicroWorlds

Now what is a microtheory ? Well, with respect to a microworld, it is a
theory of what goes on in the microworld. And since the microworld itself is a
made-up, presentational model, whether made by an educator, a parent, or a
software designer, the situation is one where the child is developing piecemeal
a theory for something that has already been simplified.

My speculation is that the distance between a child’s microtheory for what is
happening in a microworld and the ultimate knowledge about what is going on in
the microworld, that difference is much less than it would be for a child
constructing microtheories about what is happening in the larger world. In a
sense then, the possible educational gain of microworlds comes from a more
intimate fit between possible microtheories and the way the microworld really

Ultimately then, the main thing that a person gets from working with a
microworld is the experience of doing a kind of virtual science, of saying
“Here is something interesting enough to be worthwhile explaining. I’ll come
up with my best shot, try it out; if it doesn’t work, well we’ll debug it and
improve our theory.” That approach is in the best traditions of science.

A further observation I can make is that we are looking at intermediate kinds
of objects. We really don’t care with respect to any microworld what the
child’s ultimate knowledge is. But the interesting thing here is the notion
that microtheories are kinds of intermediate theories. The reason there might
be something deep here is that this resonates with Piaget’s notion of the
grouping as a kind of precursor structure that does not yet have the full
competence and status of a mathematical group. The grouping is a way station
on the path to the ultimate knowledge that one would like to reach. So these
microtheories for microworlds are intermediate structures

I would like to draw to a conclusion if I may, then. As you can imagine, I am
leaving out a lot here, fascinating to me, perhaps a little less so to you.
The essential message I have been talking about with microtheories is that we
want to look at the intermediate structures. Why is that important ?
Let’s think about life. We all know how it begins and where it ends. All of
interest happens in between
. I would say to you that in cognitive development,
that despite our great haste to have children grow right smack up and become
ace scientists or mathematicians or writers or whatever, it is better to let
them have the choice and freedom to follow their own paths and become their own
authentic beings. One part of this is that their minds should be stocked more
with their own personally worked out theories than with ideas adopted from
others but never understood. This is the greatest gift we can give to any of
the young people who come under our influence as educators….

Publication notes:

  • This text is abstracted from the final “keynote” talk at the International Conference on
    Technology and Education (ICTE) in 1993. Cambridge, MA. Unpublished.

Text notes:

  1. Viking Paperback Press, 1971.
  2. This line is, as many will recognize, a wisecrack from Iolanthe (by W. S. Gilbert) wherein the heroine defends herself by putting down the pretensions of British nobility.
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