[From Rick Marken (960226.2130)]
could you present the kind of learning data that you feel HPCT should
be able to predict?
Shannon Williams (960226.15:30) --
If a person is presented with a problem (he is having difficulty making
some perception match its reference), and I present some partial
solution to the problem, I want to be able to predict if my partial
solution gives him enough information to solve his problem.
OK. That helps a lot.
The kind of problems you are talking about clearly involve control. Take
a water jar problem, for example. You have 3 jars and are told that they
can hold 8, 5 and 3 units of water, respectively. You are also told that
the first jar is full while the others are empty; so the contents of jars
is 8,0,0, respectively. The goal is to divide the water in the first jar
equally between the first and second jar so that you end up with the
contents of the jars being 4,4,0, respectively. You are to reach this goal
by pouring water from one jar to another.
Control is involved because you want to bring the current perceptual state
of the contents of the jars (8,0,0) to the reference state (4,4,0). You do
this by producing intermediate perceptual states that follow the constraints
of the problem. For example, you might start by pouring from jar 1 into
jar 2, changing the perceived contents of the jars from (8,0,0) to (3,5,0).
The next move might be to pour from jar 2 into jar 3, resulting in (3,2,3).
A person who knows how to solve water jar problems will change the initial
state of such a problem into the goal (reference) state in something
close to the minimum number of moves (in this case, about 7). A person
who does not know how to solve such a problem may make hundreds of
moves before hitting on the solution; I saw one person spend nearly an
hour making moves and never getting the solution.
A water jar problem like this involves both some ability to control (the
ability to correctly change from one problem state to another, for example;
just knowing what state results when you are in state (6,2,0) and you
pour from jar 1 into jar 2 involves the ability to do some complex
controlling--in imagination and reality) and learning. You can't tell
whether any particular action (move) is part of a control or a learning
process just by looking at it. For example, is the person who moves the
problem from state (6,2,0) to state (6,0,2) cleverly controlling for
having 1 remaining in jar 1 that can then be added to 3 from jar 3; or
is the person making moves randomly to see what will happen next
(trying to learn what is important to control about the problem)?
I can't see how you could know this (whether the problem solver is
controlling or learning to control) without doing something like the
Test to determine whether the person intended to produce a particular
state (6,0,2) and, if so, to produce it as part of a process of controlling
for a more complex variable (producing 1 to add to 3) or whether it was
produced as part of a process of exploration, where the result might have
been intended, but not as part of a process of controlling for anything
other than producing the final goal state.
To the extent that the problem solver is in control of the problem --
that is, the person knows which perceptions to control and how to control
them -- then you can predict each move and predict the effect of
disturbances to any state of the problem. To the extent, however, that the
problem solver is not in control of the problem -- that is, the person has
little idea what perceptions to control or how to control them -- then it
will be difficult to predict anything other than the fact that moves will
be made nearly randomly; nearly, because the learning process is assumed
to be a _biased_ random walk; control processes -- and the moves that support
them -- that produce an approach to the ultimate goal (problem solution)
will persist longer than those that produce an apparent move away from
the ultimate goal (indeed, there is conventional problem solving data that
suggests that this is the case; a means-ends strategy, which makes the
current state of the problem look more like the goal state, seems to persist
-- and interfere with the ability to find the correct control strategy --
throughout problem solving).
I have always wanted to apply control theory to this kind of problem
solving. The first thing I would do is allow a subject to become skillful at
solving a certain class of problems, like the water jar problem. A person
is skilled when they can solve any version of the same problem (in this
case, any set of 3 jar capacities) in the minimum number of moves. Once
the person is "in control" of the problem, I would start testing to see
what is being controlled; I would try to determine what this (and several
other) skilled problem solvers control in order to solve the problem.
Once I knew what variables were controlled by the skilled water jar
problem solvers, I would start studying how novices learn to solve
these problems. I would do this by testing for control of the variables
that were controlled by the experts and I would do this throughout the
learning process. My goal would be to determine whether people learn to
control a particular "expert" variable suddenly (all or none) or gradually;
whether control of a particular "expert" variable is tried, abandoned and
re-tried; whether several "expert" variables must be tried all at once in
order to gain control of the problem.
These are really interesting questions (to me) but I think it would be
hard to answer them before I knew what variables are controlled by skilled