Teaching, no grades; computerized educational control

[From Chris Cherpas (961011.1118 PT)]
  [re: > Bruce Gregory (961010.1745 EDT)]
     [re: >>Chris Cherpas (961010.1316 PT)}
cc:

...Instead, a student would have a continually (measured in
seconds, or less, not weeks, months, or years) updated file
that includes estimates of the student's ability to control
any given subset of a full constellation/network of perceptions
relevant to being educated...

BG

I've come to same conclusion. Implementing it is another thing
altogether!

cc:
The way Mario Zanotti and I are (approaching) doing it, is to put an
entire -K-12 curriculum into a computer system with each "exercise"
associated with a set of variables which the student is supposed
to "control" (Suppes & Zanotti called them "structural variables,"
but I'm just starting to think in PCT terms); each "exercise"
is also linked (in a node graph) to other such units, mostly
indicating presumed prerequisite relationships. We think of this
network structure as always incomplete/falsifiable, but it provides a
default ordering that can be used at run-time and when looking at longer
stretches of data off-line (from nothing comes nothing). The content
represented by this collection is taken from national/state/district
standards which are increasingly published due to programs like "Goals 2000"
(The first conference on international standards was held this
year in Italy), as well as primary/secondary sources, texts, other
curricula, intuition, and previous versions of our own curriculum.

But, finally, to the point (all of this content and its structure
is necessary, but not sufficient, for a learning process): On top of
all this is, well..., a control system, which is continuously collecting
data on how each individual student is performing, and making decisions
as to where to move each student in the network. I can't get too
specific about the algorithms and student model here, but what we get is
a process which eventually (and relatively efficiently) converges to the
maximum rate of learning (defined in this context) for each student,
regardless of where s/he started. During the process, one can state
the probability (the system is Bayesian) of a given student's performance
within any given exercise. Here's an interesting (I think) result:

The average (across students and content) probability of error (i.e., in
the crude sense of obtained relative frequency of "wrong" answers
to questions posed) is between .30 and .35, when the learning trajectory
is steepest. Again, I'm sorry to throw around terms so vaguely here
(e.g., "learning trajectory"), but I can at least point you to the
Suppes & Zanotti (1996) reference (see Part III) I posted yesterday.
The point is that each individual (and it could be different for the
same individual for different topics, etc.) can learn fastest when
they commit errors about a third of the time. But we can go further
in both the subjectivist/Bayesian direction and the PCT direction, by
considering: what if we could model and estimate the "uncertainty"
the student is experiencing even when s/he overtly gets "correct"
answers? Then we might have a process in which the student experiences
error subjectively (at the .30 to .35 level?), but brings it under
control before committing to making a "response" or otherwise constructing
something which the system can evaluate. So, it would be possible for the
student to never hear the system say anything like, "That's not correct.
The correct answer is...," and yet the system (and the student) would be
"correcting" all the time.

We try to model and throw in every possible approach or mode that people out
there in the purchasing/using community say they want, such as "tests,"
but we don't really need or use these data in any special way. It's
strange, but governments and other folks pushing educational standards
seem to forget that to have standards, you have to find out if someone
can really meet them, and then, to do anything with that, you need to have
learning processes in place that reliably converge on people's actually meeting
these standards in a given amount of time -- otherwise, what's the point?
  (...other than to throw around the usual blame on teachers, students, parents,
genes, not enough money, not enough community control, not enough free
enterprise/choice, blah, blah, ...).

It's not company policy for me to say this, but personally I think teachers
are not the ones to be given the "freedom" to say what to teach and, in many
ways, how. Teachers without curricula that have been tested/testable
at least as well as the FDA requires drug companies to test drugs, are like
physicians having to either use off-the-shelf potions or put together their
own medications. Why are teachers expected to be such experts on everything?
In science, we try not to rely on some hermit to just know everything;
but somehow in the classroom it's expected that, instead of institutionalizing
a control process -- whereby _generations_ of people, dedicated to analyzing
and synthesizing knowledge and educating -- crucially and cumulatively tests
all along the way (as part of the control process), some poor individual
has to be brilliant all day long, individualize to each student's needs,
have complete mastery of their domain (and let's face it, if you want to
teach elementary math correctly, you better _know where it's leading_,
not just 1 + 1 = 2).

Computers are the way. It's not an obvious fact yet, but I think it will
become clear that automation of crucial parts of educating (and I don't
mean "administration" systems) is, like any other form of production
or service, inevitable. The stuff should be teacher-proof! A truly
"free" teacher could concentrate on what can't be automated, and to
make the best use of what can. And, I should mention, the real payoff
is going to happen before Kindergarten. All the evidence I've seen on
Head Start, for example, shows that it doesn't start soon enough. So,
computer-based education has not only got to be teacher-proof, it's got
to be parent-proof. Parent-friendly, yes. Teacher-friendly, yes. But
in a way that redefines these roles, so that each infant/child/person can
start benefitting from World Knowledge asap. It only takes one generation
of universally educated smart kids, and (so the dream goes...) we can start
having some decent generations of parents and teachers!

A long-winded reply indeed (hurricane warnings are already being issued);
but, alas, such a world-sized vision is often kept in clearer focus by writing
"imaginative" email messages than by actually doing the hard that would make
the email messages unnecessary.

Best regards,
cc