In mathematics education, one of the most important studies in our
history was an analysis of the Individually Prescribed Instruction
(IPI) approach of 1960s vintage that Stanley Erlwanger (1973) exposed as
generating pathological mathematical conceptions and meta-conceptions.
Since then, our field has gone on to embrace qualitative research
methods, interpretive research, field based teaching experiments,
and a variety of research methods that seek to reflect the complexity
of human understanding and human interaction.
But at the same time, the technology and psychology of teaching-in-
a-box also has evolved, making quantum leaps in theoretical sophistication
and technical implementation. Thus John Anderson and Christian Lebiere (1998)
in _The Atomic Components of Thought_ are able to claim to having identified
the basic building blocks of cognition, from which they can in principle
(and increasingly in practice) simulate any cognitive functions.
What a seductive enterprise. At a plenary session to a recent national
mathematics education research conference, one of our leading researchers
steeped in the history of our field, and himself having toyed at the
fringes of the situated cognition movement, explained his current research
agenda of capturing in computational detail the essence of exemplary teaching
practices.
Up until now it has always been possible to point to the shoddy products
promulgated on the basis of reductionist theories, and to attack the
theory on the basis of the product. This is becoming, and will continue
to become, more and more difficult to do. As John Haugland (1985) noted
in his homage to computational science, with each new advance in what
technology can do, critics raise the bar as to what would be required
to demonstrate truly intelligent behavior. But given our penchant for projecting
ourselves onto animate-like entities, it is inevitable that the Turing
test (essentially a test as to whether a programmed computer can get
us to identify with it as a cognizing agent) will be passed. At that
point we will be forced to defend our beliefs in the emergent and
irreductionist nature of being against the evidence of our own sympathies
--to 'search our soul', as it were, and make sure we've really got one.
David Kirshner
Louisiana State University
Anderson, J. R., & Lebiere, C. (1998). Introduction. In J. R. Anderson & C.
Lebiere (Eds.), The atomic components of thought (pp. 1-17). Mahwah, NJ:
Lawrence Erlbaum Associates.
Erlwanger, S. H. (1973). Benny's conception of rules and answers in IPI
mathematics. The Journal of Mathematical Behavior, 1(2), 7-26.
Haugland, J. (1985). The nature and plausibility of cognitivism. In J. Haugland
(Ed.), Mind design. Cambridge, MA: MIT Press.
bison who-is-at mail.utexas.edu on 12/18/98 12:28:25 PM
To: xmca who-is-at weber.ucsd.edu@internet
cc:
Subject: RE: worry, worry, worry....
ken wrote:
> Steve, the robot is the epitome of teaching machines and since there are
> strong pressures to keep teachers from thinking for themselves
> (itselves?) there should be a great market. Any teacher who can't make
> mistakes can't vary from the program that controls it.
Yes. I think the machines will explode when their circuits overload from
their internal paradox: they are both "completely autonomous in a
highly complex environment" and yet never make a mistake.
-dave
DS Hendler, Assistant Instructor
University of Texas, Austin
"Singing is what makes the work go better. When you're singing, you forget."