They note that for nearly a hundred years (maybe more) lab
psychologists have been trying to figure out just how two
tasks need to be seen as similar before transfer happens.
What they do not tell us are all the things we would really
like to know, such as:
Given their view of the kinds and degrees of similarity that
favor transfer, just how similar typically are school tasks
and non-school tasks which deploy mathematics or any other
abstract theoretical knowlege/know-how?
How much, and what kind of work does it take to teach people
how to see two tasks as similar which the researchers can
see as similar but the subjects initially do not?
In other words, what is the likely _practical usefulness_
of coontinuing to base education almost exclusively on the
premise that learning abstract theoretical practices will
make people much more successful in doing what people mostly
do in our society?
I am sure that there are some domains and some kinds of people
for which abstraction-based learning is helpful enough to be
worth doing; I am not sure, however, that these domains extend
much beyond the sort of reasoning that academic disciplinary
specialists do part of the time (nor very far into these domains,
either) or to people whose dispositions for learning and
action are shaped by typical life experiences very different
from Herb Simon's or mine.
Even within my own experience, I can remember that the more
abstract the curriculum in mathematics I experienced, the more
difficult it became to figure out how to transfer advanced
mathematics concepts to problems in physics. It was often
easier to re-learn the mathematics (if indeed these differently
contextualized and contextualizing practices, with different
valences and affordances should be called 'the same' mathematics)
in different forms and contexts, closer to the terms in which
I understood the physics (and closer to the historically original
formulations of the mathematics, often closely linked to physics
where the new more abstract formulations are more closely linked
to other topics in mathematics) than it was to 'transfer' what
I had already learned in a math class. (I am speaking here of
experiences in advanced undergraduate math and physics at the
University of Chicago.)
There was in fact, as I'm sure has happened often elsewhere, a
conflict between the math and physical sciences departments over
who should control the curriculum for these topics, and endless
compromises. When the science people taught 'the mathematics', it
was not 'really' mathematics to the mathematicians (because it was
not abstracted far enough, nor as integrated into the rest of
their discipline as it is constructed today). When it was taught
by the mathematicians as they really wanted to teach it (without
compromises, for math majors) it became nearly impossible to
'transfer' it, even for gifted 'A' students in both subjects.
Cognitive science, as practiced in the paradigm that evolved at
CMU under Simon's influence, is abstracting in much the same way
that mathematics is (as Simon learned to do as an economist):
it constructs similarities (call common cognitive strategies,
processes, or algorithms) between otherwise wildly different
activities (though most convincingly for very similar activitities)
in domains such as 'problem-solving' (which the discipline itself
defines, then limits so as to produce results). If people were
explicitly taught these strategies (as in the older 'heuristics'
notion) at an abstract level, only a few would manage to make
good use of them in practical situations. If the strategies are
regarded as either innate, or unconscious, they may still be
subject to practice effects which can show up as a form of
transfer. But all this assume that in some sense they 'exist'
rather than that they are selectively foregrounded from the
infinite set of possible similarities of any two tasks or
activities. To the extent that such general transfers 'work'
I would have to assume that they do so because of the cultural
consistency across domains of what are regarded as effective
practices or strategies, and that they will especially work
where the domains themselves are constructed according to these
same principles or strategies. In this sense cognitive science
is truly a science of the artificial, a sort of mentalist
experimental cultural anthropology.
How independent of gender, social class, and culture are
transfer effects? i.e. the size of the effects as well as
whether they can be reliably established at all? It is not
even clear (cf. Mike Cole and others' studies in Africa)
that it is possible to define tasks across cultures (or
subcultures?) in a way which allows such comparisons to be made.
So I think that as far as the practical educational policy
implications of 'transfer' and 'abstraction' are concerned,
the practically important questions remain unaddressed:
who benefits, how much, how often, with what degree of effort --
and is it worth it, compared to other feasible alternatives?
JAY.
JAY LEMKE.
City University of New York.
BITNET: JLLBC who-is-at CUNYVM
INTERNET: JLLBC who-is-at CUNYVM.CUNY.EDU