Applications and Misapplications of Cognitive Psychology
to Mathematics Education
John R. Anderson
Lynne M. Reder
Herbert A. Simon
http://www.psy.cmu.edu/~mm4b/misapplied.html
Following Jay Lemke and Peter Smagorinsky...
Here are my three (of course not only two)
Pfennige's worth of opinion
about this triple-double-U article.
Sadness fills me about the state of affairs of applied psychology, not
so much about the real kind, which would be reports from people who know
the practice field, here education and teacher training. No-no. I am
really shocked, taken aback, even grieved: about the ideas that eminent
figures of pure psychology seem to have concerning the path that their
findings should take until they will be somehow somewhen "implemented".
The implicit assumption, not discussed at all, is that we should trust
only carefully planned and conducted experimental studies. There is no
mention of a possible other route: Conduct interviews with experienced
teachers about their ideas and values regarding situatedness, constructi-
vism, discovery learning, behaviorism, Walden II -- all the issues that
these three experts boast to know so much about, by their chosen style
of writing the piece, not by explicit bragging.
I am in the neutral position of not having read the criticised texts about
constructivist strategies for classrooms, therefore in this respect I
will take as fair the picturing of these in the target article, for the
moment at least. I *have* read Jean Lave's book (together with Etienne
Wenger) which the authors do not cite. Their last quote is from the year
when Jean first presented the gist of what is now known as the LPP theory
of learning. Therefore, the moment of grace for ARS might be quite short,
judging from their treatment of Lave.
The most depressing characteristic of the article is, how simple and
controllable the school learning seems to be for these scientists.
Just decompose the tasks, look for trainable units, find a "context"
that furthers "transfer" (which is a result variable, namely reproduction
of a performance in a new "context"), and --- That's it. So simple that
*they* don't need to show that it works. It has to, or else *I'm* stupid ?
At 15:54 18 May 1996, Peter Smagorinsky wrote:
>........................ the CMU group's article primarily
>(perhaps exclusively) references experimental research conducted in labs,
>with knowledge transfer measured in designed tasks. I think it's very hard
>to generalize from these studies to situated transfer where the need to
>transfer knowledge is less obvious, the cues are less explicit, and the
>interference is greater.
But what really drives me to the keyboard today is the weak defense
they have against this truly absurd statement:
>Knowledge cannot be represented symbolically
i.e. their Claim 2 of "constructivism". If this is indeed what
Cobb, Yackel, and Wood (1992) say, then they deserve an education in
semiotics, maybe also some lectures of what shades of meaning "knowledge"
has had in philosophy until the cognitive sciences tried to overtake
those long-gone scholars with some new machines.
But what do they get from ARS ? -- Just this:
>The representational view of mind, as practiced in cognitive psychology,
>certainly makes no claims that the mind represents the world accurately
>or completely, and no strong claims about the nature of knowledge as
>a philosophical issue. The true representational position is compatible
>with a broad range of notions about the relation of the mind to the
>world, and about the accuracy or inaccuracy and completeness or
>incompleteness of our internal representations of the world's features.
>Its claim simply:
>
>Cognitive competence (in this case mathematical competence) depends on
>the availability of symbolic structures (e.g., mental patterns or mental
>images) that are created in response to experience.
The trick is in the "e.g." -- they can always include other examples,
like for instance external symbol structures, and say that the meant
it all along. "Structures", "patterns", "images" -- can you be more
cloudy ? And I don't refer to "software implementations" here.
That's cheating, it seems to me.
But maybe Cobb, Yackel, and Wood (1992) do deserve the bashing ?
Please, members of the xmca, educate this poor stranger to education:
Arne.
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