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Re: Concrete vs Abstract (was Middle School PS Texts~)

I am more than perfectly willing to agree. The labels abstract and concrete
or as Anton Lawson in his book said hypothetical-deductive, and
empirical-inductive are really arbitrary cut offs in a continuum of thinking
skills based on Piagetian tests. This is similar to the A,B,... cutoffs
that are made by every teacher. I have observed that there are students who
can answer some of the more difficult formal reasoning questions, while
missing the easy ones. Proportional reasoning is particularly fragile.
Students seem to acquire and drop it, but other forms of reasoning seem to
be much more stable. I would defend the terms as meaning the upper 30% or
lower 30% on a certain Piagetian tests, and as such can be useful in
defining the thinking skills of students. Maybe other terms should be used,
but these are familiar and have some meaning to most people. I also have
the distinct impression that many of the psychology terms go in and out of
fashion much more quickly than physics terms.

However the fact that elementary school teachers tend to score low on
Piagetian tests has been pointed out by Arons on starting at section 13.4 of
the 1997 of his book "Teaching Introductory Physics". Low scoring
individuals are not as capable of conceptual understanding of biology and
physics, and in the case of elementary school teachers this might hamper
their ability to understand how to help students improve their thinking.
Arons also point out that most of these individuals can be helped to achieve
higher scores. Shayer and Adey in England have used the Piagetian based
taxonomy and skills as the basis for a very successful intervention in
middle school. While their experiment does not validate a strict taxonomy
involving levels of thought, it certainly shows that the Piagetian ideas can
be used to design superior programs. While the observational experiments of
Piaget and Karplus are very important, the experiments such as Shayer and
Adey's which actively use the ideas to increase thinking skills are even
more persuasive.

As far as the difference between adolescents and adults goes, adults are
actually modifiable at much older ages than many have suspected. There is
an ERICH summary paper that shows how thinking skills rise in college when
students take science courses. And then of course there is the work of
Feuerstein where he took children as old as 15 with IQs estimated as low as
65 and raised their IQs to the normal range or above. So biology just
provides the opportunity for the human organism to develop, but the thinking
skill is strongly determined by the environment, which is sadly deficient in
most of our school system.

John M. Clement

Hi all-
People switch back and forth among Piaget's stages. This fact
was demonstrated experimentally by Case in "The New Structuralism in
Cognitive Development" (Karger 1993). But we also know that adolescents
are still undergoing brain development. Teachers are beyond that stage.
So it is highly inaccurate to characterize teachers as being at the
same level as middle-school students.

While we're on the suggestion of Piagetian stages, a notion Piaget himself
had apparently largely discarded by the time English speakers were picking
it up in the late 70's, the stages are not about concrete vs abstract.
Piaget's own descriptions of the evidence of thinking of babies are
evidence of abstractions.

Case and others including Piaget have demonstrated that the "stages" are
not what they have been made out to be by "interpreters" of Piaget's work.
Hence, to label others as concrete thinkers and equate them with their
students for that reason alluding to Piaget does the teachers,
the students
and Piaget a disservice.

If we're all going to get prickly over the meaning of the word
"heat," then
we should get square about the work of people in other fields.

Just my opinion...


Dewey I. Dykstra, Jr. Phone: (208)426-3105
Professor of Physics Dept: (208)426-3775
Department of Physics/MCF421/418 Fax: (208)426-4330
Boise State University
1910 University Drive Boise Highlanders
Boise, ID 83725-1570 novice piper: GHB, Uilleann

"As a result of modern research in physics, the ambition and hope,
still cherished by most authorities of the last century, that physical
science could offer a photographic picture and true image of reality
had to be abandoned." --M. Jammer in Concepts of Force, 1957.

"If what we regard as real depends on our theory, how can we make
reality the basis of our philosophy? ...But we cannot distinguish
what is real about the universe without a makes no sense
to ask if it corresponds to reality, because we do not know what
reality is independent of a theory."--S. Hawking in Black Holes
and Baby Universes, 1993.