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Re: "quantization"



Shapiro, Mark wrote:

For those of you who would like to read some cogent counter
arguments to the constructivist philosphy of education, I strongly
recommend the following two books:

Uncommon Sense, The Heretical Nature of Science by Alan Cromer
(Oxford University Press, 1993) ISBN 0-19-509636-3

and

Connected Knowledge, Science, Philosophy, and Education also by
Alan Cromer (Oxford University Press, 1997) ISBN 0-19-510240-1


Constructivism in education is fairly new to me, having been brought to
my attention by a teacher who had just read Alan Cromer's _Connected
Knowledge, Science, Philosophy, and Education_. In particular he was
appalled that lecture-demonstration tables had been removed from all
the science classrooms in New Zealand in support of the nonobjectivity
of constructivist educators. According to Cromer, "This is to prevent
teachers from claiming to know more than their students, thus unduly
influencing how the students' construct their own knowledge." (p. 11).
Cromer states, "The positivists Auguste Compte and Ernst Mach were pure
empiricists because of their profound distaste and fear of metaphysics,
whereas many constructivists are pure empiricist because of their
ignorance of the scientific process." (p. 20). Cromer leads one to
believe that constructivist educators do not regard competence in one's
subject matter to be a matter of very high priority, citing examples of
consructivist inquiry lessons that did not go very well. At first I was
about to join the ranks of the anti-constructivists. Cromer is
persuasive, and I see that his book was favorably reviewed in Scientific
American.
Cromer traces the roots of constructivism to Piaget, Vico, and
Berkeley. One gets the impression that Cromer thinks that the cognitive
psychology of Piaget is of a lower scientific standard that the more
positivistic behaviorism of B. F. Skinner (pp. 65-66). There are some
essays on constructivism on the Internet at
http://www.inform.umd.edu/UMS+State/UMD-Projects/MCTP/WWW/Essays.html.
The article, _Constructivist Teaching Stratagies_ by Graham W. Dettrick
introduces an interesting distinction in terminology:

"Inquiry" should not be confused with "discovery". Discovery assumes a
realist or logical positivist approach to the world which is not
necessarily present in "inquiry". Inquiry tends to imply a > constructionist
approach to teaching science. Inquiry is open-ended and on-going.
Discovery concentrates upon closure on some important process, fact,
principle, or law which is required by the science syllabus.

It is clearly "discovery" in this sense that Alan Cromer has in mind in
his SEED program (_Science Education through Experiments and
Demonstrations_), I believe this is called "guided discovery." The
"underpinnings" of this project are based on the work of Dr. Arnold
Arons -- the introduction the concepts of length, mass, time, area, and
volume, followed by density, pressure, etc. (p. 185). I don't know how
Dr. Arons stands with respect to constructivism, but he certainly has
made use of Piaget's ideas in discussing how children learn. In
particular, I still have some notes that I took from his series of three
lectures on elementary science education at the 1976 Philadelphia NSTA
meeting. One of the topics discussed was the understanding of division
as related to density. According to my somewhat garbled notes, he poses
the problem, "Given D and M, find V." He said that using the formula
D = M/V, accepted as understanding, really amounts to rearranging
objects (D, M, V) in space, calling this "strictly concrete
operational." He also used the Piagetian concept of _reversibility_ in
this discussion. This is also discussed at the beginning of his book
_Teaching Introductory Physics_, Wiley, 1997 ("reversibility" on p. 7).
While I think that following Piaget doesn't necessarily imply that one
is a constructivist, it seems to indicate that Dr. Aron's model of the
learning process is not completely positivistic. I became more
apprehensive about blindly accepting Cromer's anti-constructivism stance
when it seemed that some of his supporting examples were quite
anecdotal. In particular he seems to attribute the errors of middle
school science textbooks to the constructivism of their authors, citing
Mario Iona's compilation of two pages of errors in one of them. I recall
that Mario Iona found similar errors in a traditional physics text that
was in no way connected with constructivism. Cromer lashes at the
inaccuracy of the treatment of buoyancy in _Middle School Science &
Technology_ developed by BSCS. While this text series has a
constructivist label, it is not clear that constructivism is the source
of the incorrect physics. One could probably find good educatioal
materials written by consructivists as I am being led to believe from
following some of the discussions. I attended the Workshop on Physics
and the Development of Reasoning (New York, 1976) which used Piaget's
ideas as a basis for explaining and demonstrating how students think,
with examples of how the progression from concrete operational to formal
operational might be facilitated. Robert Fuller, in his Millikan lecture
1992, (http://www.unl.edu/physics/Education/Millikan.html) mentions that
many of the ideas of one of his Piagetian-based programs has become
known as the "constructivist way of knowing."
Although I am at an early stage in learning about constructivism and
do not intend to join the higher level philosophical discussions, I
think Alan Cromer's interesting book would best serve those already
familiar with constructivism.

Hugh Logan