From: "Jack Park" <email@example.com>
What a profound group this is. What, IMHO, started out to be the discussion
of a modern implementation of Augment is turning out to be a discussion of
just about everything, the ultimate answer for which is 42, I am told.
Henry's discussion of constructivism struck some potent nerves in this
reader. I hope he continues that thread.
It strikes me that the topics of:
mathematics of knowledge
methods of learning/teaching
are, themselves, so profound in their importance to those of us who follow
this list that a second list for such explorations might be started, and
leave this or another list to the nitty-gritty of implementation issues. Or,
maybe we are not supposed to be thinking implementation here. Not sure on
Another 0.02 euros
From: Henry van Eyken <firstname.lastname@example.org>
Re comments about self-learning, there is a problem here in that some of
the most important, real learning calls for a mental gymnastics that
constructivists call "accomodation." It is the truly painful part of
learning, to accomodate in one's mind things that don't fit, notions for
which the mind had not been properly prepared. The following piece is
A person merely reading tends to make short shrift of things that test
his patience. He will bulldoze right through. It is, I believe from
personal experience, a practice that damages the capacity to fully
employ native mental capabilities. One can readily become a parot of
I know, for this is your parot speaking ...
Letter To My Dawson Colleagues
M A S C A R A
March 4, 1990
Nelson Mendela looks straight at me. His face on the magazine's cover
can be described only as noble - noble, that is, in the light of what I
now know of him. How, I wonder, would I describe the same face if it
were to belong to a person I don't know?
Turning to the lead editorial, "Freedom Man," I find it to contribute
little of value to my inventory. But it does contain a startling
comment, one my mind can't readily accomodate. It goes, "Mr. Mendela's
first job is to make sure that ...", &c. That, it seems to me, is quite
an assertion, made, as it is, by someone not in Mr. Mendela's shoes. I
question whether an editor, even one so excellent and privileged as to
serve on that important and highly respected weekly, The Economist,
should tell Mr. Mendela what he ought to do first. One would think by
now that Mr. Mendela has earned the right to select his own priorities.
But, then again, I may be misinterpreting the true content of the
editor's phrasing. The sentence may not mean the same exactly inside my
head as it does inside his. The editor's world and mine are different
worlds, and Mr. Mendela's is one different still. Every person is a
world. Every person is sovereign in his or her own Kingdom.
Constructivism is a modern theory of knowledge. Unfortunately, and as a
professional educator I hate to admit it, I know next to nothing about
theories of knowledge - a subject, incidentally, so important it is
proposed for inclusion in the science curriculum in the United States.
Can anyone imagine a brain surgeon who doesn't know his way about
brains? How then can one be a mind surgeon without understanding mind?
Ought I not to be booked for malpractice, really, and brought before a
Because of my scant knowledge of constructivism, I shall broach the
subject simply by quoting some quotes already quoted elsewhere.
"The idea that knowledge is constructed in the mind of the learner on
the basis of pre-existing cognitive structures or schemes provides a
theoretical basis for Ausubel's distinction between meaningful and
"'To learn meaningfully, individuals must choose to relate their
knowledge to relevant concepts and propositions they already know. In
rote learning ... new knowledge may be acquired simply by verbatim
memorization and arbitrarily incorporated into a person's knowledge
structure without interacting with what is already there.'"
"Without INTERACTING with what is already there." Recognize the
phenomenon? Of course you do as an observant teacher. But let's
"... as Ausubel has stated,
'If I had to reduce all of educational psychology to just one principle
I would say this: The most important single factor influencing learning
is what the learner already knows.'"
These quotes are from George M. Bodner, "Constructivism: A Theory Of
Knowledge," J.Chem.Ed., Oct. 1986, pp. 873-878. The quotes within quotes
are from D.P. Ausubel, J.D. Novak, and H. Hanesian, "Educational
Psychology: A Cognitive View," 2nd ed., Holt, Rhinehart, Winston, New
We know what we know, according to Piaget - whose name certainly needs
no introduction here - by active construction of our own world. This
constructing is not done by any teacher; it is done by learners
themselves. The teacher's role is merely to determine what building
materials are required next and then to supply them. After that it is up
to the student, to put the pieces in place either by simple ASSIMILATION
into an existing mental schema or, if they don't fit, by ACCOMODATION,
which is a change of mind such that new knowledge will fit properly.
Accomodation involves resistance or struggle and, hence, may require
attention and patience and strategies for prodding things along a
little. Most people are not readily of accomodative mind. Theirs is made
up. They are usually viewed as the staunch, dependable types. Detractors
call them pigheaded. But by whatever name one knows them, it is among
these people we find the cause of our country's breaking up. [Canada
was, still is, trying to come to grips with Québec nationalists who wish
to manipulate the province's overwhelming French-speaking population
into voting for the separation of Québec from the ROC -- Rest of Canada.
As I mentioned, the subject of how we acquire knowledge is so important
it should be taught in school. Here is the way the tenets of
constructivism are outlined in "Science For All Americans: A Project
2061 Report on Literacy Goals in Science, Mathematics, and
Technology," American Association for the Advancement of Science, 1989
"People's ideas can affect learning by changing how they interpret new
perceptions and ideas: People are inclined to respond to, or seek
information that supports the ideas they already have and on the other
hand to overlook or ignore information that is inconsistent with the
ideas. If the conflicting information is not overlooked or ignored, it
may provoke a reorganization of thinking that makes sense of the new
information, as well as of all previous information. Successive
reorganizations of one part or another of people's ideas usually result
from being confronted by new information or circumstances. Such
reorganization is essential to the process of human maturation and can
continue throughout life."
A good climate in the classroom is vital for effective learning and one
way of providing it is by doing on the blackboard lots and lots of
exercises. Students, as far as I know, love this approach. Naturally,
they expect that their exams will be composed of the same type of
questions whose solutions now appear in their notes. Learning can be a
tiresome business and students can do without too many unpleasant
surprises. Especially if he or she holds down some job while going to
college, or has to do much travelling to and from school.
However, students will learn better if they do many exercises themselves
and in many instances the examples in the textbook ought to be quite
sufficient only to start them off. One doesn't become a better
figure-skater by watching the World Figure-Skating Championships. And
students doing exercises on their own frees classroom time for other
use. There are plenty of things to be done beside demonstrations of how
a teacher handles simple routines. I believe, though, that a teacher
ought to demonstrate how he himself or with the suggestions of his
students tackles REAL problems, but that subject is beyond the scope
of these letters. A classic marvel about it is G. Polya's "How To Solve
It," Princeton University Press. And for some related beliefs that I
myself hold you might look up, in the Dawson library "Fleabyte
Fundamentals - Promoting More Meaning ful Learning," J. Coll. Sci.
Teaching, Nov. 1989, p. 70. [see
more meaningful learning ]
If you do follow up on that latter suggestion you will understand why I
emphasize in my general chemistry classes that I wish students to be
capable of more than performing routine exercises. I tell them that,
although I consider those exercises important steps in acquiring skill
at solving more complex problems - problems more like real ones - they
cannot be considered ends in themselves. Don't they know that computers
can do those problems automatically, faster, and without error? Well,
why then should anyone pay them a salary for something a $100 gadget can
Classroom time is much needed for matters that urgently require
ACCOMODATION, that somewhat painful process of engaging and modifying
mental structures to acquire the kind of knowledge a modern chemistry
course ought, by its nature and original intention, to inculcate. One
problem I encounter is that a substantial amount of elementary knowledge
that should have been accomodatively acquired in some earlier course
never was, but had only been ASSIMILATED. Teachers pass on their chores
to subsequent teachers who should be less than grateful for that. Why?
Wrongly assimilated knowledge does not fit properly. It is not a
functional component of thought, it is merely some mental junk waiting
to interfere with thought at some crucial moment. You may have
experienced this kind of thing in your own mind as I certainly have. It
does not serve good purpose and probably damages the student. And it
degrades subsequent courses.
A teacher, or some committee, can get many students with such
deficiencies to pass a course by constructing exams that simply avoid
detecting what's wrong. He may load up his examinations with routine
exercises for which the more capable students have memorized the steps.
He then simply forgives them for not knowing what they are doing.
Indeed, a time-tested way of avoiding difficulties is to not face them.
Ask Mr. Mendela.
Henry K. van Eyken
How To Solve It
In the corner of her eye
mascara began to run
under torture of my teaching.
"I UNDERSTAND the problem, but not the way YOU do it,"
"Look, Sir, I DID it! Same as in the book!"
she said and showed me,
high-lighted in yellow,
the writer's rote routine.
How often I've wished I'd done a problem
same as in the book,
My lesson sanctioned by the powers
vested in the printed word.
for a class fed fare
barely a Fleabyte fit.
MacTeaching at its comfy best ...
-- Fleabyte -- http://www.fleabyte.org -- is an evolving, experimental web-publication devoted to public computency, which, like common literacy, is regarded as essential to an environmentally healthy, democratic society.
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