This talk about "teaching" abstraction makes me feel like I come from
another planet or something. I really am unclear on what you mean.
To me abstraction is what we do. It's like breathing. When an infant looks
up from her crib and says, "Mamma," she is using a verbal utterance to
represent something else. This is abstraction. Abstraction is even more
fundamental than this, however. Brain research shows how sensory signals
from the eyes, ears and other organs, spread from neuron to neuron in
cascading branch-like patterns until, in a miraculous fashion, we make sense
of the vibrations, photons, and chemicals which impinge upon our bodies. The
whole process of perception is one of abstraction and it is apparently not
something which has to be learned.
Somewhere along the line, we begin to think of abstraction as transforming
and expressing an idea using different terms. Instead of just counting the
blocks, we say 1+1=2. We take something that is more concrete, like blocks,
and extend it into something that is less concrete, like the
linguistic/arithmetic expression. At this point, 1+1=2 makes just as much
sense to us as the blocks, and we can move on to form other abstractions.
This jumping from one level to the next is where I see Piagetian
assimilation and accommodation -- learning, but its the "what" that's
learned, not the process. Is this what you mean by "teaching" abstraction, Bill?
One problem I have is deciding where (or even if) the line should be drawn
between perception/abstraction and concept/abstraction. According to the
biopsychologists, its all part of the same process of trying to make sense
of the world.
The direction the process takes is another issue I wonder about. Abstraction
must go from more concrete to less concrete, but what is concrete? One might
argue that a person who knows and blindly accepts the MTM=P rule, because
everything works when you accept it, may have an equally great and difficult
leap to abstraction when s/he tries to formulate "concrete" models of it as
another person who starts with the models and goes the other way.
Thinking about concrete and perception, here is something that seems
concrete on the surface, but it severely shakes my confidence in knowing
what I perceive is real.
Read the following sentence one time. Then read it again counting the "f's"
that appear.
FINISHED FILES ARE THE
RESULT OF YEARS OF SCIENTIFIC
STUDY COMBINED WITH THE
EXPERIENCE OF MANY YEARS.
There are a total of six f's in the sentence. You are not alone if you
counted fewer than six, but please try counting them again. Any theories of
what's going on here?
Tom
"Does the name Pavlov ring a bell?"
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